The collision velocity of the bullet cluster in conventional and modified dynamics
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Bullet Physics LibraryUser ManualLast updated by Erwin Coumans on Friday, 29 February 2008IndexIntroduction (4)Main Features (4)Download and supporting physics Forum (4)Quickstart (5)Integration overview (6)Debugging (6)Bullet Rigid Body Dynamics (7)World Transforms and btMotionState (7)Static, Dynamic and Kinematic Objects using btRigidBody (7)Simulation frames and interpolation frames (8)Bullet Collision Shapes (9)Convex Primitives (9)Compound Shapes (9)Convex Hull Meshes (10)Concave triangle meshes (10)Convex Decomposition (10)Height field (10)Scaling of Collision Shapes (11)Collision Margin (12)Bullet Constraints (13)btPoint2PointConstraint (13)btHingeConstraint (13)btConeTwistConstraint (13)btGeneric6DofConstraint (13)Bullet Vehicle (14)btRaycastVehicle (14)Bullet Character Controller (14)Basic Demos (15)CCD Physics Demo (15)COLLADA Physics Viewer Demo (15)BSP Demo (16)Vehicle Demo (16)Character Demo (16)General Tips for Bullet users (17)Avoid very small and very large collision shapes (17)Avoid large mass ratios (differences) (17)Combine multiple static triangle meshes into one (17)Use the default internal fixed timestep (17)For ragdolls use btConeTwistConstraint (17)Don‟t set the collision margin to zero (17)Use less then 100 vertices in a convex mesh (17)Avoid huge or degenerate triangles in a triangle mesh (18)Advanced Topics (18)Per triangle friction and restitution value (18)Custom Constraint Solver (18)Custom Friction Model (18)Collision Filtering (disabling collisions) (19)Collision groups and masks (19)Disable collisions between a pair of instances of objects (19)Collision Matrix (20)Registering custom collision shapes and algorithms (20)Advanced Low Level Technical Demos (21)Collision Interfacing Demo (21)Collision Demo (21)User Collision Algorithm (21)Gjk Convex Cast / Sweep Demo (21)Continuous Convex Collision (22)Raytracer Demo (22)Concave Demo (22)Simplex Demo (22)Bullet Collision Detection and Physics Architecture (23)Bullet Library Module Overview (24)Bullet Collision Detection Library Internals (25)Multi threaded version (26)Cell SPU / SPURS optimized version (26)Unified multi threading (26)Win32 Threads (26)IBM Cell SDK 3.x, libspe2 SPU optimized version (26)Future support for pthreads (26)Contributions / people (27)Contact (27)Further documentation and references (28)Links (28)Books (28)IntroductionBullet Physics is a professional open source collision detection and physics library, related tools, demos, applications and a community forum at It is free for commercial use under the ZLib license.Bullet started in 2003 as a continuous collision detection research project by Erwin Coumans, former Havok employee. Since 2005 it has been open sourced, and many professional game developers are using, contributing and collaborating in the project. Target audience for this work are professional game developers as well as physics enthusiasts who want to play with collision detection and rigidbody dynamics.Bullet is used in several games for Playstation 2 and 3, XBox 360, Nintendo Wii and PC, either fully or just the multi threaded collision detection parts. It is under active development and some of the recent new developments are the addition of a universal multi-threaded C++ version and a C# port that supports Windows and Xbox 360 XNA. Authoring of physics content can be done using the COLLADA Physics specification. 3D modelers like Maya, Max, XSI, Blender and Ageia‟s CreateDynamics tools support COLLADA physics xml .dae files. Bullet is also integrated in the free Blender 3D modeler, . The integration allows real-time simulation and also baking the simulation into keyframes for rendering.See the References for other integrations and links.Main Features✓Discrete and Continuous collision detection including ray casting✓Collision shapes include concave and convex meshes and all basic primitives ✓Rigid body dynamics solver with auto deactivation✓Cone-twist, hinge and generic 6 degree of freedom constraint for ragdolls etc.✓Vehicle simulation with tuning parameters✓COLLADA physics import/export with tool chain✓Compiles out-of-the-box for all platforms, including COLLADA support✓Open source C++ code under Zlib license and free for any commercial use✓C# port available that runs on XNA on Windows and Xbox 360✓Cell SPU optimized version available through Sony PS3 DevNet✓Multi-threaded version for multi core public availableDownload and supporting physics ForumPlease visit for download, support and feedback.QuickstartStep 1: DownloadWindows developers should download the zipped sources from of Bullet from .Mac OS X, Linux and other developers should download the gzipped tar archive.Step 2: BuildingBullet should compile out-of-the-box for all platforms, and includes all dependencies. Visual Studio projectfiles for all versions are available in Bullet/msvc. The main Workspace/Solution is located in Bullet/msvc/8/wksbullet.slnCMake adds support for many other build environments and platforms, including XCode for Mac OSX, KDevelop for Linux and Unix Makefiles. Download and install Cmake from . Run cmake without arguments to see the list of build system generators for your platform. For example, run cmake . –G Xcode to auto-generate projectfiles for Mac OSX Xcode.Jam: Bullet includes jam-2.5 sources from /jam/jam.html. Install jam and run ./configure and then run jam, in the Bullet root directory.Step 3: Testing demosTry to run and experiment with CcdPhysicsDemo executable as a starting point. Bullet can be used in several ways, as Full Rigid Body simulation, as Collision Detector Library or Low Level / Snippets like the GJK Closest Point calculation. The Dependencies can be seen in th e doxygen documentation under …Directories‟.Step 4: Integrating Bullet Rigid Body Dynamics in your application Check out CcdPhysicsDemo how to create a btDynamicsWorld , btCollisionShape, btMotionState and btRigidBody, Stepping the simulation and synchronizing the transform for your graphics object. Requirements:#include “btBulletDynamicsCommon.h” in your source fileRequired include path: Bullet /src folderRequired libraries: libbulletdynamics, libbulletcollision, libbulletmathStep 5 : Integrate only the Collision Detection LibraryBullet Collision Detection can also be used without the Dynamics/Extras. Check out the low level demo Collision Interface Demo, in particular the class CollisionWorld. Requirements:#include “btBulletCollisionCommon.h” at the top of your fileAdd include path: Bullet /src folderAdd libraries: libbulletcollision, libbulletmathStep 6 : Use snippets only, like the GJK Closest Point calculation. Bullet has been designed in a modular way keeping dependencies to a minimum. The ConvexHullDistance demo demonstrates direct use of GjkPairDetector.Integration overviewIf you want to use Bullet in your own 3D application, it is best to follow the steps in the CcdPhysicsDemo. In a nutshell:✓Create a btDynamicsWorld implementation like btDiscreteDynamicsWorld This btDynamicsWorld is a high level interface that manages your physics objects and constraints. It also implements the update of all objects each frame. A btContinuousDynamicsWorld is under development to make use of Bullet‟s Continuous Collision Detection. This will prevent missing collisions of small and fast moving objects, also known as tunneling. Another solution based on internal variable timesteps called btFlexibleStepDynamicsWorld will be added too.✓Create a btRigidBody and add it to the btDynamicsWorldTo construct a btRigidBody or btCollisionObject, you need to provide: -Mass, positive for dynamics moving objects and 0 for static objects-CollisionShape, like a Box, Sphere, Cone, Convex Hull or Triangle Mesh-btMotionState use to synchronize the World transform to controls the graphics -Material properties like friction and restitution✓Update the simulation each frame: stepSimulationCall the stepSimulation on the btDynamicsWorld. The btDiscreteDynamicsWorld automatically takes into account variable timestep by performing interpolation instead of simulation for small timesteps. It uses an internal fixed timestep of 60 Hertz. stepSimulation will perform collision detection and physics simulation. It updates the world transform for active objecs by calli ng the btMotionState‟s setWorldTransform. There is performance functionality like auto deactivation for objects which motion is below a certain threshold.A lot of the details are demonstrated in the Demos. If you can‟t find certain functionality, please use the FAQ or the physics Forum on the Bullet website. DebuggingYou can get additional debugging feedback by registering a derived class from IDebugDrawer. You just need to hook up 3d line drawing with your graphics renderer. See the CcdPhysicsDemo OpenGLDebugDrawer for an example implementation. It can visualize collision shapes, contact points and more. This can help to find problems in the setup. Also the Raytracer demo shows how to visualize a complex collision shape.Bullet Rigid Body DynamicsWorld Transforms and btMotionStateThe main purpose of rigid body simulation is calculating the new world transform, position and orientation, of dynamic bodies. Usually each rigidbody is connected to a user object, like graphics object. It is a good idea to derive your own version of btMotionState class.Each frame, Bullet dynamics will update the world transform for active bodies, by calling the btMotionState::setWorldTransform. Also, the initial center of mass worldtransform is retrieved, using btMotionState::getWorldTransform, to initialize the btRigidBody. If you want to offset the rigidbody center of mass world transform, relative to the graphics world transform, it is best to do this only in one place. You can use btDefaultMotionState as start implementation.Static, Dynamic and Kinematic Objects using btRigidBodyThere are 3 different types of objects in Bullet:-Dynamic rigidbodieso positive masso User should only use apply impulse, constraints orsetLinearVelocity/setAngularVelocity and let the dynamics calculatethe new world transformo every simulation frame and interpolation frame, the dynamics world will write the new world transform usingbtMotionState::setWorldTransform-Static rigidbodieso cannot move but just collideo zero mass-Kinematic rigidbodieso animated by the usero only one-way interaction: dynamic objects will be pushed away but there is no influence from dynamics objectso every simulation frame, dynamics world will get new world transform using btMotionState::getWorldTransformAll of them need to be added to the dynamics world. The rigid body can be assigned a collision shape. This shape can be used to calculate the distribution of mass, also called inertia tensor.Simulation frames and interpolation framesBy default, Bullet physics simulation runs at an internal fixed framerate of 60 Hertz (0.01666). The game or application might have a different or even variable framerate. To decouple the application framerate from the simulation framerate, an automatic interpolation method is built into stepSimulation: when the application delta time, is smaller then the internal fixed timestep, Bullet will interpolate the world transform, and send the interpolated worldtransform to the btMotionState, without performing physics simulation. If the application timestep is larger then 60 hertz, more then 1 simulation step can be performed during each …stepSimulation‟ call. The user can limit the maximum number of simulation steps by passing a maximum value as second argument.When rigidbodies are created, they will retrieve the initial worldtransform from the btMotionState, using btMotionState::getWorldTransform. When the simulation is running, using stepSimulation, the new worldtransform is updated for active rigidbodies using the btMotionState::setWorldTransform.Dynamic rigidbodies have a positive mass, and their motion is determined by the simulation. Static and kinematic rigidbodies have zero mass. Static objects should never be moved by the user.If you plan to animate or move static objects, you should flag them as kinematic. Also disable the sleeping/deactivation for them. This means Bullet dynamics world will get the new worldtransform from the btMotionState every simulation frame.Bullet Collision ShapesBullet supports a large variety of different collision shapes, and it is possible to add your own.Convex PrimitivesMost primitive shapes are centerd around the origin of their local coordinate frame:btBoxShape : Box defined by the half extents (half length) of its sides btSphereShape : Sphere defined by its radiusbtCapsuleShape: Capsule around Y axis. Also btCapsuleShapeX/Z. btCylinderShape : Cylinder around the Y axis. Also btCylinderShapeX/Z. btConeShape : Cone around the Y axis. Also btConeShapeX/Z. btMultiSphereShape : Convex hull of multiple spheres, that can be used to create a Capsule (by passing 2 spheres) or other convex shapes.Compound ShapesMultiple convex shapes can be combined into a composite or compound shape, using the btCompoundShape. This is a concave shape made out of convex sub parts, called child shapes. Each child shape has its own local offset transform, relative to the btCompoundShape.Convex Hull MeshesFor moving objects, concave meshes can be passed into btConvexHullShape,. This automatically collides with the convex hull of the mesh:Concave triangle meshesGeneral triangle meshes that represent static environment can best be represented in Bullet by using the btBvhTriangleMeshShape. It is possible to directly use existing graphics meshes, without duplicating the indices and vertices.Internally, Bullet creates an acceleration structure (bounding volume hierarchy, aabb tree), and this structure supports local deformations (refitting the tree based on an bounding box that contains the local vertex deformation).Convex DecompositionIdeally, concave meshes should only be used for static artwork. Otherwise its convex hull should be used by passing the mesh to btConvexHullShape. If a single convex shape is not detailed enough, multiple convex parts can be combined into a composite object called btCompoundShape. Convex decomposition can be used to decompose the concave mesh into several convex parts. See the ConvexDecompositionDemo for an automatic way of doing convex decomposition. The implementation is taken from Ageia CreateDynamics tool, which can do the same with some fancy user interface. CreateDynamics can export to COLLADA Physics, so Bullet can import that data.An optional contribution called GIMPACT can handle moving concave meshes. See Demos/MovingConcaveDemo for its usage.Height FieldBullet provides support for the special case of a flat 2D concave terrain through the btHeightfieldTerrainShape. See VehicleDemo for its usage.Non-uniform local scaling of Collision ShapesSome collision shapes can have local scaling applied. UsebtCollisionShape::setScaling(vector3). Non uniform scaling with different scaling values for each axis, can be used for btBoxShape, btMultiSphereShape, btConvexShape, btTriangleMeshShape. Note that a non-uniform scaled sphere can be created by using a btMultiSphereShape with 1 sphere. Uniform scaling of Collision ShapesbtUniformScalingShape allows to re-use collision shapes with different scaling factor, to reduce memory.Collision MarginBullet uses a small collision margin for collision shapes, to improve performance and reliability of the collision detection. It is best not to modify the default collision margin, and if you do use a positive value: zero margin might introduce problems. By default this collision margin is set to 0.04, which is 4 centimeter if your units are in meters (recommended).Dependent on which collision shapes, the margin has different meaning. Generally the collision margin will expand the object. This will create a small gap. To compensate for this, some shapes will subtract the margin from the actual size. For example, the btBoxShape subtracts the collision margin from the half extents. For a btSphereShape, the entire radius is collision margin so no gap will occur. Don‟t override the collision margin for spheres. For convex hulls, cylinders and cones, the margin is added to the extents of the object, so a gap will occur, unless you adjust the graphics mesh or collision size. For convex hull objects, there is a method to remove the gap introduced by the margin, by shrinking the object. See the BspDemo for this advanced use.The yellow in the following picture described the working of collision margin for internal contact generation.Bullet ConstraintsThere are several constraints implemented in Bullet. See Demos/ConstraintDemo for an example of each of them. All constraints including the btRaycastVehicle are derived from btTypedConstraint. Constraint act between two rigidbodies, where at least one of them needs to be dynamic.btPoint2PointConstraintPoint to point constraint, also known as ball socket joint limits the translation so that the local pivot points of 2 rigidbodies match in worldspace. A chain of rigidbodies can be connected using this constraint.btHingeConstraintHinge constraint, or revolute joint restricts two additional angular degrees of freedom, so the body can only rotate around one axis, the hinge axis. This can be useful to represent doors or wheels rotating around one axis. The user can specify limits and motor for the hinge.btConeTwistConstraintTo create ragdolls, the conve twist constraint is very useful for limbs like the upper arm. It is a special point to point constraint that adds cone and twist axis limits. btGeneric6DofConstraintThe generic D6 constraint. This generic constraint can emulate a variety of standard constraints, by configuring each of the 6 degrees of freedom (dof). The first 3 dof axis are linear axis, which represent translation of rigidbodies, and the latter 3 dof axis represent the angular motion. Each axis can be either locked, free or limited. On construction of a new btGenericD6Constraint, all axis are locked. Afterwards the axis can be reconfigured. Note that several combinations that include free and/or limited angular degrees of freedom are undefined.Following is convention:For each axis:-Lowerlimit == Upperlimit -> axis is locked.-Lowerlimit > Upperlimit -> axis is free-Lowerlimit < Upperlimit -> axis it limited in that rangeBullet VehiclebtRaycastVehicleFor most vehicle simulations, it is recommended to use the simplified Bullet vehicle model as provided in btRaycastVehicle. Instead of simulation each wheel and chassis as separate rigid bodies, connected by constraints, it uses a simplified model. This simplified model has many benefits, and is widely used in commercial driving games. The entire vehicle is represented as a single rigidbody, the chassis. The collision detection of the wheels is approximated by ray casts, and the tire friction is a basic anisotropic friction model.See Demos/VehicleDemo for more details, or check the Bullet forums.Changing the up axis of a vehicle., see #define FORCE_ZAXIS_UP in VehiceDemo.Bullet Character ControllerA basic player or NPC character can be constructed using a capsule shape, sphere or other shape. To avoid rotation, you can set the …angular factor‟ to zero, which disables the angular rotation effect during collisions and other constraints. See btRigidBody::setAngularFactor. Other options (that are less recommended) include setting the inverse inertia tensor to zero for the up axis, or using a angular-only hinge constraint.Basic DemosBullet includes several demos. They are tested on several platforms and use OpenGL graphics and glut. Some shared functionality like mouse picking and text rendering is provided in the Demos/OpenGL support folder. This is implemented in the DemoApplication class. Each demo derives a class from DemoApplication and implements its own initialization of the physics in the …initPhysics‟ method.CCD Physics DemoThis is the main demo that shows how to setup a physics simulation, add some objects, and step the simulation. It shows stable stacking, and allows mousepicking and shooting boxes to collapse the wall. The shooting speed of the box can be changed, and for high velocities, the CCD feature can be enabled toavoid missing collisions. Try out advanced features using the #defines at thetop of CcdPhysicsDemo.cppCOLLADA Physics Viewer DemoImports and exports COLLADA Physics files. It uses the included libxml and COLLADA-DOM library.The COLLADA-DOM imports a .dae xml file that is generated by tools andplugins for popular 3D modelers. ColladaMaya with Nima fromFeelingSoftware, Blender, Ageia‟s free CreateDynamics tool and othersoftware can export/import this standard physics file format. TheColladaConverter class can be used as example for other COLLADA physicsintegrations.BSP DemoImport a Quake .bsp files and convert the brushes into convex objects. Thisperforms better then using triangles.Vehicle DemoThis demo shows the use of the build-in vehicle. The wheels are approximated by ray casts. This approximation works very well for fast moving vehicles. For slow vehicles where the interaction between wheels and environment needs to be more precise the Forklift Demo is more recommended. The landscape iseither triangle mesh or a heightfield.Character DemoA basic character controller demo has been added with a reusable btCharacterController class, see Demos/CharacterDemo.General Tips for Bullet usersShare collision shapes between rigid bodiesFor better performance and reduced memory use, it is better to re-use collision shapes, among different rigid bodies.Avoid very small and very large collision shapesThe minimum object size for moving objects is about 0.2 units. When using default gravity of 9.8, those units are in meters so don‟t create objects smaller then 20 centimeter. It is recommended to keep the maximum size of moving objects smaller then about 5 units/meters.Avoid large mass ratios (differences)Simulation becomes unstable when a heavy object is resting on a very light object. It is best to keep the mass around 1. This means accurate interaction between a tank and a very light object is not realistic.Combine multiple static triangle meshes into oneMany small btBvhTriangleMeshShape pollute the broadphase. Better combine them. Use the default internal fixed timestepBullet works best with a fixed internal timestep of at least 60 hertz (1/60 second).For safety and stability, Bullet will automatically subdivide the variable timestep into fixed internal simulation substeps, up to a maximum number of substeps specified as second argument to stepSimulation. When the timestep is smaller then the internal substep, Bullet will interpolate the motion.This safety mechanism can be disabled by passing 0 as maximum number of substeps (second argument to stepSimulation): the internal timestep and substeps are disabled, and the actual timestep is simulated. It is not recommended to disable this safety mechanism.For ragdolls use btConeTwistConstraintIt is better to build a ragdoll out of btHingeConstraint and/or btConeTwistLimit for knees, elbows and arms. Alternatively, the btGenericD6Constraint can be used, see Demos/GenericJointDemo.Don’t set the collision margin to zeroCollision detection system needs some margin for performance and stability. If the gap is noticeable, please compensate the graphics representation.Use less then 100 vertices in a convex meshIt is best to keep the number of vertices in a btConvexHullShape limited. It is better for performance, and too many vertices might cause instability.Avoid huge or degenerate triangles in a triangle meshKeep the size of triangles reasonable, say below 10 units/meters. Also degenerate triangles with large size ratios between each sides or close to zero area can better be avoided.Advanced TopicsPer triangle friction and restitution valueBy default, there is only one friction value for one rigidbody. You can achieve per shape or per triangle friction for more detail. See the Demos/ConcaveDemo how to set the friction per triangle. Basically, add CF_CUSTOM_MATERIAL_CALLBACK to the collision flags or the rigidbody, and register a global material callback function. To identify the triangle in the mesh, both triangleID and partId of the mesh is passed to the material callback. This matches the triangleId/partId of the striding mesh interface.Custom Constraint SolverBullet uses its btSequentialImpulseConstraintSolver by default. You can use a different constraint solver, by passing it into the constructor of your btDynamicsWorld. For comparison you can use the Extras/quickstep solver from Open Dynamics Engine.Custom Friction ModelIf you want to have a different friction model for certain types of objects, you can register a friction function in the constraint solver for certain body types.See #define USER_DEFINED_FRICTION_MODEL in Demos/CcdPhysicsDemo.cpp.Collision Filtering (disabling collisions)Collision groups and masksTo disable collision detection between certain shapes, collision groups and collision filter masks are used. By default, when a rigidbody is added to the btDynamicsWorld, the collision group and mask is chosen to prevent collisions between static objects at a very early stage. You can specify the group and mask in …btDynamicsWorld::addRigidBody’ and…btCollisionWorld::addCollisionObject’.The broadphase checks those filter flags to determine wether collision detection needs to be performed using the following code:You can override this default filtering behaviour after the rigidbody has been added to the dynamics world by assigning new values to collisionFilterGroup and collisionFilterMask.Disable collisions between a pair of instances of objectsWhen two bodies share a constraint, you can optionally disable the collision detection between those instances. Pass true as optional second argument to btDiscreteDynamicsWorld::addConstraint (this bool disableCollisionsBetweenLinkedBodies defaults to false).Collision MatrixFor each pair of shape types, Bullet will dispatch a certain collision algorithm, by using the dispatcher. By default, the entire matrix is filled with the following algorithms. Note that Convex represents convex polyhedron, cylinder, cone and capsule and other GJK compatible primitives. GJK stands for Gilbert Johnson Keethi, the people behind this convex distance calculation algorithm. EPA stands for Expanding Polythope Algorithm by Gino van den Bergen. Bullet has its own free implementation of GJK and EPA.Registering custom collision shapes and algorithmsThe user can register a custom collision detection algorithm and override any entry in this Collision Matrix by using the btDispatcher::registerCollisionAlgorithm. See UserCollisionAlgorithm for an example, that registers SphereSphere collision algorithm.Advanced Low Level Technical DemosCollision Interfacing DemoThis demo shows how to use Bullet collision detection without the dynamics.It uses the CollisionWorld class, and fills this will CollisionObjects.performDiscreteCollisionDetection method is called and the demo shows how to gather the contact points.Collision DemoThis demo is more low level then previous Collision Interfacing Demo. Itdirectly uses the GJKPairDetector to query the closest points between twoobjects.User Collision AlgorithmShows how you can register your own collision detection algorithm thathandles the collision detection for a certain pair of collision types. A simplesphere-sphere case overides the default GJK convex collision detection.Gjk Convex Cast / Sweep DemoThis demo show how to performs a linear sweep between to collision objects and returns the time of impact. This can be useful to avoid penetrations incamera and character control.。
2023届山东省泰安市高三下学期三模英语试题学校:___________姓名:___________班级:___________考号:___________一、阅读理解Let’s take a look at these traditional events in the UK.World Gurning ChampionshipsGurning is a British word meaning to pull a funny facial expression. The World Gurning Championships sets out to crown(加冕) a contestant who can pull the strangest face of all. The contest takes place every year in Egremont, Cumbria, as part of the town’s Crab Fair, which dates back to 1267.Nettle eating contestHosted by the Bottle Inn pub in Marsh wood, Dorset every year, this 20-year-old nettle eating contest sees dozens of competitors take part in eating as many nettle stalks(荨麻茎) as possible within one hour. Winners normally eat around 70ft of nettle stalks!Whittlesea Straw Bear FestivalEvery January, the Whittlesea Straw Bear Festival takes place, which dates back more than 200 years. The strange festival consists of a performer wearing a five-stone metal and straw bear costume, while parading through the town streets with a group of Appalachian and Morris dancers.Wife carrying raceIf you think your husband is strong enough to carry you in a race, then you may be in with a chance of winning this odd tradition, held in Dorking, Surrey every March. The sport actually originates from the Viking invasion(入侵) of 793 AD.The tradition wasn’t revived in the UK until 2008, but now comes with a friendlier feel. The winner receives £100, while the carrier of the heaviest wife is given a pound of sausage.1.What do we know about World Gurning Championships?A.It was briefly banned.B.It is part of another activity.C.It attracts funny-looking players.D.It originates from an English word. 2.Which event has the longest history?A.Wife carrying race.B.Nettle eating contest.C.Whittlesea Straw Bear Festival.D.World Gurning Championships. 3.What do the listed events have in common?A.They are held in the wild.B.They are yearly events.C.They are invented by farmers.D.They’re only for strong players.Liam Gamer was just 17 years old when he started out on his big adventure — a32,000-kilometer bike trip from Alaska to Argentina. In early January, 2023, he finally finished his trip, 17 months after he started.Liam, an experienced cyclist, had previously ridden from Los Angeles to San Francisco. He made short videos of that trip, and shared them on the social media app TikTok, some of which became quite popular. After reading a book by adventurer Jedidiah Jenkins, who biked from Oregon to Argentina, Liam decided to cycle from Prudhoe Bay, Alaska, the northernmost point in the United States accessible by road, to Ushuaia, Argentina, the southernmost point of South America.Liam set out on August 1, 2021. At first Liam’s parents weren’t too happy about him taking such a long bike trip by himself though it wouldn’t take that much money. But as he carried on, his parents became his strongest supporters.After about three months, Liam had crossed the US, going south along the West Coast. By early December, he had reached Mexico, from which his parents came to the US many years ago. “So crossing the entire country on a bike and reconnecting with my culture and learning the language in the place my family is from is so deeply important to me,” Liam explained emotionally. But Liam also faced challenges in Mexico.He was robbed in Mexico, and at one point, he considered quitting because the incredible heat made biking extremely difficult. In all, he was robbed five times on the trip. He got very sick more than once. In Colombia, he had a bike accident that left him injured and required surgery. In spite of it all, he kept going through rain, sun, heat, cold, deserts and mountains.Liam finally arrived in his destination on January 10, 2023 — 527 days after he started. He had travelled through 14 countries along the way.4.What contributed to Liam’s decision to bike through 14 countries?A.His previous related experiences.B.His parents’ encouragement.C.A desire to shoot short videos.D.A book by Jedidiah Jenkins.5.Why did Liam feel special in Mexico?A.He went there for the first time.B.He found his family tree’s roots.C.He biked there as scheduled.D.He had to speak another language. 6.What can we say about Liam’s bike trip from Alaska to Argentina?A.It’s eventful.B.It’s pleasant.C.It’s costly.D.It’s romantic. 7.What is the author’s purpose in writing the text?A.To inspire our love for nature.B.To promote low-carbon travel.C.To encourage us to see our strengths.D.To call on us to learn a kind of spirit.Europe’s ski resorts (胜地) haven’t been getting enough snow.Amedeo Reale is president of Sci Club 18, in Cortina d’Ampezzo, a town in Italy’s Dolomite Mountains. In 2026, the area will host the Women’s Winter Olympics downhill skiing events. “The only thing we are scared of is having one or two months of hot weather,” Reale says. “But in Cortina d’Ampezzo, I don’t think there is any problem.” At more than 5,000 feet above sea level, the slopes (坡) stay cold enough for artificial snow.But other parts of Italy are not so lucky. They’ve been getting a taste of a much warmer future. The only plan for saving Italy’s ski industry is to use artificial snow as much as possible, says Rolando Galli, who runs a ski lift in there sort of Abetone, in Italy. It has done more than $2 million less business this season because of the lack of snow. Even if there’s snow for the rest of the season, Galli says, there’s no way to make up for this year’s lost income. He ran the lifts without snow, just for the views, but not many tourists showed up.The changing weather is making it hard to find the right conditions for winter-sports competitions. Promoting summertime sports is probably a good business strategy. The government and mountain towns should invest in lakes. In summer, these could be tourist destinations-for fishing, boating, and sightseeing. They might also provide water to fight bush fires. Clinate change is something that we have to face. We can’t just put our heads in the ground and ignore it.Since 1924, 21 cities have hosted the Winter Olympies. The first was Chamonix, France. If global temperatures continue rising at the current rate, only four of those places will have conditions appropriate for competition by 2050. That’s the prediction of a recent scientific report. Cortina d’ Ampezzo, in Italy, would be rated “unacceptable”, the report says. Only Sapporo, Japan, is considered a reliable bet for the 2078 or 2082 games.calculations, the vibration felt by passengers during a400 km/h trip will be 5% higher than at present. That might seem like a small difference, but it can increase the wavelength of the vibrations felt along the train by 15%. If not effectively controlled, this can make passengers uncomfortable during the journey, even unsafe. Research shows that lifting sleepers by just a few millimeters can resist this impact.Trains with different speeds can operate on the same track, but each speed setting requires different sleepers. Existing Chinese safety standards allow only an error of one millimeter when adjusting the sleepers. China has more than 40,000 km of high-speed railways in operation. To make them all suitable for 400 km/h trains will be a difficult task. However, it’s necessary to find a solution soon because according to the government’s 5-year plan, the new generation of high-speed train, the CR450, will be completed and put into operation in less than 3years.12.What does the underlined phrase “get complacent” mean in paragraph 2? A.Convenient.B.Successful.C.Respected.D.Satisfied. 13.What is paragraph 4 mainly talking about?A.The way wheels and tracks interact.B.The effect of vibration on passengers.C.The difficulty in adjusting the sleepers.D.The reason why existing sleepers should be lifted.14.What can we know about China’s existing high-speed railways?A.Their sleepers need adjusting all the time.B.The more these railways are built, the better.C.Enough of them will be in use in three years.D.It’s hard to make 400 km/h trains run on all of them.15.What’s the best title for the text?A.China Develops 400 km/h Bullet TrainB.China’s Trains Care More for PassengersC.China’s CR450s Replace Other TrainsD.China Focuses on Railway Technology二、七选五三、完形填空五、其他应用文46.假定你班最近选出了“班级之星”(Class Star)李华,请你向校英文报“我们的榜样”栏目写篇报道,内容包括:1.感人事迹;2.你的感想。
玩具枪的子弹进了眼睛会样作文英文回答:When a toy gun bullet enters the eye, it can cause serious damage and potentially lead to vision loss. The impact of the bullet can cause a range of injuries, including corneal abrasions, retinal detachment, and even damage to the optic nerve.Corneal abrasions occur when the surface of the cornea, the clear outer layer of the eye, is scratched or scraped. This can cause pain, redness, and blurred vision. If the bullet is traveling at a high velocity, it can penetrate deeper into the eye and cause more severe damage, such as retinal detachment. Retinal detachment is a serious condition where the retina, the light-sensitive tissue at the back of the eye, pulls away from its normal position. This can result in vision loss or blindness if not treated promptly.Another potential injury from a toy gun bullet entering the eye is damage to the optic nerve. The optic nervecarries visual information from the eye to the brain, and any damage to this nerve can lead to permanent vision loss. In some cases, the bullet may also cause damage to other structures within the eye, such as the lens or the iris.It is essential to seek immediate medical attention ifa toy gun bullet enters the eye. An ophthalmologist will thoroughly examine the eye and determine the extent of the injury. Treatment options may include the removal of the bullet, medication to prevent infection, and surgery to repair any damage.中文回答:当玩具枪的子弹进入眼睛时,可能会造成严重的伤害,甚至导致视力丧失。
物理练习题英语Physics Practice Problems1. Speed and VelocityA car travels 120 miles in 2 hours. Calculate the average speed of the car.2. Force and AccelerationA 5 kg object is subjected to a force of 45 N. What is the acceleration of the object?3. Work DoneA force of 20 N is applied to move an object 10 meters in the direction of the force. How much work is done?4. Energy ConservationA 3 kg ball is dropped from a height of 5 meters. What is the kinetic energy of the ball just before it hits the ground?5. MomentumA 2 kg object moving at 6 m/s collides with a stationary 8 kg object. If the collision is perfectly inelastic, what is the final velocity of the combined objects?6. Gravitational Potential EnergyA 10 kg rock is lifted to a height of 20 meters. Calculate the gravitational potential energy of the rock.7. Electric FieldA proton is placed in an electric field with a strength of 2 N/C. What is the force experienced by the proton?8. Ohm's LawA resistor has a resistance of 10 ohms and is connected to a12 V battery. What is the current flowing through the resistor?9. Wavelength and FrequencyIf the speed of light is 3 x 10^8 m/s and the frequency of a light wave is 5 x 10^14 Hz, what is the wavelength of the light wave?10. Boyle's LawA gas with an initial pressure of 2 atm is compressed to half its original volume. If the temperature remains constant, what is the final pressure of the gas?Solutions1. Average speed = Total distance / Total time = 120 miles /2 hours = 60 miles/hour.2. Acceleration = Force / Mass = 45 N / 5 kg = 9 m/s^2.3. Work done = Force x Distance = 20 N x 10 m = 200 Joules.4. Kinetic energy = 1/2 x Mass x (Velocity^2). First, find the velocity using v = sqrt(2 x g x h) = sqrt(2 x 9.81 m/s^2 x 5 m) = 7 m/s. Then, kinetic energy = 1/2 x 3 kg x (7 m/s)^2 = 44.1 Joules.5. Total momentum before collision = m1 x v1 + m2 x v2 = 2 kg x 6 m/s + 8 kg x 0 m/s = 12 kg m/s. After the collision,v_final = Total momentum / Total mass = 12 kg m/s / (2 kg + 8 kg) = 1.2 m/s.6. Gravitational potential energy = Mass x g x h = 10 kg x 9.81 m/s^2 x 20 m = 1962 Joules.7. Force = q x E = 1.6 x 10^-19 C x 2 N/C = 3.2 x 10^-19 N.8. Current = Voltage / Resistance = 12 V / 10 ohms = 1.2 A.9. Wavelength = Speed of light / Frequency = (3 x 10^8 m/s) / (5 x 10^14 Hz) = 0.6 meters.10. Final pressure = Initial pressure x (Final volume /Initial volume) = 2 atm x (1/2) = 1 atm.。
MICRO-FLODigital Paddlewheel Flow meterOperating Manual5300 Business Drive Huntington Beach, CA 92649USAPhone: 714-893-8529 FAX: 714-894-9492E mail:********************or **************************Website: Blue-WhiteIndustries, Ltd.MICRO-FLOPage 21.0IntroductionThe Micro-Flo flowmeter is designed to display flow rate and flow total on a six digit LCD display. The meter can measure bi-directional flows in either vertical or horizontal mounting orientation. Six flow ranges and four optional pipe and tubing connections are available. Pre-programmedcalibration K-factors can be selected for the corresponding flow range or a custom field calibration can be performed for higher accuracy at a specific flow rate. The meter is factory programmed for the correct K-factor ofthe body size included with the meter.TABLE OF CONTENTS1.....Introduction ....................................................................................22.....Features ..........................................................................................33.....Model number matrix ....................................................................34.....Specifications . (4)4.1..Temperature and pressure limits................................................44.2..Dimensions...............................................................................54.3..Replacement parts.....................................................................55.....Installation .. (6)5.1..Wiring connections...................................................................65.2..Circuit board connections.........................................................65.3..Flow verification output signal..................................................65.4..Panel or wall mountings............................................................76.....Operation . (7)6.1..Theory of operation...................................................................76.2..Control panel............................................................................86.3..Flow stream requirements.........................................................86.4..Run mode display......................................................................86.5..Run mode operation..................................................................96.6..Viewing the K-factor.................................................................97.....Programming . (9)7.1..Field Calibration.......................................................................97.2..Programming for body size/range S1 - S6.................................107.3..Field calibration range setting S0..............................................11Warranty information .. (12)2.0Features!Four connection options available:1/8” F/NPT, 1/4” F/NPT, 1/4” OD x .170 ID Tubing & 3/8” OD x 1/4” ID Tubing sizes.!Six body size/flow range options available:30 to 300 ml/min, 100 to 1000 ml/min, 200 to 2000 ml/min, 300 to 3000 ml/min, 500 to 5000 ml/min, 700 to 7000 ml/min.!3 model display variations:FS = Sensor mounted displayFP = Panel mounted display (includes 6’ cable)FV = No display. Sensor only. 5vdc current sinking output !6 digit LCD, up to 4 decimal positions.!Displays both rate of flow and total accumulated flow.!Open collector alarm setpoint.!User selectable or custom programmable K-factor. Flow units: Gallons, Liters, Ounces, milliliters Time units: Minutes, Hours, Days!V olumetric field calibration programming system.!Non-volatile programming and accumulated flow memory.!Total reset function can be disabled.!Clear PVC viewing lens or PVDF chemical resistant lens.!Weather resistant Valox PBT enclosure. NEMA 4XPage 3MICRO-FLOMETER FUNCTIONFS = Flow rate and Totalizing. On-sensor mounting FP = Flow rate and Totalizing. Remote panel mounting FV = Flow sensor only (no display)POWER SUPPLY1 = Transformer U.S. 115VAC/15VDC2 = Transformer E.U. 220VAC/15VDC3 = Transformer U.S. 230VAC/15VDC None = No selection (customer supplied)FLOW RANGE SELECTION10 = 30-300 ml/min 20 = 100-1000 ml/min 30 = 200-2000 ml/min 40 = 300-3000 ml/min 50 = 500-5000 ml/min 60 = 700-7000 ml/minO-RING SEALV = Viton E = EPDMCONNECTOR4 = .250” OD tubing PVDF5 = .125” Female NPT PVC6 = .375” OD tubing PVDF7 = .250” Female NPT PVCLENS MATERIAL0 = Clear PVC 1 = Opaque PVDF3.0 Model number matrix4.0SpecificationsMax. Working Pressure: o o PVC lens, 130 psig (9 bar) @ 70 F (21 C) o o PVDF lens,150 psig (10 bar) @ 70 F (21 C) Max. Fluid Temperature: o o PVC lens, F/NPT connectors 130 F (54 C) @ 0 PSI o o PVDF lens, tubing connectors 200 F (93 C) @ 0 PSI Full scale accuracy+/- 6%Input Power requirement: 9 - 28 VDC (31mA @ 15Vdc)Sensor only output cable: 3-wire shielded cable, 6ftPulse output signal:Digital square wave (2-wire) 25ft max.V oltage high = 5Vdc, V oltage low < .25Vdc 50% duty cycle Output frequency range: 4 to 500HzAlarm output signal:NPN Open collector. Active low aboveprogrammable rate set point.30Vdc maximum, 50mA max load.Active low < .25Vdc2K ohm pull up resistor required.Enclosure:NEMA type 4X, (IP56)Approximate shipping wt:1 lb. (.45 kg)MICRO-FLOPage 4Maximum Temperature vs. Pressure30(2)60(4)90(6)120(8)150(10)STATIC PRESSURE PSI (BAR)o o70F (21C)o o 96F (36C)o o 122F (50o o148F (64o o 200F (93C)T E M P E R A T U R Eo o174F (79C)4.1 Temperature and Pressure limits12345678219101415131920161718228PARTS LIST Key Part No. Description Qty.1 90011-081 Screw 6-32x.50 Phil Flt SS 4290002-227 Lens Cap Clear PVC 190002-228 Lens Cap Opaque PVDF 3 90003-143 O-Ring Viton 190003-146O-Ring EP 4 90002-230 Paddle PVDF 15 90007-592 Axle PVDF 16 90003-012 O-Ring Viton 290003-011 O-Ring EP776001-300 Body S1 PVDF (30-300ml/min)176001-301 Body S2 PVDF(100-1000ml/min)76001-302 Body S3 PVDF (200-2000ml/min)76001-303 Body S4 PVDF (300-3000ml/min)76001-304 Body S5 PVDF (500-5000ml/min)76001-305 Body S6 PVDF (700-7000ml/min)8 90011-113 Screw #4x.50 Phil Blk 4976000-137 Adapter .250 F/NPT PVC 276000-456Adapter .125 F/NPT PVC90002-038 Adapter .37OD x .25ID Tube PVDF 90002-042 Adapter .25OD x .17ID Tube PVDF 10 90012-252 Sensor 113 90002-242 Enclosure, Valox 114 90012-254 LCD display 115 90010-260 Circuit board 116 90006-604 Gasket, rear enclosure 117 90002-243 Cover, enclosure rear 118 90008-199 Liquid Tight Connector Set 119 90011-178 Screw #4x.62 Phil SS Blk 420 90011-177 Screw #2x.25 L Phil St 221 76001-299 Tubing connector seal 12290006-605Gasket, sensor mount seal 1Page 5MICRO-FLO5.00 in [127 mm]3.51 in [89.03 mm]1.48 in [37.71 mm]2.22 in [56.26 mm]4.2 Dimensions4.3 Replacement PartsMICRO-FLO Page 65.0 Installation5.1 Wiring ConnectionsOn sensor mounted units, the output signal wires must be installed through the back panel using a second liquid-tite connector (included). To install the connector, remove the circular knock-out. Trim the edge if required. Install the extra liquid-tite connector.On panel or wall mounted units, wiring may be installed through the enclosure bottom or through the back panel. See below.ribbon cable connection30 VDC max50mA max50% duty cycle5.3 Flow Verification Output SignalWhen connected to external equipment such as a PLC, data logger, or Blue-White metering pump, the pulse output signal can be used as a flow verification signal. When used with Blue-White metering pumps, connect the positive (+) terminal on the Micro-Flow circuit board to the pump’s yellow signal input wire and the negative (-) terminal to the black input wire.5.2 Circuit Board ConnectionsPage 7MICRO-FLOWiring through enclosure mounting screw locations1.00 in [25 mm]1.75 in [45 mm]Recommended panel or wall mounting cut-outfor wire connection opening5.4 Panel or wall mounting6.0Operation6.1 Theory of operationThe Micro-Flo flowmeter is designed to measure the flow rate and accumu-late the total volume of a fluid. The unit contains a paddle wheel that has six (6) through holes to allow infrared light to pass through, a light-detecting circuit and a LCD-display electronic circuit.As fluid passes through the meter body, the paddle wheel spins. Each time the wheel rotates a DC square wave is output from the sensor. There are six (6) compete DC cycles induced for every revolution of the paddle wheel. The frequency of this signal is proportional to the velocity of the fluid in the conduit. The generated signal is then sent into the electronic circuit to be processed.The meter is factory programmed for the correct K-factor of the body size included with the meter.The Micro-flo flowmeter includes the following features:!Displays either the flow rate or the accumulated total flow.!Provides a pulse output signal that is proportional to the flow rate.!Provides an open collector alarm output signal. Active low at flow rates above the user programmed value.!Provides user selectable, factory preset calibration k-factors.!Provides a field calibration procedure for more precise measurement. !Front panel programming can be disabled by a circuit board jumper pin.6.2 Control PanelEnter Button (right arrow) -!Press and release - Toggle between Rate, Total, and Calibrate screens in the run mode. Select program screens in the program mode.!Press and hold 2 seconds - Enter and exit program mode. (Automatic exit program mode after 30 seconds of no inputs).MICRO-FLOPage 86.4Run mode display6.5Run mode operationFLOW RATE DISPLAY - Indicates rate of flow, S1= body size/range #1, ML = units displayed in milliliters, MIN = time units in minutes, R = flow rate displayed.FLOW TOTAL DISPLAY - Indicates accumulated total flow, S1 = body size/range #1, ML = units displayed in milliliters, T = total accumulated flow displayed.T = Flow total indicatedHr = Rate per hour Day = Rate per daySetP (flashing) = alarm none = not programmedClear/Cal (up arrow) -!Press and release - Clear total in the run mode. Scroll through and Select options in the program mode.6.3 Flow stream requirements!The Micro-flo flowmeter can measure fluid flow in either direction.!The meter must be mounted so that the paddle axle is in a horizontal o position - up to 10 off the horizontal is acceptable.!The fluid must be capable of passing infra-red light.!The fluid must be free of debris. A 150 micron filter is recommended - especially when using the smallest body size (S1), which has a 0.031” through hole.Page 9MICRO-FLO7.0ProgrammingThe Micro-Flo flowmeter uses a K-factor to calculate the flow rate and total. The K-factor is defined as the number of pulses generated by thepaddle per volume of fluid flow. Each of the six different body sizes have different operating flow ranges and different K-factors. The meter is factory programmed for the correct K-factor of the body size included with the meter.The meter’s rate and total displays can be independently programmed to display units in milliliters (ML), ounces (OZ), gallons (GAL), or liters (LIT). Rate and total can be displayed in different units of measure. The factory programming is in milliliters (ML).The meter’s rate display can be independently programmed to display time base units in minutes (Min), Hours (Hr), or Days (Day). The factory programming is in minutes (Min).For greater accuracy at a specific flow rate, the meter can be field cali-brated. This procedure will automatically over-ride the factory K-factor with the number of pulses accumulated during the calibration procedure. The factory default settings can be re-selected at any time.7.1 Field CalibrationAny body size/range can be field calibrated. Calibration will take into account your specific application’s fluid properties, such as viscosity and flow rate, and increase the accuracy of the meter in your application.The Body Size/Range must be set for “S0” to enable the calibration mode. Follow the programming instructions on pages 10 & 11 to reset the BodySize/Range and perform the calibration procedure.to display the K-factor.6.6Viewing the K-factor (pulses per unit)to return to run mode.Useful formulas 60 / K = rate scale factorrate scale factor x Hz = flow rate in volume per minute1 / K = total scale factor total scale factor x n pulses = total volumeMICRO-FLOPage 107.2Programming for body size/ranges S1through S6 -Press and Hold ENTER to initiate the programming mode.> LITS4 > S5 > 6 > S0S 0.000 > 0.0000> LIT0.000 > 0.00000.0 > 0.00 > 0.000MICRO-FLOPage 11 7.3Field calibration size/range setting S0 - Continuation of programmingsequence when range “S0” is selected.The meter should be installed as intended in the application. Array The amount of fluid that flows through the meter during the calibrationprocedure must be measured at the end of the calibration procedure.Allow the meter to operate normally, in the intended application, for a period of time. A test time of at least one minute is recommended. Note - the maximum number of pulses possible is 52,000. Pulses will accumulate in the display. After the test time period, Stop the flow through the meter. The pulse counter willstop.Determine the amount of fluid that passed through the meter using a graduatedcylinder, scale, or other method. The measured amount must be entered incalibration screen #4 “MEASURED VALUE INPUT.”0.00 ># 80000-406Rev. 2/28/20085300 Business DriveHuntington Beach, CA 92649USAPhone: 714-893-8529 FAX: 714-894-9492E mail:********************or **************************Website: Blue-WhiteBLUE-WHITE INDUSTRIES LIMITED WARRANTYFLOWMETERS are warranted to be free of defects in material and workmanship for up to 12 months from the date of factory shipment. Warranty coverage is limited to repair or replacement of the defective flowmeter only. Blue-WhiteIndustries does not assume responsibility for any other damage that may occur. This warranty does not cover damage to the flowmeter that results from misuse or alterations, nor damage that occurs as a result of: meter misalignment,improper installation, over tightening, use of non- recommended chemicals, use of non-reccomended adhesives or pipe dopes, excessive heat or pressure, or allowing the meter to support the weight of related piping. Flowmeters are tested and calibrated with water and air only. Although meters may be suitable for other chemicals, Blue-White cannot guarantee their suitability.Flowmeters are repaired at the factory only. Call or write the factory to receive a Return Material Authorization number, carefully pack the flowmeter to bereturned, including a brief description of the problem. Note the RMA number on the outside of the carton.Prepay all shipping costs. The factory does not accept COD Shipments. Damagethat occurs during shipping is the responsibility of the sender.Users of electrical and electronic equipment (EEE) with the WEEE marking per Annex IV of the WEEE Directive must not dispose of end of life EEE as unsorted municipal waste, butuse the collection framework available to them for the return, recycle, recovery of WEEEand minimize any potential effects of EEE on the environment and human health due to the presence of hazardous substances. The WEEE marking applies only to countries within the European Union (EU) and Norway. Appliances are labeled in accordance with EuropeanDirective 2002/96/EC.Contact your local waste recovery agency for a Designated Collection Facility in your area.。
如何提高弹头威力英语作文英文:To increase the power of a bullet, there are several factors to consider. First, the type of gun and ammunition being used plays a crucial role. For example, a huntingrifle will have more power than a handgun due to the larger size and higher caliber of the bullet. Additionally, the type of bullet used can also impact its power. Hollow point bullets, for instance, are designed to expand upon impact, causing more damage to the target.Another factor to consider is the velocity of the bullet. The faster the bullet travels, the more kinetic energy it will have upon impact. This can be achieved by using a longer barrel or using a higher caliber bullet. Additionally, using a propellant with a higher energy output can also increase the velocity of the bullet.Furthermore, the design of the bullet itself can alsoaffect its power. For example, a bullet with a pointed tip will have better aerodynamics, allowing it to travelfurther and with more force. Additionally, the weight ofthe bullet can also impact its power, with heavier bullets generally having more stopping power.In addition to these factors, the skill and techniqueof the shooter also play a role in maximizing the power ofa bullet. Proper stance, grip, and aiming can allcontribute to the accuracy and impact of a shot.Overall, increasing the power of a bullet involves a combination of factors including the type of gun and ammunition, the velocity of the bullet, the design of the bullet, and the skill of the shooter.中文:要提高子弹的威力,有几个因素需要考虑。
1. At a certain time a moving particle ’s position vector is r , what is it speed?A) dr dt B) dr dt C) d r dt D)2. Which of the following is correct? A) , , d r dv v a dt dt ==B) , d v dr v a dt dt τ== C), ds dv v a dt dtτ== D) , dr dv v a dt dt==3. Identical guns fire identical bullets horizontally at the same speed from the sameheight above level planes, one on the Earth and one on the Moon. Which of the following three statements is/are true?I. The horizontal distance traveled by the bullet is greater for the Moon. II. The flight time is less for the bullet on the Earth.III. The velocity of the bullets at impact are the same.A) III only B) I and II only C) I and III only D) II and III only4. Two objects are traveling around different circular orbits with constant speed. They both havethe same acceleration but object A is traveling twice as fast as object B. The orbit radius for object A is _______ the orbit radius for object B.A) one-fourth B) one-half C) the same as D) four times5. The inertia of a body tends to cause the body to:A) speed up B) slow down C) resist any change in its motion D) decelerate due to friction6. 12. The "reaction" force does not cancel the "action" force because:A) the action force is greater than the reaction force B) they act on different bodiesC) they are in the same direction D) the reaction force exists only after the action force is removed7. Three identical springs (X,Y ,Z) are arranged as shown. When a4.0-kg mass is hung on X, the mass descends 3.0 cm. When a6.0-kg mass is hung on Y , the mass descends:A) 2.0 cmB) 4.0 cmC) 6.0 cmD) 9.0 cm8. A 12-N horizontal force is applied to a 40-N block on a rough horizontal surface. The blockis initially at rest. If s μ= 0.5 and k μ= 0.4, the frictional force on the block is:A) 8 N B) 12 N C) 16 N D) 20 N9.When a certain rubber band is stretched a distance x, it exerts a restoring force F = ax + bx2,where a and b are constants. The work done in stretching this rubber band from x = 0 to x = L is:A) aL2 + bLx3B) aL + 2bL2C) a + 2bL D) aL2/2 + bL3/310.At time t = 0 a particle starts moving along the x axis. If its kinetic energyincreases uniformly with t the net force acting on it must be:A) constant B) proportional to t D)proportional to11.An escalator is used to move 20 people (60 kg each) perminute from the first floor of a department store to thesecond floor, 5 m above. The power required isapproximately:A) 100 W B) 200 W C) 1000 W D) 2000 W12.Two objects interact with each other and with no other objects. Initiallyobject A has a speed of 5 m/s and object B has a speed of 10 m/s. In thecourse of their motion they return to their initial positions. Then A has aspeed of 4 m/s and B has a speed of 7 m/s. We can conclude:A) the potential energy changed from the beginning to the end of the trip.B) mechanical energy was increased by nonconservative forces.C) mechanical energy was decreased by nonconservative forces.D) mechanical energy was increased by conservative forces.13.The sum of the kinetic and potential energies of a system of objects isconserved:A) only when no external force acts on the objects.B) only when the objects move along closed paths.C) only when the work done by the resultant external force is zero.D) none of the above.14.A thick uniform wire is bent into the shape of the letter "U" asshown. Which point indicates the location of the center ofmass of this wire?A) A B) B C) C D) D15.At one instant of time a rocket is traveling in outer space at2500 m/s and is exhausting fuel at a rate of 100 kg/s. If thespeed of the fuel as it leaves the rocket is 1500 m/s, relative tothe rocket, the thrust is:A) 0 B) 1.0 ×105 N C) 1.5 ×105 N D) 2.5 ×105 N16.A He4nucleus (atomic weight 4) moving with speed vbreaks up into a neutron (atomic weight 1) and a He3nucleus. The neutron moves off at right angles to theoriginal He4as shown. If the neutron speed is 3v, thefinal speed of the He3 nucleus is:A) zero B) v C) 4v/3 D) 5v/317.The angular velocity vector of a spinning body points out of the page. If theangular acceleration vector points into the page then:A) the body is slowing downB) the body is speeding upC) the body is starting to turn in the opposite directionD) the axis of rotation is changing orientation18.For a wheel spinning on an axis through its center, the ratio of the radialacceleration of a point on the rim to the radial acceleration of a point halfwaybetween the center and the rim is:A) 1/4 B) 2 C) 1/2 D) 419.Four identical particles, each with mass m, are arranged in the x, y planeas shown. They are connected by light sticks to form a rigid body. If m =2.0 kg and a = 1.0 m, the rotational inertia of this array about the y-axisis:A) 4.0 kg/m2 B) 12 kg/m2C) 9.6 kg/m2D) 4.8 kg/m220.A rod is pivoted about its center. A 5-N force isapplied 4 m from the pivot and another 5-N force isapplied 2 m from the pivot, as shown. The magnitudeof the total torque about the pivot (in N m) is:0 B) 5 C) 8.7 D) 1521.A man, with his arms at his sides, is spinning on a light frictionless turntable.When he extends his arms:A) his angular velocity increases.B) his rotational inertia decreases.C) his rotational kinetic energy increases.D) his angular momentum remains the same.22.A uniform disk has radius R and mass M. When it is spinning with angularvelocity w about an axis through its center and perpendicular to its face its angular momentum is Iw . When it is spinning with the same angle velocity abouta parallel axis a distance h away its angular momentum is:A)(I -MR2)w B) (I + Mh2)w C) (I -Mh2)w D) (I + MR2)w23.The escape velocity at the surface of Earth is approximately 8 km/s. What is theescape velocity for a planet whose radius is 4 times and whose mass is 100 times that of Earth?A) 1.6 km/s B) 8 km/s C) 40 km/s D) 200 km/s24. In planetary motion the line from the star to the planet sweeps out equal areas inequal times. This is a direct consequence of:A) the conservation of energy B) the conservation of momentumC) the conservation of angular momentum D) the conservation of mass25. The amplitude of any oscillator can be doubled by:A) doubling only the initial displacement B) doubling only the initial speedC) doubling the initial displacement and halving the initial speedD) doubling both the initial displacement and the initial speed26. A certain spring elongates 9 mm when it is suspended vertically and a block ofmass M is hung on it. The natural frequency of this mass-spring system is:A) need to know M B) 5.3 Hz C) 31.8 Hz D) 181.7 Hz27. 40. A block attached to a spring undergoes simple harmonic motion on ahorizontal frictionless surface. Its total energy is 50 J. When the displacement is half the amplitude, the kinetic energy is:A) 50 J B) 12.5 J C) 25 J D) 37.5 J28. Both the x and y coordinates of a point execute simple harmonic motion. Theresult might be a circular orbit if:A) the amplitudes are the same but the frequencies are differentB) the amplitudes and frequencies are both the sameC) the amplitudes and frequencies are both differentD) the phase constants are the same but the amplitudes are different29. The displacement of a string is given by ()(),sin m y x t y kx t ω=+. The wavelength of the wave is: A) 2πk /w B) k /w C) wk D) 2π/k30. Suppose the maximum speed of a string carrying a sinusoidal wave is v s . Whenthe displacement of a point on the string is half its maximum, the speed of the point is:A) 2s B) 2v s C) v s /4 D) 3v s /431. Two traveling sinusoidal waves interfere to produce a wave with themathematical form (,)sin()m y x t y kx t ωα=++. If the value of φ is appropriately chosen, the two waves might be:A) 1(,) (/3)sin() m y x t y kx t ω=+and 2(,) (/3)sin( )m y x t y kx t ωϕ=++B) 1(,) 0.7sin() m y x t y kx t ω=-and 2(,) 0.7sin( )m y x t y kx t ωϕ=-+C) 1(,) 0.7sin() m y x t y kx t ω=+ and 2(,) 0.7sin( )m y x t y kx t ωϕ=++D)1(,) (/3)sin()my x t y kx tω=-and2(,) (/3)sin( )my x t y kx tωϕ=++32.When a certain string is clamped at both ends, the lowest four resonantfrequencies are 50, 100, 150, and 200 Hz. When the string is also clamped at its midpoint, the lowest four resonant frequencies are:A) 50, 100, 150, and 200 HzB) 50, 150, 250, and 300 HzC) 100, 200, 300, and 400 HzD) 25, 50 75, and 100 Hz33.The diagram shows four situations in which a source of sound S and a detector Dare either moving or stationary. The arrows indicate the directions of motion. The speeds are all the same. Detector 3is stationary. Rank the situationsaccording to the frequencydetected, lowest to highest.A) 1, 2, 3, 4 B) 4, 3, 2, 1 C) 1, 3, 4, 2 D) 2, 1, 2, 334.Heat is:A) energy transferred by virtue of a temperature differenceB) energy transferred by macroscopic workC) energy content of an objectD) a property objects have by virtue of their temperatures35.According to the first law of thermodynamics, applied to a gas, the increase in theinternal energy during any process:A) equals the heat input minus the work done on the gasB) equals the heat input plus the work done on the gasC) equals the work done on the gas minus the heat inputD) is independent of the heat input36.According to the kinetic theory of gases, the pressure of a gas is due to:A) change of kinetic energy of molecules as they strike the wallB) change of momentum of molecules as the strike the wallC) average kinetic energy of the moleculesD) force of repulsion between the molecules37.The mass of an oxygen molecule is 16 times that of a hydrogen molecule. Atroom temperature, the ratio of the rms speed of an oxygen molecule to that of a hydrogen molecule is:A) 16 B) 4 C) 1/16 D) 1/438.The "Principle of Equipartition of Energy" states that the internal energy of a gasis shared equally:A) among the moleculesB) between kinetic and potential energyC) among the relevant degrees of freedomD) between translational and vibrational kinetic energy39. The average speeds v and molecular diameters d of five ideal gases are givenbelow. The number of molecules per unit volume is the same for all of them. For which is the collision rate the greatest?A) v = v 0 and d = d 0 B) v = 2v 0 and d = d 0/2C) v = 3v 0 and d = d 0 D) v = v 0 and d = 2d 040. The mean free path of a gas molecule is:A) average distance a molecule travels between intermolecular collisionsB) the cube root of the volume of the containing vesselC) approximately the diameter of a moleculeD) average distance between adjacent molecules41. In a reversible process the system:A) is always close to equilibrium statesB) is close to equilibrium states only at the beginning and endC) might never be close to any equilibrium stateD) is close to equilibrium states throughout, except at the beginning and end E) is none of the above42. The difference in entropy B A S S S ∆=- for two states A and B of a system can computed as the integral BA dQ T ⎰provided:A) A and B are on the same adiabatB) A and B have the same temperatureC) a reversible path is used for the integralD) the work done on the system is first computed43. According to the second law of thermodynamics:A) heat energy cannot be completely converted to workB) work cannot be completely converted to heat energyC) for all cyclic processes we have dQ/T < 0D) the reason all heat engine efficiencies are less than 100% is friction, which is unavoidable44. Choose the correct statement concerning electric field lines:A) field lines may crossB) field lines are close together where the field is largeC) field lines point away from negative chargeD) a point charge released from rest moves along a field line 45. Consider Gauss's law:0E dA q ε=⎰. Which of the following is true?A)E must be the electric field due to the enclosed chargeB) If q = 0 then E = 0 everywhere on the Gaussian surfaceC) If the charge inside consists of an electric dipole, then the integral is zeroD) If a charge is placed outside the surface, then it cannot affect E on the surface46. Positive charge Q is distributed uniformly throughout an insulating sphere ofradius R , centered at the origin. A positive point charge Q is placed at x = 2R on the x axis. The magnitude of the electric field at x = R /2 on the x axis is:A) ()20Q/4R πε B) ()20Q/8R πε C) ()20Q/72R πε D) ()2017Q/72R πε47. A positive point charge Q is placed outside a large neutral conducting sheet. Atany point in the interior of the sheet the electric field produced by charges on the surface is directed:A) toward the surface B) away from the surface C) toward Q D) away from Q48. A hollow conductor is positively charged. A small uncharged metal ball islowered by a silk thread through a small opening in the top of the conductor and allowed to touch its inner surface. After the ball is removed, it will have:A) a positive charge B) a negative charge C) no appreciable chargeD) a charge whose sign depends on what part of the inner surface it touched49. A particle with mass m and, charge –q is projected with speed v 0 intothe region between two parallel plates as shown. The potentialdifference between the two plates is V and their separation is d . Thechange in kinetic energy of the particle as it traverses this region is:A) –qV/d B) )202qV mv C) qV D) 202mv50. Eight identical spherical raindrops are each at a potential V , relative to thepotential far away. They coalesce to make one spherical raindrop whose potential is:A) 8V B ) V C) 2V D) 4V。
第三章翻译的过程一位法国译者说过:“翻译就是理解和使人理解”(Traduire, c’est comprendre et faire comprendre)。
翻译的过程就是译者理解原文,并把这种理解恰当地传递给读者的过程;它由三个相互关联的环节组成,即理解、传达和校改。
在这一部分里,我们将详细讨论在这三个环节里可能遇到的一些问题。
第一节理解理解原文是整个翻译过程的第一步。
这是最关键、也是最容易出问题的一步。
理解是译文这座大厦的地基。
地基没打扎实,大厦迟早是要倒塌的。
许多译文里含糊不清、语焉不详的地方,正是译者没有透彻理解原文的地方。
大部分的翻译错误都起源于译者的理解错误。
没有正确的理解,翻译者传达的就不是原作的意思,翻译活动就从根本上失去了意义。
理解原文并不像一些初习翻译的人和读者想象得那么容易。
实际翻译中,在最难料到会出理解问题的地方,却偏偏会出问题。
例如,在一片追忆周恩来的个人印象散记里,有这样一句形容周恩来神态举止的话:An extraeodinary mobile face, now ironical, mow jesting, now with his head thrown back in laughter; then at some commen t, instantly alert and attentive.不少人把at some comment (当一听到某句评论时)译成“当要对某物作出评论时”。
一位中国学者竟把《红楼梦》中“(王熙凤)自幼假充男儿教养,学名叫做王熙凤”一句译成:Who, as a child, disguised herself as a boy in order to go to school.把贾母像林黛玉介绍王熙凤时说的话:“他是我们这里有名的一个泼辣货”译成:She’s one of those notorious gossips here.难怪美国中文学者阿基里斯•方(Achillis Fang)在谈到理解原文之难时指出:“所有关于翻译问题的研究都认为这是理所当然的事,即翻译者已经领会原作的语言和思想。
a r X i v :0704.0381v 2 [a s t r o -p h ] 2 S e p 2007Mon.Not.R.Astron.Soc.000,1–8(2007)Printed 1February 2008(MN L A T E X style file v2.2)The collision velocity of the bullet cluster in conventionaland modified dynamicsG.W.Angus 1⋆,S.S.McGaugh 2†1SUPA,School of Physics and Astronomy,University of St.Andrews,Scotland KY169SS2Departmentof Astronomy,University of Maryland,College Park,MD 20742-242USAAccepted ...Received ...;in original form ...ABSTRACTWe consider the orbit of the bullet cluster 1E 0657-56in both CDM and MOND using accurate mass models appropriate to each case in order to ascertain the maximum plausible collision velocity.Impact velocities consistent with the shock velocity (∼4700km s −1)occur naturally in MOND.CDM can generate collision velocities of at most ∼3800km s −1,and is only consistent with the data provided that the shock velocity has been substantially enhanced by hydrodynamical effects.Key words:gravitation -dark matter -galaxies:clusters:individual (1E 0657-56)1INTRODUCTIONMany lines of observational evidence now oblige us to be-lieve that the universe is filled with a novel,invisible form of mass that dominates gravitationally over normal baryonic matter.In addition,a dark energy component which exerts negative pressure to accelerate the expansion of the universe is also necessary (Chernin et al.2007).Though this ΛCDM paradigm is well established,we still have only ideas about what these dark components might be,and no laboratory detections thereof.One possible alternative to ΛCDM is the Modified New-tonian Dynamics (MOND;Milgrom 1983a,b,c).This hy-pothesis has been more successful than seems to be widely appreciated (McGaugh &de Blok 1998;Sanders &Mc-Gaugh 2002),and has received a theoretical boost from the introduction of generally covariant formulations (Bekenstein 2004;Sanders 2005;Zlosnik,Ferreira,&Starkman 2006,7).The dark matter and alternative gravity paradigms are rad-ically different,so every observation that might distinguish between them is valuable.ΛCDM is known to work well on large scales (e.g.,Spergel et al.2006)while MOND is known to work well in in-dividual galaxies (Sanders &McGaugh 2002).This success,incorporating the tight correlation between dark and lumi-nous mass in the DM framework (McGaugh 2005;Famaey et al.2007b)extends over five decades in mass (Fig.1)rang-ing from tiny dwarfs (e.g.,Milgrom &Sanders 2007)through spirals of low surface brightness (de Blok &McGaugh 1998),our own Milky Way (Famaey &Binney 2005)and other high⋆email:gwa2@ †email:ssm@surface brightness (Sanders 1996;Sanders &Noordermeer 2007)to massive ellipticals (Milgrom &Sanders 2003).The recent observations of tidal dwarf galaxies by Bournaud et al.(2007)provides a severe challenge to CDM but is natu-rally explained in MOND with zero free parameters (Mil-grom 2007;Gentile et al.2007).Having said that,MOND persistently fails to completely explain the mass discrepancy in rich clusters of galaxies.Consequently,clusters require substantial amounts of non-luminous matter in MOND.That rich clusters contain more mass than meets the eye in MOND goes back to Milgrom’s original papers (Mil-grom 1983c).At the time,the discrepancy was very much larger than it is today,as it was not then widely appreci-ated how much baryonic mass resides in the intra-cluster medium.Further work on the X-ray gas (e.g.,Sanders 1994,1999)and with velocity dispersions (McGaugh &de Blok 1998)showed that MOND was at least within a factor of a few,but close inspection revealed a persistent discrepancy of a factor of two or three in mass (e.g.,Gerbal et al.1992;The &White 1998;Pointecouteau &Silk 2005,Buote &Canizares 1994).Weak gravitational lensing (Angus et al.2007a;Takahashi &Chiba 2007;Famaey,Angus et al.2007)provides a similar result.To make matters worse,the distribution of the unseen mass does not trace that of either the galaxies or the X-ray gas (Aguirre et al.2001;Sanders 2003;Angus et al.2007b;Sanders 2007).In Fig.1we plot the baryonic mass of many spiral galaxies and clusters against their circular velocity together with the predictions of MOND and CDM.MOND is missing mass at the cluster scale.CDM suffers an analogous missing baryon problem on the scale of individual galaxies.The colliding bullet cluster 1E-0657-56(Clowe et al.2G.W.Angus and S.S.McGaugh2004,2006,Bradac et al.2006,Markevitch et al.2004, Markevitch&Vikhlinin2007)illustrates in a spectacular way the residual mass discrepancy in MOND.While cer-tainly problematic for MOND as a theory,it does not con-stitute a falsification thereof.Indeed,given that the need for extra mass in clusters was already well established,it would have been surprising had this effect not also manifested it-self in the bullet cluster.The new information the bullet cluster provides is that the additional mass must be in some collision-less form.It is a logical fallacy to conclude that because extra mass is required by MOND in clusters,that dark matter is required throughout the entire universe.While undeni-ably problematic,the residual mass discrepancy in MOND is limited to groups and rich clusters of galaxies:these are the only systems in which it systematically fails to remedy the dynamical mass discrepancy(see discussion in Sanders 2003).Could we be absolutely certain that we had accounted for all the baryons in clusters,then MOND would indeed be falsified.But CDMsuffers an analogous missing baryon problem in galaxies(Fig.1)in addition to the usual dynam-ical mass discrepancy,yet this is not widely perceived to be problematic.In either case we are obliged to invoke the ex-istence of some dark mass which is presumably baryonic(or perhaps neutrinos)in the case of MOND.In neither case is there any danger of violating big bang nucleosynthesis constraints.The integrated baryonic mass density of rich clusters is much less than that of all baryons;having the required mass of baryons in clusters would be the proverbial drop in the bucket with regards to the global missing baryon problem.A pressing question is the apparently high relative ve-locity between the two clusters that comprise the bullet cluster1E0657-56(Clowe et al.2006,Bradac et al.2006, Markevitch et al.2004,Markevitch&Vikhlinin2007).The relative velocity derived from the gas shockwave is v rel= 4740+710−550km s−1(Clowe et al.2006).Taken at face value, this is very high,and seems difficult to reconcile withΛCDM (Hyashi&White2006).The problem is sufficiently large that it has been used to argue for an additional long range force in the dark sector(Farrar&Rosen2007).Here we ex-amine the possibility of such a large velocity in both CDM and MOND.One critical point that has only very recently been ad-dressed is how the shock velocity relates to the collision ve-locity of the clusters.Naively,one might expect the dissipa-tional collision of the gas clouds to slow things down so that the shock speed would provide a lower limit on the colli-sion speed.Recent hydrodynamical simulations(Springel& Farrar2007;Milosavljevic et al.2007)suggest the opposite.A combination of effects in the two hydrodynamical sim-ulations show that the shock velocity may be higher than the impact velocity.The results of the two independent hy-drodynamical simulations do not seem to be in perfect con-cordance,and the precise result seems to be rather model dependent.Nevertheless,it seems that the actual relative velocity lies somewhere in the range3500-4500km s−1.The difficulties posed by a high collision velocity for CDM have been discussed previously by Hayashi&White (2006)and Farrar&Rosen(2007).Whereas Springel&Far-rar(2007)and Milosavljevic et al.(2007)consider the com-plex hydrodynamic response of the two gas clouds during Figure1.Shows baryonic mass against circular velocity.Rotat-ing galaxies(blue circles)are from McGaugh(2005)and clusters (green triangles)are from Sanders(2003)using the measured tem-perature to estimate the circular velocity assuming isothermality. The solid orange line is the CDM M-V relation(Steinmetz& Navarro1999)assuming M b=f b M vir with f b=0.17(Spergel et al.2006)and the dashed red line is the MOND prediction.The spirals lie directly on the MOND prediction,but the clusters are generally2-3times in mass below it.The CDM expectation is nicely consistent with clusters,but implies many dark baryons in spirals in addition to the non-baryonic dark matter.the ongoing collision,here we investigate the ability of two clusters like those comprising the bullet cluster to accelerate to such a high relative velocity in the case of both CDM and MOND prior to the merger.We compute a simple free fall model for the two clusters in an expanding universe with realistic mass models,and ask whether the observed colli-sion velocity can be generated within the time available.We take care to match the mass models to the specific observed properties of the system appropriate to eachflavor of grav-ity in order to realistically evaluate the orbit of the clusters prior to their collision.2MODELING THE FREEF ALLWe wish to address a simple question.Given the observed masses of the two clusters,is it possible to account for the measured relative velocity from their gravitational freefall? The expansion of the universe mitigates against large veloc-ities,since the clusters must decouple from the Hubbleflow before falling together.Presumably it takes some time to form such massive objects,though this is expected to occur earlier in MOND than inΛCDM(Sanders1998,2001;Mc-Gaugh1999,2004;Nusser2002;Stachniewicz&Kutschera 2002;Knebe&Gibson2004;Dodelson&Liguori2006).The clusters are observed at z=0.3,giving at most9Gyrs for them to accelerate towards each other.This imposes an up-per limit to the velocity that can be generated gravitation-ally.Without doing the calculation,it is not obvious whether the larger masses of the clusters in CDM or the stronger long range force in MOND will induce larger relative velocities.Since we know the state of the system directly prior to collision,it makes sense to begin our simulations from thefinal state and work backwards in time towards when the relative velocity was zero.This point,where the clus-The collision velocity of the bullet cluster in conventional and modified dynamics3 ters have zero relative velocity,is when they turned aroundfrom the Hubbleflow and began their long journey gravi-tating towards each other.Working backwards in time leadsto potentially counter-intuitive discussions(such as Hubblecontraction),which we try to limit.We must account for the Hubble expansion in a mannerrepresenting the universe before z=0.3.The detailed form ofthe expansion history of the universe a(t)is not known inthe case of MOND,so we take the scale factor ofΛCDM inboth modelsda(t)da(t)m200r−1 r+r200c−1 −2,A−1=ln(1+c)−c4π4G.W.Angus and S.S.McGaughFigure 3.The total enclosed masses for the main cluster as a function of time,where 9.3Gyr marks the collision of the two clusters and 0Gyr represents the Big Bang.The three lines corre-spong to different mass assembly rates α=0.5(black),1.0(blue)and 1.5(red).The mass loss is halted at m 200/50.m (r )=Am 200 ln1+crr v−1(4)For the main cluster they give m 200=1.5×1015M ⊙,r 200=2100kpc and concentration c=1.94.For the sub clus-ter,m 200=1.5×1014M ⊙,r 200=1000kpc and c=7.12.We augment the DM with a baryon fraction of 17%(Spergel et al.2006)which was part of the total mass during freefall.We ran dynamical time steps (negative)such that ∆t =10−4×√1+x.(9)A well known problem with implementing the MOND force law innumerical computations is that the original for-mulation (Eq 7)does not conserve momentum (Felten 1984;Bekenstein 2007).This was corrected with the introduction of a Lagrangian formulation of MOND (Bekenstein &Mil-grom 1984;Milgrom 1986)which has the modified Poisson equation∇·[µ(|∇Φ|/a o )∇Φ]=4πGρ.(10)This formulation has been shown to obey the necessary conservation laws (Bekenstein &Milgrom 1984;Bekenstein 2007).With some rearrangement,it leads to µ(x )g =g N +∇×h ,(11)The collision velocity of the bullet cluster in conventional and modified dynamics5 which we recognize as Eq7with the addition of a curlfield.Unfortunately,implementing a numerical formulation ofthe modified Poisson equation is not a simple one-line changeto typical N-body codes:this fails to obey the conservationlaws.Instead,one needs an entirely different numerical ap-proach than is commonly employed.Progress has been madealong these lines(e.g.,Brada&Milgrom1995,1999;Ciotti,Londrillo,&Nipoti2006;Nipoti,Londrillo&Ciotti2007ab;Tiret&Combes2007;see also Nusser2002;Knebe&Gib-son2004),but we do not seek here a full N-body treatmentof complex systems.Rather,we wish to develop and applya simple tool(Angus&McGaugh,in preparation)that canprovide some physical insight into basic problems.For thespecific case of the large collision velocity of the bullet clus-ter,it suffices to treat the curlfield as a small correctionto the center of mass motion(Milgrom1986).The externalfield effect(see Milgrom1983a,Bekenstein2007)is crudelyapproximated as a constant of appropriate magnitude(Mc-Gaugh2004).We checked the effect of varying the externalfield,which is modest.It is not possible to do better withoutcomplete knowledge of the mass distribution in the environ-ment of the clusters.When modeling the bullet cluster in MOND,Angus etal.(2007a)fitted the convergence map of Clowe et al.(2006)using spherical potential models for the four mass compo-nents.Their bestfit gives masses for all four components inMOND and standard gravity.Unfortunately,the map is onlysensitive out to250kpc from the respective centres which ne-glects an over large portion of the dynamical mass.So,in or-der to remain consistent with the CDM simulations,we takethe NFW profile and calculate what the MOND dynamicalmasses for the two commonly used interpolating functions(Eq.8&9)are,as shown in Fig.2.The Newtonian mass forthe main cluster is twice that of the MOND dynamical masswith the standardµand three times when the simpleµisused.The mutual gravity imposed upon the sub cluster bythe main cluster isµ |g sub+g ex|a o .The directionand amplitude of g ex is unknown at all times.The MON-Dian additional acceleration becomes minor when the accel-eration drops below g ex.We use g ex=a o/30(Aguirre et al.2001;McGaugh2004)which is roughly the externalfield imposed on the Milky Way by M31and vice versa(Famaey et al.2007a,Wu et al.2007).5N-BODY COLLISIONOurfirst attempt at simulating the collision in Newtonian gravity was using a standard N-body tree code.The benefit it gives is that in principal,we can more accurately compute the mutual gravity at the beginning of the simulation when the two clusters overlap.However,this is fraught with diffi-culties and inconsistencies.Thefirst being that tidal effects undoubtedly stretch the two clusters and2-body interac-tions may eject particles from the two halos.Therefore,it makes better sense to begin such a simulation from high redshift where the clusters are greatly separated and tidal effects are negligible and let them freefall in the expanding universe and when they collide,the tidal effects will be well accounted for.Of course,the problem is that it is not triv-ial to then sample collision velocities because the separation and time at which the two clusters began their freefall is not simply related.Moreover,the truncation of the two halos and different mass models are not easily varied.Neverthe-less,we did attempt a CDM N-body model with truncation at r200for both halos.We found a similar result to that from the semi-analytical models of3800km s−1.6RESULTSThe ability of the two clusters that comprise the bullet to bring each other to a halt at afinite time in the past is sen-sitive to both theflavour of gravity at work and the true relative velocity.For velocities larger than the maximum, the relative velocity never reaches zero and increase sharply at early times(large z).The two clusters do not gravitate strongly enough to generate such high velocities and would have to have had a huge relative velocity towards each other in the early universe in order to overcome the Hubble expan-sion and fall together with such a high relative velocity at z=0.3.Fig.4shows how the relative velocity of the two clus-ters varies with time for a large sample of initial(meaning collisional)relative velocities for a CDM and MOND sample simulation.A difference of just100km s−1can have a signif-icant impact on the time required to generate such a large velocity and by the same token,the longer the two clusters free-fall,the larger a velocity they can generate.Sadly,there is only afinite time(∼9Gyr))since the Big Bang for this to happen.In Table1we’ve put the key results of the simulations so as to give the reader a feel for what the maximum rela-tive velocity that can be achieved is.Each velocity is that achieved with an initial separation of425kpc,where taking 350or500kpc induces an increase or decrease of100km s−1 which we take as the minimum error.The most extreme CDM model is to have no truncation of the DM halos,ex-tending them out to r1.This absurd extreme allows a maxi-mum relative velocity of4500km s−1.Then,if we still allow the halos to extend to r1,but account for some assembly of the halos withα=1then the relative velocity reduces to 4200km s−1.More realistically,if we truncate the halos at r200and try four different halo assembly rates such thatα=0.0,0.5, 1.0&1.5we get respective maximum relative velocities of 4000,3900,3800and3800km s−1.These numbers repre-sent the plausible maximum relative velocities in the CDM framework.For the MOND case we ran simulations with both the simple(Eq.9)and standard(Eq.9)µfunctions.The stan-dard function leads to higher dynamical masses from the6G.W.Angus and S.S.McGaughFigure 4.Shows the relative velocity of the two clusters plotted against time (a)CDM and (b)MOND.Time=0Myr is the current (z=0.3)relative velocity of the two clusters with larger times corresponding to higher redshifts.Black lines correspond to relative velocities that are achievable,whereas red lines are not.In (a)we use the simulation (CDM2c)for which α=1.0,d=425kpc and we truncate the halos at r 200.The relative velocities used are v rel =3500-4200km s −1in intervals of 100km s −1.In (b)we use the simulation (MONDst2)which uses the standard µfunction and α=0.5,d=425kpc.The relative velocities used are v rel =4100-4800km s −1in intervals of 100km s −1.The 4dashed lines are the predicted relative velocities according to the mean and 1σerror of the original relative velocity from Markevitch &Vikhlinin (2007)in blue,the simulations of Milosavljevic (2007)in green and Springel &Farrar (2007)in turquoise.The high observed collision velocity is more readily obtained in MOND than CDM.Model Max V rel [km s −1]Truncation RadiusαGravity CDM1a 4500r 10.0Newtonian CDM1b 4200r 1 1.0Newtonian CDM2a 4000r 2000.0Newtonian CDM2b 3900r 2000.5Newtonian CDM2c 3800r 200 1.0Newtonian CDM2d 3800r 200 1.5Newtonian MONDst14800r 2000.0MOND-standard µMONDst24500r 2000.5MOND-standard µMONDsi14600r 2000.0MOND-simple µMONDsi24500r 2000.5MOND-simple µTable 1.Shows the parameters used in the different models and gives the maximum attainable relative velocity for each.NFW profile,but lower 2-body gravity.The standard (sim-ple)function with no accretion and with α=0.5gener-ate 4800(4600)and 4600(4500)km s −1respectively and for comparison,the maximum CDM velocity with those reduced masses is just 2700(2300)km s −1.This is a clear demonstra-tion of the expectation in MOND for larger peculiar veloc-ities.We use the lower assembly parameter α=0.5be-cause structure is expected to form more swiftly in MOND (Sanders 1998,2001).An important factor is that of the fitted NFW density profile to the convergence map,in which matter is extrapo-lated to 2100kpc and 1000kpc for the main and sub cluster respectively.Presumably the significance of the detection of this mass is negligible and the NFW fit has been made as-suming if we know the details in the central 250kpc,then we know the density out to r 200.The mass sheet degeneracy is broken by constraining the mass at the edges of the fit based on the slope of the profile in the inner regions -but if themass profile is wrong then it could lead to the completely wrong measurement for the value of the mass sheet (Clowe,de Lucia and King 2004).All of this means that the density profiles of the two clusters could be moderately different in reality.However,the actual shape of any profile is less important to the rela-tive velocity than simply the normalisation of the total mass.To this end we have simulated the collision with 10%more and 10%less mass for both clusters (with assembly param-eter α=1).The effect is to increase (10%more mass)or decrease (10%less mass)the relative velocity by 200km s −1from 4800km s −1for model MONDst1.Another concern is that the clusters are unlikely to be spherically symmetric (Buote &Canizares 1996)and are presumably elongated in the direction of motion.Again this could lead to an incorrect density profile,whereas ellipticity itself would have little effect on our results.The collision velocity of the bullet cluster in conventional and modified dynamics77SUMMARYWe have constructed specific mass models for the bullet cluster in both CDM and MOND.We integrate backwards from the observed conditions to check whether the large (∼4700km s−1)apparent transverse velocity can be at-tained in either context.Wefind that it is difficult to achieve v rel>4500km s−1under any conditions.Never-theless,within the range of the uncertainties,the appropri-ate velocity occurs fairly naturally in MOND.In contrast,ΛCDM models can at most attain∼3800km s−1and are more comfortable with considerably smaller velocities.Taken at face value,a collision velocity of4700km s−1 constitutes a direct contradiction toΛCDM.Ironically,this cluster,widely advertised as a fatal observation to MOND because of the residual mass discrepancy it shows,seems to pose a comparably serious problem forΛCDM.It has often been the case that observations which are claimed to falsify MOND turn out to make no more sense in terms of dark matter.Two critical outstanding issues remain to be clarified. Thefirst is the exact density profiles and virial masses of the two clusters and the second is how the observed shock ve-locity relates to the actual collision velocity of the two grav-itating masses.The recent simulations of Springel&Farrar (2007)and Milosavljevic et al.(2007)seem to suggest that, contrary to naive expectations,hydrodynamic effects reduce the relative velocity of the mass with respect to the shock.A combination of effects is responsible,being just barely sufficient to reconcile the data withΛCDM.Hydrodynam-ical simulations are notoriously difficult,and indeed these two recent ones do not agree in detail.It would be excellent to see a fully self-consistent simulation including both hy-drodynamical effects and a proper mass model and orbital computation like that presented here.There are a number of puzzling aspects to the hydrody-namical simulations.First of all,Springel&Farrar(2007) use Hernquist profiles for the DM distribution in the clus-ters and not NFW halos.Furthermore,theyfind that the morphology of the bullet is reproduced only for a remark-ably dead head-on collision.If the impact parameter is even 12kpc—a target smaller than the diameter of the Milky Way—quite noticeable morphological differences ensue. This can be avoided if the separation of mass centres hap-pens to be along our line of sight—quite a coincidence in a system already remarkable for having the vector of its collision velocity almost entirely in the plane of the sky.Fur-thermore,the mass models require significant tweaking from that infered from the convergence map and are unable to re-produce the currently observed,post merger positions of the gas and DM.It appears to us that only thefirst rather than the last chapter has been written on this subject.Getting this right is of the utmost importance,as the validity of both paradigms rests on the edge of a knife,separated by just a few hundred km s−1.More generally,the frequency of bullet-like clusters may provide an additional test.The probability of high collision velocities drops with dramatic rapidity inΛCDM(Hyashi& White2006).In contrast,somewhat higher velocities seem natural to MOND.Naively it would seem that high impact velocity systems like the bullet would be part and parcel of what might be expected of a MOND universe.With this in mind,it is quite intriguing that many bullet cluster like systems have been detected(although none quite as unique). The dark ring around Cl0024+17tentatively observed by Jee et al.(2007;see also Famaey et al.2007c),the dark core created by the“train wreck”in Abell520by Mahdavi et al. (2007),Cl0152+1357(Jee et al.2005a),MS1054+0321(Jee et al.2005b)and the line of sight merger with>3000km s−1 relative velocity observed by Dupke et al.(2007)for Abell 576may all provide examples and potential tests. 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