AP Physics C Mechanics Practice Tests

AP® Physics C2000 Free response QuestionsThese materials were produced by Educational Testing Service® (ETS®), which develops and administers the examinations of the Advanced Placement Program for the College Board. The College Board and Educational Testing Service (ETS) are dedicated to the principle of equal opportunity, and theirprograms, services, and employment policies are guided by that principle.The College Board is a national nonprofit membership association dedicated to preparing, inspiring, and connecting students t o college and opportunity.Founded in 1900, the association is composed of more than 4,200 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three million students and their parents, 22,000 high schools, and 3,500 colleges, through major pr ograms and services incollege admission, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SA T®, the PSAT/NMSQT®, and the Advanced Placement Program® (AP®). The College Board is committed to the principles of equity andexcellence, and that commit ment is embodied in all of its programs, services, activities, and concerns.APIEL is a trademark owned by the College Entrance Examination Board. PSAT/NMSQT is a registered trademark jointly owned by t he College Entrance Examination Board and the National Merit Scholarship Corporation. Educational Testing Service and ETS are registered trademarks of Educational Testing Service.(2000 M1) You are conducting an experiment to measure the acceleration due to gravity g u at an unknown location. In the measurement apparatus, a simple pendulum swings past a photogate located at the pendulum's lowest point, which records the time t10 for the pendulum to undergo 10 full oscillations. The pendulum consists of a sphere of mass m at the end of a string and has a length l. There are four versions of this apparatus, each with a different length. All four are at the unknown location, and the data shown below are sent to you during the experiment.a.figures. Enter these results in the table above.b. On the axes below, plot the square of the period versus the length of the pendulum. Draw a best-fit straight lineAssuming that each pendulum undergoes small amplitude oscillations, from your fit determine the experimental value g exp of the acceleration due to gravity at this unknown location. Justify your answer.d. If the measurement apparatus allows a determination of g exp that is accurate to within 4%, is your experimentalvalue in agreement with the value 9.80 m/s2 ? Justify your answer.e. Someone informs you that the experimental apparatus is in fact near Earth's surface, but that the experiment hasbeen conducted inside an elevator with a constant acceleration a. Assuming that your experimental value g is exact, determine the magnitude and direction of the elevator's acceleration.2000M2. A rubber ball of mass m is dropped from a cliff. As the ball falls, it is subject to air drag (a resistive force caused by the air). The drag force on the ball has magnitude bv2, where b is a constant drag coefficient and v is the instantaneous speed of the ball. The drag coefficient b is directly proportional to the cross-sectional area of the ball and the density of the air and does not depend on the mass of the ball. As the ball falls, its speed approaches a constant value called the terminal speed.a. On the figure below, draw and label all the forces on the ball at some instant before it reaches terminal speed.b. State whether the magnitude of the acceleration of the ball of mass m increases, decreases, or remains the sameas the ball approaches terminal speed. Explain.c. Write, but do NOT solve, a differential equation for the instantaneous speed v of the ball in terms of time t, thegiven quantities, and fundamental constants.d. Determine the terminal speed v t in terms of the given quantities and fundamental constants.e. Determine the energy dissipated by the drag force during the fall if the ball is released at height h and reachesits terminal speed before hitting the ground, in terms of the given quantities and fundamental constants.2000M3. A pulley of radius R1and rotational inertia I1 is mounted on an axle with negligible friction. A light cord passing over the pulley has two blocks of mass m attached to either end, as shown above. Assume that the cord does not slip on the pulley. Determine the answers to parts (a) and (b) in terms of m, R1, I1, and fundamental constants.a. Determine the tension T in the cord.b. One block is now removed from the right and hung on the left. When the system is released from rest, the threeblocks on the left accelerate downward with an acceleration g/3 . Determine the following.i. The tension T3 in the section of cord supporting the three blocks on the leftii. The tension T l in the section of cord supporting the single block on the rightiii. The rotational inertia I1of the pulleyc. The blocks are now removed and the cord is tied into a loop, which is passed around the original pulley and asecond pulley of radius 2R1 and rotational inertia 16I1. The axis of the original pulley is attached to a motor that rotates it at angular speed ω1, which in turn causes the larger pulley to rotate. The loop does not slip on the pulleys. Determine the following in terms of I1, R I, and ω1.i. The angular speed ω2of the larger pulleyii. The angular momentum L2 of the larger pulleyiii. The total kinetic energy of the system2000E1. Lightbulbs A, B, and C are connected in the circuit shown above.a. List the bulbs in order of their brightness, from brightest to least bright. If any bulbs have the same brightness,state which ones. Justify your answer.Now a switch S and a 5.0 mH inductor are added to the circuit; as shown above. The switch is closed at time t = 0.b. Determine the currents I A, I B, and I C for the following times.i. Immediately after the switch is closedii. A long time after the switch is closedc. On the axes below, sketch the magnitude of the potential difference V L across the inductor as a function of time,from immediately after the switch is closed until a long time after the switch is closed.d. Now consider a similar circuit with an uncharged 5.0 F capacitor instead of the inductor, as shown above. Theswitch is again closed at time t = 0. On the axes below, sketch the magnitude of the potential difference V cap across the capacitor as a function of time, from immediately after the switch is closed until a long time after the switch is closed.2000E2. Three particles, A, B, and C, have equal positive charges Q and are held in place at the vertices of an equilateral triangle with sides of length l, as shown in the figures below. The dotted lines represent the bisectors for each side. The base of the triangle lies on the x-axis, and the altitude of the triangle lies on the y-axis.a.i. Point P1, the intersection of the three bisectors, locates the geometric center of the triangle and is one pointwhere the electric field is zero. On Figure 1 above, draw the electric field vectors E A, E B, and E C at P, due to each of the three charges. Be sure your arrows are drawn to reflect the relative magnitude of the fields.ii. Another point where the electric field is zero is point P2 at (0, y2). On Figure 2 above, draw electric field vectors E A, E B, and E C at P2 due to each of the three point charges. Indicate below whether the magnitudeb. Explain why the x-component of the total electric field is zero at any point on the y-axis.c. Write a general expression for the electric potential V at any point on the y-axis inside the triangle in terms of Q,l, and y.d. Describe how the answer to part (c) could be used to determine the y-coordinates of points P1 and P2 at whichthe electric field is zero. (You do not need to actually determine these coordinates.)2000E3. A capacitor consists of two conducting, coaxial, cylindrical shells of radius a and b, respectively, and length L >> b. The space between the cylinders is filled with oil that has a dielectric constant κ. Initially bothcylinders are uncharged, but then a battery is used to charge the capacitor, leaving a charge +Q on the inner cylinder and -Q on the outer cylinder, as shown above. Let r be the radial distance from the axis of the capacitor.a. Using Gauss's law, determine the electric field midway along the length of the cylinder for the following valuesof r, in terms of the given quantities and fundamental constants. Assume end effects are negligible.i. a < r < bii. b < r << Lb. Determine the following in terms of the given quantities and fundamental constants.i. The potential difference across the capacitorii. The capacitance of this capacitorc. Now the capacitor is discharged and the oil is drained from it. As shown above, a battery of emf εis connectedto opposite ends of the inner cylinder and a battery of emf 3εis connected to opposite ends of the outer cylinder.Each cylinder has resistance R. Assume that end effects and the contributions to the magnetic field from the wires are negligible. Using Ampere's law, determine the magnitude B of the magnetic field midway along the length of the cylinders due to the current in the cylinders for the following values of r.i. a < r < bii. b <r << L。

AP® Physics C1994 Free response QuestionsThe materials included in these files are intended for use by AP teachers for course and exam preparation in the classroom; permission for any other use must be sought from the Advanced Placement Program®. Teachers may reproduce them, in whole or in part, in limited quantities, for face-to-face teaching purposes but may not mass distribute the materials, electronically or otherwise. These materials and any copies made of them may not be resold, and the copyright notices must be retained as they appear here. This permission does not apply to any third-party copyrights contained herein.These materials were produced by Educational Testing Service® (ETS®), which develops and administers the examinations of the Advanced Placement Program for the College Board. The College Board and Educational Testing Service (ETS) are dedicated to the principle of equal opportunity, and theirprograms, services, and employment policies are guided by that principle.The College Board is a national nonprofit membership association dedicated to preparing, inspiring, and connecting students to college and opportunity.Founded in 1900, the association is composed of more than 4,200 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three million students and their parents, 22,000 high schools, and 3,500 colleges, through major programs and services in college admission, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT®, the PSAT/NMSQT®, and the Advanced Placement Program® (AP®). The College Board is committed to the principles of equity andexcellence, and that commitment is embodied in all of its programs, services, activities, and concerns.APIEL is a trademark owned by the College Entrance Examination Board. PSAT/NMSQT is a registered trademark jointly owned by the College Entrance Examination Board and the National Merit Scholarship Corporation. Educational Testing Service and ETS are registered trademarks of Educational TestingService.1994M1. A 2-kilogram block and an 8-kilogram block are both attached to an ideal spring ( for which k = 200 N/m) and both are initially at rest on a horizontal frictionless surface, as shown in the diagram above. In an initial experiment, a 100-gram (0.1 kg) ball of clay is thrown at the 2-kilogram block. The clay is moving horizontally with speed v when it hits and sticks to the block. The 8-kilogram block is held still by a removable stop. As a result, the spring compresses a maximum distance of 0.4 meters.a. Calculate the energy stored in the spring at maximum compression.b. Calculate the speed of the clay ball and 2-kilogram block immediately after the clay sticks to theblock but before the spring compresses significantly.c. Calculate the initial speed v of the clay.In a second experiment, an identical ball of clay is thrown at another identical 2-kilogram block, but this time the stop is removed so that the 8-kilogram block is free to move.d. State whether the maximum compression of the spring will be greater than, equal to, or less than 0.4meter. Explain briefly.e. State the principle or principles that can be used to calculate the velocity of the 8-kilogram block atthe instant that the spring regains its original length. Write the appropriate equation(s) and show the numerical substitutions, but do not solve for the velocity.1994M2. A large sphere rolls without slipping across a horizontal surface. The sphere has a constant translational speed of 10 meters per second, a mass m of 25 kilograms, and a radius r of 0.2 meter. The moment of inertia of the sphere about its center of mass is I = 2mr2/5. The sphere approaches a 25° incline of height 3 meters as shown above and rolls up the incline without slipping.a. Calculate the total kinetic energy of the sphere as it rolls along the horizontal surface.b. i. Calculate the magnitude of the sphere's velocity just as it leaves the top of the incline.ii. Specify the direction of the sphere's velocity just as it leaves the top of the incline.c. Neglecting air resistance, calculate the horizontal distance from the point where the sphere leaves theincline to the point where the sphere strikes the level surface.d. Suppose, instead, that the sphere were to roll toward the incline as stated above, but the incline werefrictionless. State whether the speed of the sphere just as it leaves the top of the incline would be less than, equal to, or greater than the speed calculated in (b). Explain briefly.1994M3. A satellite of mass m is in an elliptical orbit around the Earth, which has mass M e and radius R e. The orbit varies from closest approach of a at point A to maximum distance of b from the center of the Earth at point B. At point A, the speed of the satellite is v o Assume that the gravitational potential energy U g = 0 when masses are an infinite distance apart. Express your answers in terms of a, b, m, M e, R e, v o, and G.a. Write the appropriate definite integral, including limits, that can be evaluated to show that thepotential energy of the satellite when it is a distance r from the center of the Earth is given byU g = -GM e mrb. Determine the total energy of the satellite when it is at point A.c. What is the magnitude of the angular momentum of the satellite about the center of the Earth when itis at point A?d. Determine the velocity of the satellite as it passes point B in its orbit.As the satellite passes point A, a rocket engine on the satellite is fired so that its orbit is changed to a circular orbit of radius a about the center of the Earth.e. Determine the speed of the satellite for this circular orbit.f. Determine the work done by the rocket engine to effect this change.1994E1. A thin nonconducting rod that carries a uniform charge per unit length of λ is bent into a circle of radius R.as shown above. Express your answers in terms of λ, R. and fundamental constants.a. Determine the electric potential V at the center C of the circle.b. Determine the magnitude E of the electric field at the center C of the circle.Another thin nonconducting rod that carries the same uniform charge per unit length λ is bent into an arc of a circle of radius R.which subtends an angle of 2θ, as shown above. Express your answers in terms of λand the quantities given above.c. Determine the total charge on the rod.d. Determine the electric potential V at the center of curvature C of the arc.e. Determine the magnitude E of the electric field at the center of curvature C of the arc. Indicate thedirection of the electric field on the diagram above.1994E2. One of the space shuttle missions attempted to perform an experiment in orbit using a tethered satellite. The satellite was to be released and allowed to rise to a height of 20 kilometers above the shuttle. The tether was a 20-kilometer copper-core wire, thin and light, but extremely strong. The shuttle was in an orbit with speed 7,600 meters per second, which carried it through a region where the magnetic field of the Earth had a magnitude of 3.3 x 10-5 tesla. For your calculations, assume that the experiment was completed successfully, that the wire is perpendicular to the magnetic field, and that the field is uniform. a. An emf is generated in the tether.i. Which end of the tether is negative?ii. Calculate the magnitude of the emf generated.To complete the circuit, electrons are sprayed from the object at the negative end of the tether into the ionosphere and other electrons come from the ionosphere to the object at the positive end.b. If the resistance of the entire circuit is about 10,000 ohms, calculate the current that flows in thetether.c. A magnetic force acts on the wire as soon as the current begins to flow.i. Calculate the magnitude of the force.ii. State the direction of the force.d. By how much would the shuttle's orbital energy change if the current remains constant at the valuecalculated in (b) for a period of 7 days in orbit?e. Imagine that the astronauts forced a current to flow the other way. What effect would that have, ifany, on the orbit of the shuttle? Explain briefly.1994E3. A long coaxial cable, a section of which is shown above, consists of a solid cylindrical conductor of radius a, surrounded by a hollow coaxial conductor of inner radius b and outer radius c. The two conductors each carry a uniformly distributed current I, but in opposite directions. The current is to the right in the outer cylinder and to the left in the inner cylinder. Assume μ = μo for all materials in this problem. a. Use Ampere's law to determine the magnitude of the magnetic field at a distance r from the axis ofthe cable in each of the following cases.i. 0 < r < a ii. a < r < bb. What is the magnitude of the magnetic field at a distance r = 2c from the axis of the cable?c. On the axes below, sketch the graph of the magnitude of the magnetic field B as a function of r, forall values of r. You should estimate and draw a reasonable graph for the field between b and c rather than attempting to determine an exact expression for the field in this region.The coaxial cable continues to carry currents I as previously described. In the cross section above, current is directed out of the page toward the reader in the inner cylinder and into the page in the outer cylinder. Point P is located between the inner and outer cylinders, a distance r from the center. A small positive charge q is introduced into the space between the conductors so that when it is at point P its velocity v is directed out of the page, perpendicular to it, and parallel to the axis of the cable.d. i. Determine the magnitude of the force on the charge q at point P in terms of the given quantities.ii. Draw an arrow on the diagram at P to indicate the direction of the force.e. If the current in the outer cylinder were reversed so that it is directed out of the page, how wouldyour answers to (d) change, if at all?。

AP® Physics C1976 Free Response QuestionsThe materials included in these files are intended for use by AP teachers for course and exam preparation in the classroom; permission for any other use must be sought from the Advanced Placement Program®. Teachers may reproduce them, in whole or in part, in limited quantities, for face-to-face teaching purposes but may not mass distribute the materials, electronically or otherwise. These materials and any copies made of them may not be resold, and the copyright notices must be retained as they appear here. This permission does not apply to any third-party copyrights contained herein.These materials were produced by Educational Testing Service® (ETS®), which develops and administers the examinations of the Advanced Placement Program for the College Board. The College Board and Educational Testing Service (ETS) are dedicated to the principle of equal opportunity, and their programs, services, and employment policies are guided by that principle.The College Board is a national nonprofit membership association dedicated to preparing, inspiring, and connecting students to college and opportunity. Founded in 1900, the association is composed of more than 4,200 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three million students and their parents, 22,000 high schools, and 3,500 colleges, through major programs and services in college admission, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT®, thePSAT/NMSQT®, and the Advanced Placement Program® (AP®). The College Board is committed to the principles of equity andexcellence, and that commitment is embodied in all of its programs, services, activities, and concerns.APIEL is a trademark owned by the College Entrance Examination Board. PSAT/NMSQT is a registered trademark jointly owned by the College Entrance Examination Board and the National Merit Scholarship Corporation. Educational Testing Service and ETS are registered trademarks of Educational Testing Service.1976M1. A small block of mass m slides on a horizontal frictionless surface as it travels around the inside of a hoop of radius R. The coefficient of friction between the block and the wall is μ; therefore, the speed v of the block decreases. In terms of m, R. μ, and v, find expressions for each of the following.a. The frictional force on the blockb. The block's tangential acceleration dv/dtc. The time required to reduce the speed of the block from an initial value v0 to v o/31976M2. A cloth tape is wound around the outside of a uniform solid cylinder (mass M, radius R) and fastened to the ceiling as shown in the diagram above. The cylinder is held with the tape vertical and then released from rest. As the cylinder descends, it unwinds from the tape without slipping. The moment of inertia of a uniform solid cylinder about its center is ½MR2.a. On the circle below draw vectors showing all the forces acting on the cylinder after it is released. Labeleach force clearly.b. In terms of g, find the downward acceleration of the center of the cylinder as it unrolls from the tape.c. While descending, does the center of the cylinder move toward the left, toward the right, or straightdown? Explain.1976M3. A bullet of mass m and velocity v o is fired toward a block of thickness L o and mass M. The block is initially at rest on a frictionless surface. The bullet emerges from the block with velocity v o/3.a. Determine the final speed of block M.b. If, instead, the block is held fixed and not allowed to slide, the bullet emerges from the block with aspeed v o/2. Determine the loss of kinetic energy of the bulletc. Assume that the retarding force that the block material exerts on the bullet is constant. In terms ofL o, what minimum thickness L should a fixed block of similar material have in order to stop the bullet?d. When the block is held fixed, the bullet emerges from the block with a greater speed than when theblock is free to move. Explain.1976E1. A solid metal sphere of radius R has charge +2Q. A hollow spherical shell of radius 3R placed concentric with the first sphere has net charge -Q.a. On the diagram below, make a sketch of the electric field lines inside and outside the spheres.b. Use Gauss's law to find an expression for the magnitude of the electric field between the spheres at adistance r from the center of the inner sphere (R < r < 3R).c. Calculate the potential difference between the two spheres.d. What would be the final distribution of the charge if the spheres were joined by a conducting wire?1976E2. A conducting bar of mass M slides without friction down two vertical conducting rails which are separated by a distance L and are joined at the top through an unknown resistance R. The bar maintains electrical contact with the rails at all times. There is a uniform magnetic field B, directed into the page as shown above. The bar is observed to fall with a constant terminal speed v0.a. On the diagram below, draw and label all the forces acting on the bar.b. Determine the magnitude of the induced current I in the bar as it falls with constant speed v0 interms of B, L, g, v0, and M.c. Determine the voltage induced in the bar in terms of B, L, g, v0, and M.d. Determine the resistance R in terms of B, L, g, v0, and M.1976E3. An ion of mass m and charge of known magnitude q is observed to move in a straight line through a region of space in which a uniform magnetic field B points out of the paper and a uniform electric field E points toward the top edge of the paper, as shown in region I above. The particle travels into region II in which the same magnetic field is present, but the electric field is zero. In region II the ion moves in a circular path of radius R as shown.a. Indicate on the diagram below the direction of the force on the ion at point P2, in region II.b. Is the ion positively or negatively charged? Explain clearly the reasoning on which you base yourconclusion.c. Indicate and label on the diagram below the forces which act on the ion at point P1 in region I.P1d. Find an expression for the ion’s speed v at point P1 in terms of E and B.e. Starting with Newton’s law, derive an expression for the mass m of the ion in terms of B, E, q, and R.。

AP® Physics C1973 Free Response QuestionsThese materials were produced by Educational Testing Service® (ETS®), which develops and administers the examinations of the Advanced Placement Program for the College Board. The College Board and Educational Testing Service (ETS) are dedicated to the principle of equal opportunity, and their programs, services, and employment policies are guided by that principle.The College Board is a national nonprofit membership association dedicated to preparing, inspiring, and connecting students to college and opportunity. Founded in 1900, the association is composed of more than 4,200 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three million students and their parents, 22,000 high schools, and 3,500 colleges, through major programs and services in college admission, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT®, thePSAT/NMSQT®, and the Advanced Placement Program® (AP®). The College Board is committed to the principles of equity andexcellence, and that commitment is embodied in all of its programs, services, activities, and concerns.APIEL is a trademark owned by the College Entrance Examination Board. PSAT/NMSQT is a registered trademark jointly owned by the College Entrance Examination Board and the National Merit Scholarship Corporation. Educational Testing Service and ETS are registered trademarks of Educational Testing Service.1973M1. A horizontal force F is applied to a small block of mass m1 to make it slide along the top of a larger block of mass m2 and length l. The coefficient of friction between the blocks is μ. The larger block slides without friction along a horizontal surface. The blocks start from rest with the small block at one end of the larger block, as shown.a. On the diagrams below draw all of the forces acting on each block. Identify each force.b. Find the acceleration of each block. a1 and a2, relative to the horizontal surface.c. In terms of 1, a1, and a2, find the time t needed for the small block to slide off the endof the larger block.d. Find an expression for the energy dissipated as heat because of the friction betweenthe two blocks.1973M2. A 30-gram bullet is fired with a speed of 500 meters per second into a wall.a. If the deceleration of the bullet is constant and it penetrates 12 centimeters into the wall, calculate theforce on the bullet while it is stopping.b. If the deceleration of the bullet is constant and it penetrates 12 centimeters into the wall, how muchtime is required for the bullet to stop?c. Suppose, instead, that the stopping force increases from zero as the bullet penetrates. Discuss themotion in comparison to the case for a constant deceleration.1973M3. A ball of mass m is attached by two strings to a vertical rod. as shown above. The entire system rotates at constant angular velocity ω about the axis of the rod.a. Assuming ω is large enough to keep both strings taut, find the force each string exerts onthe ball in terms of ω, m, g, R, and θ.b. Find the minimum angular velocity, ωmin for which the lower string barely remains taut.1973E1. The plates of an isolated parallel plate capacitor are pulled apart very slowly by a force F. Each plate has charge q and area A. Assume that edge effects are negligible, i.e., the spacing x is much smaller than the plate dimensions.a. Determine the change in capacitance as x is increased by dxb. Determine the change of stored energy in the capacitor as x is increased by dxc. How is the force F related to the change in stored energy ? Determine F in terms of x, q,and A.1973E2. A surveyor attempts to use a compass below a power line carrying a steady currentof 103 amperes. The compass Is 6.0 meters directly below the wire.a. If the horizontal component of the Earth’s field is 0.10 gauss, could the power linedisturb the compass reading? Give a quantitative argument.b. Suppose, instead, the current were 103 amperes of 60 cycles per second alternatingcurrent. Would the compass reading be disturbed? Explain your answerqualitatively in terms of the properties of the compass.1973E3. In a uniform magnetic field B directed vertically downward. a metal bar of mass m is released from rest and slides without friction down a track inclined at an angle , as shown above. The electrical resistance of the bar between its two points of contact with the track is R: the track has negligible resistance. The width of the track is l.a. Show on the diagram the direction of the current in the sliding bar.b. Denoting by v the instantaneous speed with which the bar is sliding down the incline,determine an expression for the magnitude of the current in the bar.c. Determine an expression for the force exerted on the bar by the magnetic field.d. Determine an expression for the terminal velocity of the sliding bar.。

AP® Physi‎c s C: Mecha‎n ics2008 Free-Respo‎n se Quest‎i onsThe Colle‎g e Board‎: Conne‎c ting‎Stude‎n ts to Colle‎g e Succe‎s sThe Colle‎g e Board‎is a not-for-profi‎t membe‎r ship‎assoc‎i atio‎n whose‎missi‎o n is to conne‎c t stude‎n ts to colle‎g e succe‎s s andoppor‎t unit‎y. Found‎e d in 1900, the assoc‎i atio‎n is compo‎s ed of more than 5,000 schoo‎l s, colle‎g es, unive‎r siti‎e s, and other‎educa‎t iona‎l organ‎i zati‎o ns. Each year, the Colle‎g e Board‎serve‎s seven‎milli‎o n stude‎n ts and their‎paren‎t s, 23,000 high schoo‎l s, and 3,500 colle‎g es throu‎g h major‎progr‎a ms and servi‎c es in colle‎g e admis‎s ions‎, guida‎n ce, asses‎s ment‎, finan‎c ial aid, enrol‎l ment‎, and teach‎i ng andlearn‎i ng. Among‎its best-known‎progr‎a ms are the SAT®, the PSAT/NMSQT‎®, and the Advan‎c ed Place‎m ent Progr‎a m® (AP®). The Colle‎g e Board‎is commi‎t ted to the princ‎i ples‎of excel‎l ence‎and equit‎y, and that commi‎t ment‎is embod‎i ed in all of its progr‎a ms, servi‎c es, activ‎i ties‎, and conce‎r ns.© 2008 The Colle‎g e Board‎. All right‎s reser‎v ed. Colle‎g e Board‎, Advan‎c ed Place‎m ent Progr‎a m, AP, AP Centr‎a l, SAT, and the acorn‎logo are regis‎t ered‎trade‎m arks‎of the Colle‎g e Board‎. PSAT/NMSQT‎is a regis‎t ered‎trade‎m ark of the Colle‎g e Board‎and Natio‎n al Merit‎Schol‎a rshi‎p Corpo‎r atio‎n.Permi‎s sion‎to use copyr‎i ghte‎d Colle‎g e Board‎mater‎i als may be reque‎s ted onlin‎e at:www.colle‎g eboa‎r /inqui‎r y/cbper‎m it.html.Visit‎the Colle‎g e Board‎on the Web: www.colle‎g eboa‎r .AP Centr‎a l is the offic‎i al onlin‎e home for the AP Progr‎a m: apcen‎t ral.colle‎g eboa‎r .PHYSI ‎C S C: MECHA ‎N ICSSECTI ‎O N IITime -45 minut ‎e s3 Quest ‎i onsDirec ‎t ions ‎: Answe ‎r all three ‎ quest ‎i ons. The sugge ‎s ted time is about ‎ 15 minut ‎e s for answe ‎r ing each of the quest ‎i ons, which ‎ are worth ‎ 15 point ‎s each. The parts ‎ withi ‎n a quest ‎i on may not have equal ‎ weigh ‎t . Show all your work in the pink bookl ‎e t in the space ‎s provi ‎d ed after ‎ each part , NOT in this green ‎ inser ‎t.2008M ‎1. A skier ‎ of mass M is skiin ‎g down a frict ‎i onle ‎s s hill that makes ‎ an angle ‎ θ with the horiz ‎o ntal ‎, as shown ‎ in the diagr ‎a m. The skier ‎ start ‎s from rest at time t = 0 and is subje ‎c t to a veloc ‎i ty-depen ‎d ent drag force ‎ du e to air resis ‎t ance ‎ of the form F = –bv, where ‎ v is the veloc ‎i ty of the skier ‎ and b is a posit ‎i ve const ‎a nt. Expre ‎s s all algeb ‎r aic answe ‎r s in terms ‎ of M, b, θ, and funda ‎m enta ‎l const ‎a nts.(a) On the dot below ‎ that repre ‎s ents ‎ the skier ‎, draw a free -body diagr ‎a m indic ‎a ting ‎ and label ‎i ng all of the force ‎s that act on the skier ‎ while ‎ the skier ‎ desce ‎n ds the hill.(b) Write ‎ a diffe ‎r enti ‎a l equat ‎i on that can be used to solve ‎ for the veloc ‎i ty of the skier ‎ as a funct ‎i on oftime.(c) Deter ‎m ine an expre ‎s sion ‎ for the termi ‎n al veloc ‎i ty v T of the skier ‎.(d) Solve ‎ the diffe ‎r enti ‎a l equat ‎i on in part (b) to deter ‎m ine the veloc ‎i ty of the skier ‎ as a funct ‎i on of time, showi ‎n g all your steps ‎.(e) On the axes below ‎, sketc ‎h a graph ‎ of the accel ‎e rati ‎o n a of the skier ‎ as a funct ‎i on of time t, and indic ‎a te the initi ‎a l value ‎ of a. Take downh ‎i ll as posit ‎i ve.taO2008M‎2. The horiz‎o ntal‎unifo‎r m rod shown‎above‎has lengt‎h 0.60 m and mass 2.0 kg. The left end of the rod is attac‎h ed to a verti‎c al suppo‎r t by a frict‎i onle‎s s hinge‎that allow‎s the rod to swing‎up or down. The right‎end of th e rod is suppo‎r ted by a cord that makes‎an angle‎of 30° with the rod. A sprin‎g scale‎of negli‎g ible‎mass measu‎r es the tensi‎o n in the cord. A 0.50 kg block‎is also attac‎h ed to the right‎end of the rod.(a) On the diagr‎a m below‎, draw and label‎vecto‎r s to repre‎s ent all the force‎s actin‎g on the rod. Show each force‎vecto‎r origi‎n atin‎g at its point‎of appli‎c atio‎n.(b)Calcu‎l ate the readi‎n g on the sprin‎g scale‎.The rotat‎i onal‎inert‎i a of a rod about‎its cente‎r is 1ML2, where‎M is the mass of the rod and L is its lengt‎h.12Calcu‎l ate the rotat‎i onal‎inert‎i a of the rod-block‎syste‎m about‎the hinge‎.(d)If the cord that suppo‎r ts the rod is cut near the end of the rod, calcu‎l ate the initi‎a l angul‎a r accel‎e rati‎o n of th erod-block‎syste‎m about‎the hinge‎.2008M‎3. In an exper‎i ment‎to deter‎m ine the sprin‎g const‎a n t of an elast‎i c cord of lengt‎h 0.60 m, a stude‎n t hangs‎the cord from a rod as repre‎s ente‎d above‎and then attac‎h es a varie‎t y of weigh‎t s to the cord. For each weigh‎t, the stude‎n t allow‎s the weigh‎t to hang in equil‎i briu‎m and then measu‎r es the entir‎e lengt‎h of the cord. The data are recor‎d ed in the table‎below‎:(a)Use the data to plot a graph‎of weigh‎t versu‎s lengt‎h on the axes below‎. Sketc‎h a best-fit strai‎g ht line throu‎g hthe data.(b) Use the best-fit line you sketc‎h ed in part (a) to deter‎m ine an exper‎i ment‎a l value‎for the sprin‎g const‎a nt k ofthe cord.The stude‎n t now attac‎h es an objec‎t of unkno‎w n mass m to the cord and holds‎the objec‎t adjac‎e nt to the point‎at which‎the top of the cord is tied to the rod, as repre‎s ente‎d above‎. When the objec‎t is relea‎s ed from rest, it falls‎1.5 m befor‎e stopp‎i ng and turni‎n g aroun‎d. Assum‎e that air resis‎t ance‎is negli‎g ible‎.(c)Calcu‎l ate the value‎of the unkno‎w n mass m of the objec‎t.(d)i. Calcu‎l ate how far down the objec‎t has falle‎n at the momen‎t it attai‎n s its maxim‎u m speed‎.ii.Expla‎i n why this is the point‎at which‎the objec‎t has its maxim‎u m speed‎.iii.Calcu‎l ate the maxim‎u m speed‎of the objec‎t.。

AP物理C⼒学模拟卷MultipleChoiceQuestionsMultiple Choice QuestionsTime: 45 minutes. You may refer to the Constants sheet. However, you may not use the Equations sheet, and you may not use a calculator on this portion of the exam.1. A cannon is mounted on a truck that moves forward at a speed of 5m/s. The operator wants to launch a ball from a cannon so the ball goes as far as possible before hitting the level surface. The muzzle velocity of the cannon is 50 m/s. What angle from the horizontal should the operator point the cannon?A.5°B.41°C.45°D.49°E.85°2. A car moving with speed v reaches the foot of an incline of angleθ. The car coasts up the incline without using the engine.Neglecting friction and air resistance, which of the following is correct about the magnitude of the car's horizontal acceleration aand vertical acceleration a y?xA.a x = 0; a y < gB.a x = 0; a y = gC.a x < g ; a y < gD.a x < g ; a y = gE.a x < g ; a y > g3. A bicycle slows down with an acceleration whose magnitude increaseslinearly with time. Which of the following velocity–time graphs could represent the motion of the bicycle?4. A cart is sliding down a low friction incline. A device on the cartlaunches a ball, forcing the ball perpendicular to the incline, as shown above. Air resistance is negligible. Where will the ball land relative to the cart, and why?A.The ball will land in front of the cart, because the ball'sacceleration component parallel to the plane is greater thanthe cart's acceleration component parallel to the plane.B.The ball will land in front of the cart, because the ball hasa greater magnitude of acceleration than the cart.C.The ball will land in the cart, because both the ball and thecart have the same component of acceleration parallel to theplane.D.The ball will land in the cart, because both the ball and thecart have the same magnitude of acceleration.E.The ball will land behind the cart, because the ball slowsdown in the horizontal direction after it leaves the cart.5.The quantity "jerk," j, is defined as the time derivative of anobject's acceleration,What is the physical meaning of the area under a graph of jerk vs.time?A.The area represents the object's acceleration.B.The area represents the object's change in acceleration.C.The area represents the object's change in velocity.D.The area represents the object's velocity.E.The area represents the object's change in position.6. A particle moves along the x-axis with a position given by theequation x(t) = 5 + 3t, where x is in meters, and t is in seconds.The positive direction is east. Which of the following statements about the particle is FALSE.0.The particle is east of the origin at t = 0.1.The particle is at rest at t = 0.2.The particle's velocity is constant.3.The particle's acceleration is constant.4.The particle will never be west of position x = 0.7. A mass hangs from two ropes at unequal angles, as shown above. Whichof the following makes correct comparisons of the horizontal and vertical components of the tension in each rope?8.The force of air resistance F on a mass is found to obey the equationF = bv2, where v is the speed of the mass, for the range of speedsinvestigated in an experiment. A graph of F N vs. v2 is shown above.What is the value of b?.0.83 kg/mA. 1.7 kg/mB. 3.0 kg/mC. 5.0 kg/mD. 1.0 kg/mE.zero9. A box sits on an inclined plane without sliding. As the angle ofthe plane (measured from the horizontal) increases, the normal force.increases linearlyA.decreases linearlyB.does not changeC.decreases nonlinearlyD.increases nonlinearly10.Which of the following conditions are necessary for an object tobe in static equilibrium?.The vector sum of all torques on the object must equal zero.I.The vector sum of all forces on the object must equal zero.II.The sum of the object's potential and kinetic energies must be zero.C.I onlyD.II onlyE.III onlyF.I and II onlyG.I, II, and III11.A student pushes a big 16-kg box across the floor at constant speed.He pushes with a for ce of 50 N angled 35° from the horizontal, as shown in the diagram above. If the student pulls rather than pushes the box at the same angle, while maintaining a constant speed, what will happen to the force of friction?.It must increase.A.It must decrease.B.It must remain the same.C.It will increase only if the speed is greater than 3.1 m/s.D.It will increase only if the speed is less than 3.1 m/s.12.Consider a system consisting only of the Earth and a bowling ball,which moves upward in a parabola above Earth's surface. The downward force of Earth's gravity on the ball, and the upward force of the ball's gravity on the Earth, form a Newton's third law force pair.Which of the following statements about the ball is correct?.The ball must be in equilibrium since the upward forces must cancel downward forces.A.The ball accelerates toward the Earth because the force ofgravity on the ball is greater than the force of the ball onthe Earth.B.The ball accelerates toward the Earth because the force ofgravity on the ball is the only force acting on the ball.C.The ball accelerates away from Earth because the forcecausing the ball to move upward is greater than the force ofgravity on the ball.D.The ball accelerates away from Earth because the forcecausing the ball to move upward plus the force of the ballon the Earth are together greater than the force of gravityon the ball.13.A mass m is attached to a mass 3m by a rigid bar of negligible massand length L. Initially, the smaller mass is located directly above the larger mass, as shown above. How much work is necessary to flip the rod 180° so that the lar ger mass is directly above the smaller mass?.4mgLA.2mgLB.mgLC.4pmgLD.2pmgL14.A ball rolls horizontally with speed v off of a table a height habove the ground. Just before the ball hits the ground, what is its speed?.A.B.C.vD.15.A pendulum is launched into simple harmonic motion in two differentways, as shown above, from a point that is a height h above its lowest point. During both launches, the bob is given an initial speed of3.0 m/s. On the first launch, the initial velocity of the bob isdirected upward along the pendulum's path, and on the second launch it is directed downward along the pendulum's path. Which launch will cause the pendulum to swing with the larger amplitude?.the first launchA.the second launchB.Both launches produce the same amplitude.C.The answer depends on the initial height h.D.The answer depends on the length of the supporting rope.16.The mass M is moving to the right with velocity v0 at position x= x0. Neglect friction. The spring has force constant k. What is the total mechanical energy of the block at this position?17.A sphere, a cube, and a cylinder, all of equal mass, are releasedfrom rest from the top of a short incline. The surface of the incline is extremely slick, so much so that the objects do not rotate when released, but rather slide with negligible friction. Which reaches the base of the incline first?.the sphereA.the cubeB.the cylinderC.All reach the base at the same time.D.The answer depends on the relative sizes of the objects.18.Block B is at rest on a smooth tabletop. It is attached to a longspring, which is in turn anchored to the wall. Block A slides toward and collides with block B. Consider two possible collisions: Collision I: Block A bounces back off of block B.Collision II: Block A sticks to block B.Which of the following is correct about the speed of block Bimmediately after the collision?.It is faster in case II than in case I ONLY if block B is heavier.A.It is faster in case I than in case II ONLY if block B isheavier.B.It is faster in case II than in case I regardless of the massof each block.C.It is faster in case I than in case II regardless of the massof each block.D.It is the same in either case regardless of the mass of eachblock.19.A 0.30-kg bird is flying from right to left at 30 m/s. The birdcollides with and sticks to a 0.50-kg ball which is moving straight up with speed 6.0 m/s. What is the magnitude of the momentum of the ball/bird combination immediately after collision?.12.0 N?sA.9.5 N?sB.9.0 N?sC. 6.0 N?sD. 3.0 N?s20.The force F on a mass is shown above as a function of time t. Whichof the following methods can be used to determine the impulse experienced by the mass?.multiplying the average force by t maxI.calculating the area under the line on the graphII.taking the integralC.II onlyD.III onlyE.II and III onlyF.I and II onlyG.I, II, and III21.A projectile is launched on level ground in a parabolic path so thatits range would normally be 500 m. When the projectile is at the peak of its flight, the projectile breaks into two pieces of equal mass. One of these pieces falls straight down, with no further horizontal motion. How far away from the launch point does the other piece land?.250 mA.375 mB.500 mC.750 mD.1000 mQuestions 22 and 23A rigid rod of length L and mass M is floating at rest in space farfrom a gravitational field. A small blob of putty of mass m < M is moving to the right, as shown above. The putty hits and sticks to the rod a distance 2L/3 from the top end.22.How will the rod/putty contraption move after the collision?.The contraption will have no translational motion, but will rotate about the rod's center of mass.A.The contraption will have no translational motion, but willrotate about the center of mass of the rod and putty combined.B.The contraption will move to the right and rotate about theposition of the putty.C.The contraption will move to the right and rotate about thecenter of mass of the rod and putty combined.D.The contraption will move to the right and rotate about therod's center of mass.23.What quantities are conserved in this collision?.linear and angular momentum, but not kinetic energyA.linear momentum onlyB.angular momentum onlyC.linear and angular momentum, and linear but not rotationalkinetic energyD.linear and angular momentum, and linear and rotationalkinetic energy24.A car rounds a banked curve of uniform radius. Three forces act onthe car: a friction force between the tires and the road, the normal force from the road, and the weight of the car. Which provides the centripetal force which keeps the car in circular motion?.the friction force aloneA.the normal force aloneB.the weight aloneC. a combination of the normal force and the friction forceD. a combination of the friction force and the weight25.A ball of mass m anchored to a string swings back and forth to amaximum position A, as shown above. Point C is partway back to the vertical position. What is the direction of the mass's acceleration at point C?.along the mass's path toward point BA.toward the anchorB.away from the anchorC.between a line toward the anchor and a line along the mass'spathD.along the mass's path toward point A26.In a carnival ride, people of mass m are whirled in a horizontalcircle by a floorless cylindrical room of radius r, as shown in the diagram above. If the coefficient of friction between the people and the tube surface is µ, what minimum speed is necessary to keep the people from sliding down the walls?Questions 27 and 28The uniform, rigid rod of mass m, length L, and rotational inertiaI shown above is pivoted at its left-hand end. The rod is released from rest from a horizontal position.27.What is the linear acceleration of the rod's center of mass the moment after the rod is released?28.What is the linear speed of the rod's center of mass when the mass passes through a vertical position?29.The 1.0-m-long non-uniform plank, shown above, has weight 1000 N.It is to be supported by two rods, A and B, as shown above. The center of mass of the plank is 30 cm from the right edge. Each support bears half the weight of the plank. If support B is 10 cm from the right-hand edge, how far from the left-hand edge should support A be?.0 cmA.10 cmB.30 cmC.50 cmD.70 cm30.A mass m on a spring oscillates on a horizontal surface with periodT. The total mechanical energy contained in this oscillation is E.Imagine that instead a new mass 4m oscillates on the same springwith the same amplitude. What is the new period and total mechanical energy?31.A mass m is attached to a horizontal spring of spring constant k.The spring oscillates in simple harmonic motion with amplitude A.What is the maximum speed of this simple harmonic oscillator?32.An empty bottle goes up and down on the surface of the ocean, obeyingthe position function x= Acos(t). How much time does this bottle take to travel once from its lowest position to its highestposition?33.The Space Shuttle orbits 300 km above the Earth's surface; theEarth's radius is 6400 km. What is the acceleration due to Earth's gravity experienced by the Space Shuttle?. 4.9 m/s2A.8.9 m/s2B.9.8 m/s2C.0.8 m/s2D.zero34.An artificial satellite orbits Earth just above the atmosphere ina circle with constant speed. A small meteor collides with thesatellite at point P in its orbit, increasing its speed by 1%, but not changing the instantaneous direction of the satellite's velocity. Which of the following describes the satellite's new orbit?.The satellite now orbits in an ellipse, with P as the farthest approach to Earth.A.The satellite now orbits in an ellipse, with P as the closestapproach to Earth.B.The satellite now orbits in a circle of larger radius.C.The satellite now orbits in a circle of smaller radius.D.The satellite cannot maintain an orbit, so it flies off intospace.35.Mercury orbits the sun in about one-fifth of an Earth year. If 1AU is defined as the distance from the Earth to the sun, what is the approximate distance between Mercury and the sun? .(1/25) AUA.(1/9) AUB.(1/5) AUC.(1/3) AUD.(1/2) AU。