Chapter 3 Force and Motion
Force is an interaction between objects that causes an acceleration of a body, which is, loosely speaking, a push or pull. The relationship between a force and the acceleration it causes was first understood by Isaac Newton (1642-1727) and is the subject of this chapter. The study of the relationship is called Newtonian mechanics.
3.1 Newton’s laws
1.Newton’s first law
(1). Before Galileo’s time most philosophers thought that some influence or force was need to keep a body moving. They believed that a body is in its “natural state” when it was at rest. For it to move with constant velocity, it seemingly had to be propelled in some way, by a push or pull. Otherwise, it would “naturally” stop moving.
(2). Newton’s first law: Consider a body on which no force acts. If the body is at rest, it will remain at rest. If the body is moving with constant velocity, it will continue to do so.
(3). Newton’s first law can be interpreted as a statement about reference frames. The frame in which the law of Newtonian mechanics hold is called inertial reference frame or just inertial frames. Newton’s first law is sometimes called the law of inertia.
2. Newton’s second law
(1). Newton’s first law explains what happens to an object when the resultant force acting on it is zero: the object either stays at rest or keeps moving with constant velocity. Newton’s second law answers the question of what happens to an object that has a nonzero resultant force acting on it .
(2). Newton’s second law : The acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass. The direction of the acceleration is the direction of the resultant force . In equation form, we can state Newton’s second law as:
∑
=a m F , or three scalar equations:
∑∑∑===z z y y x x ma F ma F ma F ;;
(3). From above equation, we find if no force acts on a body, the body will not be accelerated. So Newton’s second law include the statement of Newton’s first law as a special case .
3. Newton’s third law
(1). Forces come in pairs . If you push a block with a force, the block will push back the same magnitude force on you but in opposite direction
(2). Newton’s third law: Let body A in
the figure exert a force F BA on body B; experiment shows that
body B exerts a force F AB on body A. These two forces are equal in magnitude and oppositely directed . That is BA AB F F =.
(3). We can call one of these force is the action force ; the other member of the pair is then called the reaction force .
3.2 Some particular forces
1. Weight
(1). The weight W of a body is a force that pulls the body directly toward a nearby astronomical body; in everyday circumstances that astronomical body is the Earth. The force primarily due to an attraction called a gravitational attraction between the two bodies. We consider situations in which a body with mass m is located at a point where the free-fall acceleration has magnitude g, then weight can be written as
j mg g m W -==
(2). Since weight is a force, its SI unit is the newton.
(3). Normally we assume that weight is measured from an inertial frame. If it is, instead, measured from a non-inertial frame, the measurement gives an apparent weight instead of the actual weight.
2. The normal force : When a body is pressed
against a surface, the body experiences a force that is perpendicular to the surface. The force is called the normal force N, as shown in above figure, the name coming from the mathematical term normal, meaning “perpendicular”.
3.Tension: When a cord
(or a rope, cable, or
other such object) is
attached to a body and
pulled taut, the cord is
said to be under tension,
as shown in the figure.
It pulls on the body
with a force T, whose direction is away from the body and along the cord at the point of attachment.
4.Friction
(1). If we slide or
attempt to slide a body
over a surface, the
motion will be resisted
by a bonding between
the body and the surface.
The resistance is
regarded as a single
force f, called the
frictional force, or
simply friction. This
force is directed along
the surface, opposite the
direction of the intended
motion, as shown in the
figure. If in some
situation, the friction can
be negligible, the surface
is then said to be frictionless.
(2). If the body does not move, then the static frictional force f s and the component of F that is parallel to the surface are equal in magnitude, and f s is directed opposite that component of F.
(3). The magnitude of f s has a maximum value f s,max that is given by N f s s μ=m ax , where s μis the coefficient of static friction and N
is the magnitude of the normal force. If the magnitude of the component of F that is parallel to the surface exceeds max ,s f , then
the body begins to slide along the surface.
(4). If the body begins to slide along the surface, the magnitude of the frictional force rapidly decreases to a value f k given by N f K K μ=. Where K μ is the coefficient of kinetic friction .
3.3 The drag force and terminal speed
1. A fluid is anything that can flow, generally either a gas or a liquid. When there is a relative velocity between a fluid and a body, the body experiences a drag force D that oppose the relative motion and points in the direction in which the fluid flows relative to the body.
2. Here we examine only cases in which air is the fluid, the body is blunt rather than slender, and the relative motion is fast enough to that the air becomes turbulent behind the body. In such case, the magnitude of the drag force D is relative to the relative speed v by an experimentally determined drag coefficient C according to 221v A C D ρ=, where ρ is the air density (mass per volume) and A is the effective cross-
sectional area of the body (the area of a cross section taken perpendicular to the velocity v ). The drag coefficient C (typical value range from 0.4 to 1.0) is not truly a constant for a given body. Because if v varies significantly, the value of C can vary as well. Here, we ignore such complications.
3. The above equation indicates that when a blunt object falls from rest through air, drag force D gradually increases from zero as the speed of the body increases. If the body falls far enough, D eventually equal the body’s we ight W, and the net vertical force on the body is then zero. By Newton’s second law, then the acceleration must also be zero and so the body’s speed no longer increases. The body then falls at a constant terminal speed v t , which we find by setting D=mg , obtaining
A C mg v mg Av C t t ρρ2212=?=.
3.4 The force of nature
1. Gravitational force :
2. Electromagnetic force : is the combination of electrical forces and magnetic forces. The force that makes an electrically charged balloon stick to a wall and the force with which a magnet picks up an iron nail are other example of it.
3. Weak force is involved in certain kinds of radioactive decay.
4.Strong force binds together the quarks that make up protons and neutrons, and is the “glue” that holds together an atomic nucleus.