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Chapter 3 Force and Motion
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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
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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: F ma , or three
scalar equations:
F x max ; F
y may ; F
z maz
(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
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the figure exert a force FBA on body B; experiment shows that
body B exerts a force FAB on body A. These two forces are equal
in magnitude and oppositely directed. That is FAB FBA .
(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
W mg mg j
(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.
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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.
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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 fs
and the component of F that is parallel to the surface are equal
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in magnitude, and fs is directed opposite that component of F.
(3). The magnitude of fs has a maximum value fs,max that is given
by f s , m ax s N where s is 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 f s , m ax , 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 fk given by
f K K N . Where K 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
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coefficient C according to D C A v 2 , where is the air
2
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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 weight 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 vt, which we find by setting D=mg, obtaining
1 2mg
CAvt2 mg vt .
2 CA
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.
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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.
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