ch05 Halliday

Chapter 5
Force and Motion

5.2 Newtonian Mechanics
Newtonian Mechanics.
Newtonian Mechanics does not hold good for all situations.

Examples:
1. Relativistic or near-relativistic motion
2. Motion of atomic-scale particles
5.3 Newton’s First Law
Newton’s First Law:
If no force acts on a body, the body’s

velocity cannot change;
that is, the body cannot accelerate.
If the body is at rest, it stays at rest. If it

is moving, it continues to
move with the same velocity (same
magnitude and same direction).
5.4 Force
➢A force is measured by the acceleration it
produces.
➢Forces have both magnitudes and

directions.
➢When two or more forces act on a body,

we can find their net, or resultant force, by
adding the individual forces vectorially.
➢The net force acting on a body is represented

 with the
vector symbol F net
➢Newton’s First Law:

If no net force acts on a body , the body’s velocity
cannot change; that is, the body cannot accelerate
5.4 Force
The force that is exerted on a

standard mass of 1 kg to
produce an acceleration of
1 m/s2 has a magnitude of 1
newton (abbreviated N)
Inertial Reference Frames
An inertial reference frame is one in which Newton’s laws hold.
If a box is sent sliding along a short

strip of frictionless ice—the box’s
motion obeys Newton’s laws as
observed from the Earth’s surface.
(a) The path of a box sliding from the north pole as seen from a
stationary
point in space. Earth rotates to the east. (b) The path of the puck as seen
from the ground.
If the box is sent sliding along a long ice strip extending from the north pole,
and if it is viewed from a point on the Earth’s surface, the box’s path is not a
simple straight line.
The apparent deflection is not caused by a force, but by the fact that we see the
puck from a rotating frame. In this situation, the ground is a noninertial
frame.
5.5: Mass
Mass is an intrinsic characteristic of a body
The mass of a body is the characteristic that relates a

force on the body to the resulting acceleration.
The ratio of the masses of two bodies is equal to the

inverse of the ratio of their accelerations when the same
force is applied to both.
Here mi and ai are the mass and the

acceleration of particle i respectively
5.6: Newton’s second law:
The net force on a body is equal to the product of

the body’s mass and its acceleration.
In component form,
The acceleration component along a given axis is caused only

by the sum of the force components along that same axis, and
not by force components along any other axis.
5.6: Newton’s second law
The SI unit of force is newton (N):
1 N =(1 kg)(1 m/s2) = 1 kgm/s2.

5.6: Newton’s second law; drawing a free-body diagram
✓In a free-body diagram,

the only body shown is the
one for which we are
summing forces.
✓Each force on the body is

drawn as a vector arrow
with its tail on the body.
✓A coordinate system is
usually included, and the The figure here shows two horizontal forces acting on
acceleration of the body is a block on a frictionless floor.
sometimes shown with a
vector arrow (labeled as an
acceleration).
Sample problem, forces
Fig. 5-3 In three situations, forces act on a puck

that moves along an x axis.
Example, 2-D forces:
5.7: Some particular forces
The weight, W, of a body is equal to
Gravitational Force: the magnitude Fg of the
gravitational force on the
A gravitational force on a body is
body.
a certain type of pull that is
directed toward a second body. W = mg (weight),
Suppose a body of mass m is in

free fall with the free-fall
acceleration of magnitude g. The
force that the body feels as a
result is: F = m(g)
g
or Fg = mg.
Normal Force:
When a body presses against a surface,
the surface (even a seemingly rigid one)
deforms and pushes on the body with a
normal force, FN, that is perpendicular to
the surface.
In the figure, forces Fg and FN and are

the only two forces on the block and
they are both vertical. Thus, for the Fig. 5-7 (a) A block resting on a table experiences a
normal force perpendicular to the tabletop. (b) The
block we can write Newton’s second
free-body diagram for the block.
law for a positive-upward y axis,
(Fnet, y= may), as:
for any vertical acceleration ay of the table and block

Friction
If we either slide or attempt to slide a
body over a surface, the motion is
resisted by a bonding between the body
and the surface.
The resistance is considered to be

single force called the frictional force, f.
This force is directed along the surface,
opposite the direction of the intended
motion.
Tension
When a cord is attached to a body and pulled taut, the cord pulls on the body
with a force T directed away from the body and along the cord.
Fig. 5-9 (a) The cord, pulled taut, is under tension. If its mass is negligible, the cord pulls on
the body and the hand with force T, even if the cord runs around a massless, frictionless pulley
as in (b) and (c).
5.8: Newton’s Third Law
When two bodies interact, the forces on the bodies from each other are always
equal in magnitude and opposite in direction.
• The minus sign means that these two

forces are in opposite directions
• The forces between two interacting
bodies are called a third-law force pair.
5.9: Applying Newton’s Laws Key Ideas:
Sample problem 1. Forces, masses, and accelerations
are involved, and they should
Figure 5-12 shows a block S (the sliding block) suggest Newton’s second law of

with mass M =3.3 kg. The block is free to move motion: F = ma
along a horizontal frictionless surface and 
connected, by a cord that wraps over a 2. The expression F = ma is a
frictionless pulley, to a second block H (the vector equation, so we can write it
hanging block), with mass m 2.1 kg. The cord as three component equations.
and pulley have negligible masses compared to 3. Identify the forces acting on each
the blocks (they are “massless”). The hanging
of the bodies and draw free body
block H falls as the sliding block S accelerates to
the right. Find (a) the acceleration of block S, (b) diagrams.
the acceleration of block H, and (c) the tension
in the cord.
5.9: Applying Newton’s Laws
For the sliding block, S, which does not
Sample problem, cont. accelerate vertically.
Also, for S, in the x direction, there is only

one force component, which is T.
For the hanging block, because the

acceleration is along the y axis,
From the free body diagrams, write We eliminate the pulley from consideration

Newton’s Second Law F = ma in the by assuming its mass to be negligible
vector form, assuming a direction of compared with the masses of the two blocks.
acceleration for the whole system. With some algebra,
Identify the net forces for the sliding and
the hanging blocks:
5.9: Applying Newton’s Laws For convenience, we draw a coordinate system and a
free-body diagram as shown in Fig. b. The positive
Sample problem direction of the x axis is up the plane. Force from the
In Fig. a, a cord pulls on a box of sea biscuits up cord is up the plane and has magnitude T=25.0 N.
along a frictionless plane inclined at q= 30°.The The gravitational force is downward and has
box has mass m =5.00 kg, and the force from the magnitude mg =(5.00 kg)(9.8 m/s2) =49.0 N.
cord has magnitude T =25.0 N. What is the box’s Also, the component along the plane is down the
acceleration component a along the inclined plane and has magnitude mg sin q as indicated in the
plane? following figure. To indicate the direction, we can
write the down-the-plane component as -mg sin q.
Using Newton’s Second Law, we have :
which gives:
The positive result indicates that the box accelerates

up the plane.
5.9: Applying Newton’s Laws •The reading is equal to the magnitude of the
normal force on the passenger from the scale.
Sample problem, part a
•We can use Newton’s Second Law only in an
inertial frame. If the cab accelerates, then it is not
an inertial frame. So we choose the ground to be
our inertial frame and make any measure of the
passenger’s acceleration relative to it.
5.8: Applying Newton’s Laws
Sample problem, cont.

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Chapter 5

Force and Motion

Newtonian Mechanics does not hold good for all situations.

Newton’s First Law:

If no force acts on a body, the body’s

If the body is at rest, it stays at rest. If it

➢Forces have both magnitudes and

➢When two or more forces act on a body,

➢The net force acting on a body is represented

➢Newton’s First Law:

The force that is exerted on a

If a box is sent sliding along a short

Mass is an intrinsic characteristic of a body

The mass of a body is the characteristic that relates a

The ratio of the masses of two bodies is equal to the

Here mi and ai are the mass and the

The net force on a body is equal to the product of

The acceleration component along a given axis is caused only

The SI unit of force is newton (N):

1 N =(1 kg)(1 m/s2) = 1 kgm/s2.

✓In a free-body diagram,

✓Each force on the body is

Fig. 5-3 In three situations, forces act on a puck

Suppose a body of mass m is in

In the figure, forces Fg and FN and are

for any vertical acceleration ay of the table and block

The resistance is considered to be

• The minus sign means that these two

Also, for S, in the x direction, there is only

For the hanging block, because the

Using Newton’s Second Law, we have :

The positive result indicates that the box accelerates

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