Chapter 5. Force and Motion I

Download Report

Transcript Chapter 5. Force and Motion I

Chapter 5. Force and Motion I
5.1. What is Physics?
5.2. Newtonian Mechanics
5.3. Newton's First Law
5.4. Force
5.5. Mass
5.6. Newton's Second Law
5.7. Some Particular Forces
5.8. Newton's Third Law
5.9. Applying Newton's Laws
What Causes Acceleration?
Dynamics—the study of causes of
motion. The central question in dynamics
is: What causes a body to change its
velocity or accelerate as it moves?
Newtonian Mechanics
Newton’s laws fail in the following two circumstances:
• 1. When the speed of objects approaches (1%
or more) the speed of light in vacuum (c = 8×108
m/s). In this case we must use Einstein’s
special theory of relativity (1905).
• 2. When the objects under study become very
small (e.g., electrons, atoms, etc.). In this case
we must use quantum mechanics (1926).
A force is a push or a pull. Force is a vector. All forces result from interaction.
•Contact forces: forces that arise from the physical contact between two
•Noncontact forces: forces the two objects exert on one another even
though they are not touching.
• External forces include only the forces
that the environment exerts on the object
of interest.
• Internal forces are forces that one part of
an object exerts on another part of the
Combining Forces
Principle of superposition for forces
When two or more forces act on a body, we
can find their net force or resultant force by
adding the individual forces as vectors taking
direction into account.
Note: The net force involves the
sum of external forces only
(internal forces cancel each other).
Exercise 1
The figures that follow show overhead views of
four situations in which two forces acting on the
same cart along a frictionless track. Rank the
situations according to the magnitudes of the net
force on the cart, greatest first.
Newton’s FIRST LAW
Newton's First law: Consider a body on which no
net force acts. If the body is at rest, it will remain at
rest. If the body is moving, it will continue to
moving with a constant velocity.
– “Net force” is crucial. Often, several forces
act simultaneously on a body, and the net
force is the vector sum of all of them
– An inertial reference frame is the one has
zero acceleration.
– All newton’s laws are valid only in the inertia
reference frames.
• The larger the mass,
the harder is to
cause its motion
• Mass and weight
are different
1. Inertia is the natural tendency of an
object to remain at rest or in motion at a
constant speed along a straight line.
2. The mass of an object is a quantitative
measure of inertia.
SI Unit of Inertia and Mass: kilogram (kg)
When a net external force  F acts on an object
of mass m, the acceleration a that results is
directly proportional to the net force and has a
magnitude that is inversely proportional to the
mass. The direction of the acceleration is the
same as the direction
of the net force.
SI Unit of Force: kg·m/s2 =newton (N)
Only External forces are considered in the Newton’s second law.
Example 1 Pushing a Stalled Car
Two people are pushing a stalled car, as Figure 4.5a
indicates. The mass of the car is 1850 kg. One person
applies a force of 275 N to the car, while the other applies a
force of 395 N. Both forces act in the same direction. A third
force of 560 N also acts on the car, but in a direction
opposite to that in which the people are pushing. This force
arises because of friction and the extent to which the
pavement opposes the motion of the tires. Find the
acceleration of the car.
Example 2 Hauling a Trailer
A truck is hauling a trailer along a level road, as Figure
4.32a illustrates. The mass of the truck is m1=8500 kg
and that of the trailer is m2=27 000 kg. The two move
along the x axis with an acceleration of ax=0.78 m/s2.
Ignoring the retarding forces of friction and air resistance,
determine (a) the tension T in the horizontal drawbar
between the trailer and the truck and (b) the force D that
propels the truck forward.
• The net external force acting on an object is zero. Is it
possible for the object to be traveling with a velocity that
is not zero? If your answer is yes, state whether any
conditions must be placed on the magnitude and
direction of the velocity. If your answer is no, provide a
reason for your answer.
Is a net force being applied to an object when the object
is moving downward (a) with a constant acceleration of
9.80 m/s2 and (b) with a constant velocity of 9.80 m/s?
Newton’s second law indicates that when a net force
acts on an object, it must accelerate. Does this mean that
when two or more forces are applied to an object
simultaneously, it must accelerate? Explain.
Newton's Third Law
Newton's Third Law
If one object is exerting a force on a second object,
then the second object is also exerting a force back
on the first object. The two forces have exactly the
same magnitude but act in opposite directions.
FB A   FAB
•Forces always exist in
•It is very important that
we realize we are talking
about two different
forces acting on two
different objects.
A father and his seven-year-old daughter
are facing each other on ice skates. With
their hands, they push off against one
(a) Compare the magnitudes of the pushing
forces that they experience.
(b) Which one, if either, experiences the
larger acceleration? Account for your
EXAMPLE 3: Pushing Two Blocks
In Fig. 3-29a, a constant horizontal force of
magnitude 20 N is applied to block A of mass 4.0
kg, which pushes against block B of mass 6.0 kg.
The blocks slide over a frictionless surface, along
an x axis.
a) What is the acceleration of the blocks?
b) What is the force acting on block B from block A
Example 4 The Accelerations Produced by Action and Reaction Forces
Suppose that the mass of the spacecraft in
Figure 4.7 is mS=11 000 kg and that the mass
of the astronaut is mA=92 kg. In addition,
assume that the astronaut exerts a force of
P=+36 N on the spacecraft. Find the
accelerations of the spacecraft and the
Every particle in the universe exerts an attractive
force on every other particle. For two particles that
have masses m1 and m2 and are separated by a
distance r, the force that each exerts on the other is
directed along the line joining the particles and has a
magnitude given by:
The symbol G denotes the universal gravitational constant, whose
value is found experimentally to be
The weight of an object on or above the earth is the
gravitational force that the earth exerts on the object. The
weight always acts downward, toward the center of the
earth. On or above another astronomical body, the weight is
the gravitational force exerted on the object by that body.
SI Unit of Weight: newton (N)
When the height of object H above the Earth is small
M Em
M Em
M Em
W G 2 G
( RE  H )
RE 2
W  (G 2 )m  mg
g  G 2  9.8 m/s 2
The Gravitational Acceleration Constant
When air resistance can be ignored and H
any object under only gravitational force will
free fall with a constant acceleration:
g  9.8 m/s
• Mass is an intrinsic property of matter and does not
change as an object is moved from one location to
• Weight, in contrast, is the gravitational force acting on the
object and can vary, depending on how far the object is
above the earth’s surface or whether it is located near
another body such as the moon.
When a body is moved from sea level to
the top of a mountain, what changes—the
body’s mass, its weight, or both? Explain.
The force of air resistance acts to oppose the
motion of an object moving through the air. A ball
is thrown upward and eventually returns to the
• (a) As the ball moves upward, is the net force
that acts on the ball greater than, less than, or
equal to its weight? Justify your answer.
• (b) Repeat part (a) for the downward motion of
the ball.
The Normal Force
The normal force FN is one component of the
force that a surface exerts on an object with
which it is in contact—namely, the
component that is perpendicular to the
The Friction Force
When the object moves or attempts to move along a
surface, there is a component of the force that is parallel
to the surface. This parallel force component is called the
frictional force, or simply friction. It is always against the
relative motion or the attempts of the motion between
object and surface.
Tension is the force exerted by a rope or a cable attached to
an object
1. Tension in a Nonaccelerating rope: the magnitude of
tention is the same everywhere in the rope.
2. An Accelerating rope: the magnitude of tension is not
the same everywhere in the rope that has a mass;
however, the magnitude of tension is the same
everywhere in the rope that is massless.
For a massless string
1. It is always directed
along the rope.
2. It is always pulling
the object.
3. It has the same
value along the
Applying Newton's Laws
Newton's Second Law:
It can be written as two (or three) component equations:
Equilibrium Applications of Newton's Laws of Motion
equilibrium when it has zero acceleration.
Fnet  0
Fx  0 and Fy  0 and Fz  0
EXAMPLE 5: Three Cords
In Fig. 6-25a, a block B of
mass M = 15 kg hangs by a
cord from a knot K of mass
mK, which hangs from a
ceiling by means of two other
cords. The cords have
negligible mass, and the
magnitude of the
gravitational force on the
knot is negligible compared
to the gravitational force on
the block. What are the
tensions in the three cords?
Free-Body Diagrams
(1) Identify the object for which the motion is to be
analyzed and represent it as a point.
(2) Identify all the forces acting on the object and
represent each force vector with an arrow. The
tail of each force vector should be on the point.
Draw the arrow in the direction of the force.
Represent the relative magnitudes of the forces
through the relative lengths of the arrows.
(3) Label each force vector so that it is clear which
force it represents.
Example 6 Replacing an Engine
An automobile engine
has a weight W, whose
magnitude is W=3150 N.
This engine is being
positioned above an
engine compartment, as
Figure 4.29a illustrates.
To position the engine, a
worker is using a rope.
Find the tension T1 in the
supporting cable and the
tension T2 in the
positioning rope.
Example 7 Equilibrium at Constant Velocity
A jet plane is flying with a constant speed along a straight line,
at an angle of 30.0° above the horizontal, as Figure
indicates. The plane has a weight W whose magnitude is
W=86 500 N, and its engines provide a forward thrust T of
magnitude T=103 000 N. In addition, the lift force L (directed
perpendicular to the wings) and the force R of air resistance
(directed opposite to the motion) act on the plane. Find L and
Non-quilibrium Applications of Newton's Laws of Motion
An object is in nonequilibrium when it has non-zero
Fnet  ma
Fx  max and Fy  ma y and Fz  maz
Example 8 Applying Newton’s Second Law Using Components
A man is stranded on a raft
(mass of man and
raft=1300 kg), as shown in
Figure a. By paddling, he
causes an average force P
of 17 N to be applied to the
raft in a direction due east
(the +x direction). The wind
also exerts a force A on the
raft. This force has a
magnitude of 15 N and
points 67° north of east.
Ignoring any resistance
from the water, find the x
and y components of the
raft’s acceleration.
Example 9 Towing a Supertanker
A supertanker of mass m=1.50×108 kg is being towed by
two tugboats, as in Figure. The tensions in the towing
cables apply the forces T1 and T2 at equal angles of 30.0°
with respect to the tanker’s axis. In addition, the tanker’s
engines produce a forward drive force D, whose
magnitude is D=75.0×103 N. Moreover, the water applies
an opposing force R, whose magnitude is R=40.0×103 N.
The tanker moves forward with an acceleration that points
along the tanker’s axis and has a magnitude of 2.00×10–3
m/s2. Find the magnitudes of the tensions T1 and T2.
Conceptual Questions
• According to Newton’s third law, when you push on an object, the
object pushes back on you with an oppositely directed force of equal
magnitude. If the object is a massive crate resting on the floor, it will
probably not move. Some people think that the reason the crate
does not move is that the two oppositely directed pushing forces
cancel. Explain why this logic is faulty and why the crate does not
• A stone is thrown from the top of a cliff. As the stone falls, is it in
equilibrium? Explain, ignoring air resistance.
• Can an object ever be in equilibrium if the object is acted on by only
(a) a single nonzero force, (b) two forces that point in mutually
perpendicular directions, and (c) two forces that point in directions
that are not perpendicular? Account for your answers.
• A circus performer hangs stationary from a rope. She then
begins to climb upward by pulling herself up, hand over
hand. When she starts climbing, is the tension in the rope
less than, equal to, or greater than it is when she hangs
stationary? Explain.
• A weight hangs from a ring at the middle of a rope, as the
drawing illustrates. Can the person who is pulling on the
right end of the rope ever make the rope perfectly
horizontal? Explain your answer in terms of the forces that
act on the ring.