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Name ___________________________ Class ________ Date ___________
TEKS
Physics
Lesson 4D
TEKS 4D Calculate the effect of forces on objects, including the law of inertia, the
relationship between force and acceleration, and the nature of force pairs between
objects.
TEKS 4D: Newton’s Laws of Motion
Why do some cars accelerate faster than others? How does an ice skater glide far across the ice after
pushing off only once? The answers to these questions involve the concepts of mass and inertia.
How did early scientists study motion?
Modern scientists understand the relationships between force and motion. However, it took about
2000 years to develop this understanding.
Aristotle The ancient Greek scientist and philosopher Aristotle (384 B.C.E.–322 B.C.E.) made many
scientific discoveries through careful observation and logical reasoning. He was not always correct.
Aristotle incorrectly proposed that force is required to keep an object moving at constant speed. This error
held back progress in the study of motion for almost two thousand years.
Galileo Italian scientist Galileo Galilei (1564–1642) experimented to find out about the world. By
rolling balls down wooden ramps, he studied how gravity produces constant acceleration. Galileo
concluded that moving objects that were not subjected to friction or any other force would continue to
move indefinitely.
Newton In 1665, the plague broke out in London, forcing Isaac Newton to leave Trinity College in
Cambridge, England, where he was a student. Over the next two years, Newton built on the work of
scientists such as Galileo. He published his results many years later in a book entitled Principia. In this
important work, Newton first had to define mass and force. He then introduced his laws of motion.
What Is Newton’s first law of motion?
Newton summarized his study of force and motion in several laws of motion. According to Newton’s
first law of motion, the state of motion of an object does not change as long as the net force acting on the
object is zero. Thus, unless an unbalanced force acts, an object at rest remains at rest, and an object in
motion remains in motion with the same speed and direction. For example, a soccer ball resting on the
grass remains motionless until a force is applied to it in the form of a kick. The kicked ball begins rolling.
Because friction between the grass and the ball acts on the ball as it rolls, the ball slows. The force of
friction slows the ball and brings it to a stop.
Newton’s first law of motion is sometimes called the law of inertia (in UR shuh). Inertia is the tendency
of an object to resist a change in its motion. In other words, an object at rest tends to remain at rest, and an
object in motion tends to remain in motion with the same direction and speed. Note that as the soccer ball
sat motionless in the grass, the forces acting on it were balanced. The ball remained at rest until an
unbalanced force acted on it. The ball has inertia.
Think about what happens in a moving car during a front-end collision. The force of the collision acts on
the car, making it stop suddenly. Initially, no force acts on the passengers inside the car, and since they
have inertia, their forward motion continues without slowing down. As shown in the illustration on the
next page, seat belts and air bags can be used to stop this forward motion. These safety devices exert force
against the body of the dummy, opposing its forward motion and protecting it from crashing into the
steering wheel and windshield.
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Name ___________________________ Class ________ Date ___________
TEKS
Physics
Lesson 4D
What Is Newton’s second law of motion?
How do unbalanced forces affect the motion of an object? An unbalanced force causes an object’s
velocity to change. In other words, the object accelerates. For example, you apply a net force to a ball
when you throw it. The harder you throw, the more the ball accelerates. In fact, the acceleration of the
ball is directly proportional to the net force acting on it. If you double the force, the acceleration of the
ball doubles as well. Newton also learned that the acceleration of an object depends upon its mass. Mass
is a measure of the inertia of an object and depends on the amount of matter the object contains.
According to Newton’s second law of motion, the acceleration of an object is equal to the net force
acting on it divided by the object’s mass. Thus, doubling the mass of an object cuts its acceleration in
half. Newton was able to put these ideas into a single formula.
Acceleration =
a

Net force
Mass
F
m
Newton’s formula can also be written to calculate the force or the mass:
Netforce = Mass Acceleration
F  ma

Mass =

Net force
Acceleration
m


2
F
a
Name ___________________________ Class ________ Date ___________
TEKS
Physics
Lesson 4D
The acceleration of an object is always in the same direction as the net force. In using
the formula for Newton’s second law, it is helpful to realize that the units N/kg and
m/s2 are equivalent.
Sample problem An automobile with a mass of 1000 kilograms accelerates when
the traffic light turns green. If the net force on the car is 4000 newtons, what is the
car’s acceleration?
First, you record the information you are given:
Mass, m = 1000 kg
Force, F = 4000 N
Then, you identify the unknown you are trying to calculate.
Acceleration, a = ?
Of the three version’s of Newton’s formula, the first one can be used to calculate acceleration if you know
mass and force:
Acceleration =
Net force
F
OR a 
Mass
m
Now you can replace the values of the known variables and solve:

a
4000 N 4 N 
m
m

 4 kg  2  4 2
1000 kg kg
s
s
kg
Therefore, a  4

m
s2
Note that Newton’s second law also applies when a net force acts in the direction opposite to the object’s
motion. In this case, the force produces a deceleration that reduces the speed.

The shopping carts shown below further illustrate Newton’s second law. What happens if you push on a
single shopping cart? The unbalanced force causes the cart to accelerate. What happens when you push
with the same force on a chain of eight shopping carts? The acceleration of the chain of carts is much less
than that of the single cart. The chain of carts accelerates less because it has more mass.
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Name ___________________________ Class ________ Date ___________
TEKS
Physics
Lesson 4D
How do weight and mass differ?
Do you sometimes talk about weight and mass as if they were the same thing?
Although related to each other, mass and weight are not the same. Weight is the force
of gravity acting on an object. An object’s weight is the product of the object’s mass
and acceleration due to gravity acting on it.
Weight = Mass Acceleration Due to Gravity
W  mg
The weight formula is 
basically Newton’s second law. However, weight (W) is substituted for force (F)
and acceleration due to gravity (g) is substituted for acceleration (a). In other words, W = mg is a different

form of a = F/m. It corresponds to the version that is solved for force, F = ma. The value of g in the
formula is 9.8 m/s2.
In using the weight formula or Newton’s second-law formula, make sure you use the correct units. The
force (F or W) should be in newtons, the acceleration (a or g) in meters per second squared, and the mass
(m) in kilograms. The following example shows how to use the weight formula:
If an astronaut has a mass of 112 kilograms, what is his weight on Earth where the acceleration due to
gravity is 9.8 m/s2?
Weight = Mass Acceleration Due to Gravity
 112 kg  9.8

 1100 kg 

m
s2
m
 1100 N
s2
If you study the weight formula, you’ll see that mass and weight are proportional. Doubling the mass of
an object also doubles the object’s weight. Mass is a measure of the inertia of an object; weight is a

measure of the force of gravity acting on an object. Consider the same astronaut on Earth and on the
moon. On the moon, the acceleration due to gravity is only about one sixth that on Earth. Thus, the
astronaut weighs only about one sixth as much on the moon as on Earth. In both locations, the mass of the
astronaut is the same.
What is Newton’s third law of motion?
Think about physics the next time you go to an amusement park. There is no better place than an
amusement park to see Newton’s laws in action. As you experience sudden starts, stops, changes in
direction, and possibly even free fall, you can be sure that the laws of physics control your motion.
Bumper cars illustrate Newton’s third law of motion, the subject of this section.
If you have ever driven a bumper car, you know your goal is to slam into another car head on. When you
collide with the other car, you do so with enough force to jolt the other driver almost out of the seat.
There are two parts to this collision, however—the collision also causes your own car to rebound sharply.
Newton’s third law of motion explains the behavior of the bumper cars during a collision.
A force cannot exist alone. Forces always exist in pairs. According to Newton’s third law of motion,
whenever one object exerts a force on a second object, the second object exerts an equal and opposite
force on the first object. These two forces are called action and reaction forces.
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Name ___________________________ Class ________ Date ___________
TEKS
Physics
Lesson 4D
The force your bumper car exerts on the other car is the action force. The force the
other car exerts on your car is the reaction force. These two forces are equal in size and
opposite in direction.
Pressing your hand against a wall also produces a pair of forces. As you press against
the wall, your hand exerts a force on the wall. This is the action force. The wall exerts
an equal and opposite force against your hand. This is the reaction force.
A similar situation occurs when you use a hammer to drive a nail into a piece of wood. When the hammer
strikes the nail, it applies a force to the nail. This action force drives the nail into the piece of wood. Is
there a reaction force? According to Newton’s third law there must be an equal and opposite reaction
force. The nail supplies the reaction force by exerting an equal and opposite force on the hammer. It is
this reaction force that brings the motion of the hammer to a stop.
At first glance, some of the examples above appear to contradict Newton’s first law. Remember that two
forces acting on an object balance each other if they are equal in magnitude but opposite in direction, and
by Newton’s first law, neither the speed nor the direction of motion of an object will change if all the
forces acting on the object are balanced. The forces in an action-reaction pair are equal in magnitude and
opposite in direction, but there are changes in motion in some of the examples above—the hammer stops,
for example, or a bumper car is pushed sideways.
The reason why these examples do not contradict Newton’s first law is that Newton’s first law involves a
balance of forces acting on the same object. In each action-reaction pair described above, the two forces
act on different objects (the hammer and the nail, the hand and the wall, the two bumper cars). When one
bumper car hits another, the second car receives a push from the first. Newton’s third law says that the
first car also receives a push from the second. The forces are equal in magnitude and opposite in direction,
but they do not balance each other because they are not acting on the same car. Instead, each car is pushed
by a separate force.
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Name ___________________________ Class ________ Date ___________
TEKS
Physics
Lesson 4D
Lesson Check
1. Calculate A boy pushes forward on a 40.0-kg cart of groceries with a net force of 60.0 N. Use the
relationship between force and acceleration to calculate the cart’s acceleration. (TEKS 4Dii)
2. Explain A tethered ball is swung around in a circle at constant speed. (a) Is the net force acting on
the ball equal to zero or different from zero? Use the law of inertia to explain your answer. (b) If a
tethered ball with twice the mass is used instead, how does the inertia of the second ball compare
with the inertia of the first ball? (TEKS 4Di)
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Name ___________________________ Class ________ Date ___________
TEKS
Physics
Lesson 4D
3. Calculate A mover pushes a desk with a force of 200 N. The floor exerts a force
of friction equal to 20 N in the opposite direction. (a) What is the net force acting
on the desk? (b) Calculate the magnitude of the reaction force exerted by the
desk on the mover. (TEKS 4Diii)
4. Calculate A 25-N force accelerates a boy in a wheelchair at 0.5 m/s 2. Use the relationship between
force and acceleration to calculate the combined mass of the boy and the wheelchair. (TEKS 4Dii)
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Name ___________________________ Class ________ Date ___________
TEKS
Physics
Lesson 4D
5. Apply Concepts An airplane is traveling in a straight path at a constant
speed of 500 kilometers per hour. The two forces that affect its forward
motion are the thrust of its engines and the force of drag from the air,
which is pushing against the motion of the plane. According to Newton’s
first law, what must be true?
A
The drag must be less than the thrust; otherwise the plane would not be able to move forward.
B
The drag must be equal to the thrust, because the plane travels at a constant speed in a straight
path.
C
Newton’s first law does not apply in this case.
D
The magnitude of the force of drag does not matter as long as the thrust is constant.
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