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Forces
Chapter 3
Section 1: Newton’s
Second Law
1.
2.
3.
4.
What you will learn:
Define Newton’s second law of motion.
Apply Newton’s second law of motion.
Describe the three different types of
friction.
Observe the effects of air resistance on
falling objects.
Force, Mass, and Acceleration

Review:


Newton’s FIRST law of motion: the motion of an
object changes only if an unbalanced force acts on
the object.
New:

Newton’s SECOND law of motion: describes how
the forces exerted on an object, its mass, and its
acceleration are related.
Force and Acceleration
What’s different about throwing a ball
horizontally as hard as you can and tossing it
gently?
When you throw hard, you exert
a much greater force on the ball.
 A ball that is thrown hard has
a greater acceleration than a ball
that is tossed gently.

Mass and Acceleration
If you throw a softball and a baseball as hard
as you can, why don’t they
have the same speed?

Mass and Acceleration
Continued...

The difference is due to their masses.




Softball’s mass is about 0.20kg
Baseball’s mass is about 0.14kg
The acceleration of an object depends on its
mass as well as the force exerted on it.
Force, mass, and acceleration are related.
Newton’s Second Law

Newton’s second law of motion states that
the acceleration of an object is in the same
direction as the net force on the object, and
that the acceleration can be calculated from
the following equation:
Units

Important units you need to know:



acceleration: m/s2
mass: kg
force: N (newtons)
F: force (N)
m: mass (kg)
a: accel (m/s2)
1 N = 1 kg ·m/s2
F
m a
F = ma
Practice Problem #1

Solve for acceleration:


You push a wagon that has a mass of 8kg. If the
net force on the wagon is 4N, what is the wagon’s
acceleration?
Step 1: Write what you know:



m= 8kg
Fnet= 4N
Step 2: Use the formula a= Fnet/m

a= 4N/8kg=
 0.5m/s2
F
m a
Practice Problem #2

If the mass of a helicopter is 4,500kg, and
the net force on it is 18,000N, what is the
helicopter’s acceleration?

a= F/m

a= 18,000N
4,500kg

a= 4m/s2
F
m a
Practice Problem #3

What is the net force on a dragster with a
mass of 900kg if it’s acceleration is 32m/s2?

F= ma

F= (900kg)(32m/s2)

F= 28,800N
F
m a
Practice Problem #4

A car pulled by a tow truck has an
acceleration of 2.0m/s2. What is the mass of
the car if the net force on the car is 3,000N?



m= F/a
m= 3,000N
2.0m/s2
m= 1,500kg
F
m a
Friction

What happens to the skateboard if you push
it with your hand?



It rolls for some distance, then stops eventually.
Why?
The force that slows the skateboard and
brings it to a stop is friction.

Friction is the force that opposes the sliding
motion of two surfaces that are touching each
other.
What Causes Friction?

All surfaces have dips and bumps, even
polished metal!


The dips and bumps are called microwelds.
Friction occurs when 2 surfaces are in
contact and the bumps and dips touch each
other.

To move one surface over the other, a force must
be applied to break
the microwelds.
Friction Type #1: Static Friction

Static friction is the frictional force that
prevents two surfaces from sliding past each
other.

In this case the girl’s push on the box is not large
enough to break the microwelds, so the box does
not move.
Friction Type #2: Sliding Friction

Together you and your friend have exerted
enough force to break the microwelds
between the floor and the bottom of the box.
If you stop pushing, the
box quickly comes to a stop.
 Sliding friction is the
force that opposes the
motion of two surfaces
sliding past each other.

Friction Type #3: Rolling Friction

As a wheel rolls over a surface, the wheel digs
into the surface, causing both the wheel and
the surface to be deformed.

Rolling friction is the frictional force between a
rolling object and the surface it rolls on.
Air Resistance
A friction-like force called air resistance
opposes the motion of objects that move
through the air.
 Air resistance, not the object’s
mass, is why feathers, leaves,
and pieces of paper fall more
slowly than pennies, acorns,
and apples.

Terminal Velocity





As an object falls, the downward force of gravity causes the
object to accelerate.
However, as an object falls faster, the upward force of air
resistance increases.
Finally, the upward air resistance
force becomes large enough to
balance the downward force of
gravity.
Then the acceleration of the
object is also zero, and the object
falls with a constant speed called
the terminal velocity.
The terminal velocity depends on
the size, shape, and mass of a falling
object.
Did We Reach Our Learning Goals
For Section 1?
1.
Define Newton’s second law of motion.

2.
Apply Newton’s second law of motion.

3.
F= ma
Describe the three different types of friction.

4.
Acceleration is produced when a force acts on a mass. The greater the
mass (of the object being accelerated) the greater the amount of force
needed (to accelerate the object).
Static friction (friction to begin moving), sliding friction (friction to keep
moving), rolling friction (friction between a rolling object and the surface
it rolls on)
Observe the effects of air resistance on falling
objects.

Air resistance is a force that acts on objects that move through the air.
Section 2: Gravity
1.
2.
3.
4.
What you will learn:
Describe the gravitational force.
Distinguish between mass and weight.
Explain why objects that are thrown will follow a
curved path.
Compare circular motion with motion in a straight
line.
Gravity

Gravity is an attractive force between any
two objects that depends on the masses of
the objects and the distance between them.

In the picture here,
gravity of the earth
is pulling the
skydivers.
Gravity Continued…


If the mass of either of the
objects increases, the
gravitational force between
them increases.
If the objects are close
together, the gravitational
force between them
increases.
Gravity- A Basic Force
Gravity is one of the 4 basic forces.
 The other forces are:




Electromagnetic force
Strong nuclear force
Weak nuclear force
The Law of Universal Gravitation


In this equation G is a constant called the universal
gravitational constant, and d is the distance between
the two masses, m1 and m2.
The law of universal gravitation enables the force of
gravity to be calculated between any two objects if
their masses and the distance between them is known.
The Range of Gravity
According to the law of universal gravitation,
the gravitational force between two masses
decreases rapidly as the distance between
the masses increases.
 No matter how far apart two objects are, the
gravitational force between them never
completely goes to zero.
 Because the gravitational force between two
objects never disappears, gravity is called a
long-range force.

Finding Other Planets


The motion of every planet in the solar
system is affected by the gravitational pulls
of all of the other planets.
In 1846 the planet Neptune was discovered
because 2 astronomers thought there must be
a planet that was affecting the motion of
Uranus (Neptune’s neighboring planet). Their
hypothesis was based on Newton’s universal
law of gravitation.
Earth’s Gravitational
Acceleration
When all forces except gravity acting on a
falling object can be ignored, the object is in
“free fall.”
 Close to Earth’s surface, the acceleration of a
falling object in free fall is about 9.8m/s2.




This acceleration is given the symbol “g” and is
called the acceleration of gravity.
Force of gravity (N) = m (kg) x acceleration of gravity (m/s2)
F= mg
Force of Earth’s Gravity Example

What is the gravitational force on a sky diver
with a mass of 60kg?



F= mg
F= (60kg)(9.8m/s2)
F= 588N
Weight
The gravitational force exerted on an object
is called the object’s weight.
 Because the weight of an object on Earth is
equal to the force of Earth’s gravity on the
object, weight can be calculated from this
equation:

Weight and Mass
Weight and mass are not the same.
 Weight is a force and mass is a measure of
the amount of matter an object contains.
 Weight and mass are related.
Weight increases as mass
increases.

WEIGHT
depends on gravity
(N)
MASS
always the same
(kg)
Weight and Mass Continued…
The table shows how various weights on Earth
would be different on the Moon and some of
the planets.
Floating in Space
When you stand on a scale you are at rest and
the net force on you is zero.
 The scale supports you and balances your
weight by exerting an upward force.
 The dial on the scale shows
the upward force exerted by
the scale, which is your
weight.

Floating in Space Continued…
Now suppose you stand on the scale in an
elevator that is falling.
 If you and the scale were in free fall, then
you no longer would push down on the scale at
all.
 The scale dial would say you
have zero weight, even
though the force of gravity
on you hasn’t changed.

Floating in Space- Space Shuttle
A
space shuttle in orbit is in free fall,
but it is falling around Earth, rather
than straight downward.
 Everything in the orbiting space shuttle
is falling around Earth at the same rate,
in the same way you and the scale were
falling in the elevator.
 Objects in the shuttle seem to be
floating because they are all falling with
the same acceleration.
Projectile Motion
How would you aim the arrow if you wanted to
hit the center of the target?
 Earth’s gravity causes
projectiles to follow a
curved path.

Horizontal and Vertical Motions
Gravity exerts an unbalanced force on the
ball, changing the direction of its path from
only forward to forward and downward.
 The result of these two motions is that the
ball appears to travel in a curve.

Horizontal and Vertical Distance

What do you think?

If you were to throw a ball as hard as you could
from shoulder height in a perfectly horizontal
direction, would it take longer to reach the ground
than if you dropped a ball from the same height?


No!
Both balls travel the same
vertical distance in the same
amount of time.
Centripetal Force

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

When a ball enters a curve, even if its speed does not change, it
is accelerating because its direction is changing.
When a ball goes around a curve, the change in the direction of
the velocity is
toward the center of the
curve.
Acceleration toward the
center of a curved or circular
path is called centripetal
acceleration.
The net force exerted toward the
center of a curved path is called a
centripetal force.
Centripetal Force and Traction

Anything that moves in a circle is doing so
because a centripetal force is accelerating it
toward the center.
Gravity Can Be a Centripetal
Force

Earth’s gravity exerts a centripetal force on
the Moon that keeps it moving in a nearly
circular orbit.
Did We Reach Our Learning Goals
For Section 2?
1.
Describe the gravitational force.

2.
Distinguish between mass and weight.

3.
The weight of an object is related to its mass according to
the following equation: W=mg
Explain why objects that are thrown will follow a
curved path.

4.
The gravitational force between 2 objects depends on the
masses of the objects and the distance between them.
Projectiles follow a curved path because their horizontal
motion is constant, but gravity causes their vertical motion
to change.
Compare circular motion with motion in a straight
line.

The net force on an object moving in a circular path is the
centripetal force.
Section 3: The Third
Law of Motion
1.
2.
3.
4.
What you will learn:
State Newton’s third law of motion.
Identify action and reaction forces.
Calculate momentum.
Recognize when momentum is conserved.
Newton’s Third Law

Newton’s third law of motion describes
action-reaction pairs this way. When one
object exerts a force on a second object, the
second one exerts a force on the first that is
equal in strength and opposite in direction.

The wings of a bird push air downwards.
Since forces result from mutual
interactions, the air must also be
pushing the bird upwards.
Action and Reaction

When a force is applied in nature, a reaction
force occurs at the same time.


When you jump on a trampoline, for example, you
exert a downward force on
the trampoline.
Simultaneously, the
trampoline exerts an equal
force upward, sending you
high into the air.
Action and Reaction Forces Don’t
Cancel

For example, a swimmer “acts” on the water,
the “reaction” of the water pushes the
swimmer forward.


Thus, a net force, or unbalanced force, acts on the
swimmer so a change in his or her motion occurs.
So, even though
the forces are equal,
they are not balanced
because they act on
different objects.
Rocket Propulsion
In a rocket engine, burning fuel produces hot
gases. The rocket engine exerts a force on
these gases and causes them to escape out
the back of the rocket.
 By Newton’s third law, the gases exert a
force on the rocket and push it forward.

Momentum
A moving object has a property called
momentum that is related to how much force
is needed to change its motion.
 The momentum of an object is the product of
its mass and velocity.

Momentum Continued…


Momentum is given the symbol p and can be
calculated with the following equation:
The unit for momentum is kg · m/s. Notice
that momentum has a direction because
velocity has a direction.
Momentum Practice Problem #1

At the end of a race, a sprinter with a mass
of 80.0kg has a speed of 10.0m/s. What is
the sprinter’s momentum?



Use the momentum equation: p= mv
p= (80.0kg)(10.0m/s) =
800kg m/s
Momentum Practice Problem #2

What is the momentum of a car with a mass
of 1,300kg traveling at a speed of 28m/s?



p= mv
p= (1,300kg)(28m/s) =
36,400kg m/s
Momentum Practice Problem #3

A baseball has a momentum of 6.0kg x m/s.
If the mass of the baseball is 0.15kg, what is
the baseballs speed?
p= mv
 v= p
m
v= (6.0kg x m/s) = 40m/s
0.15kg

Momentum Practice Problem #4

What is the mass of a person walking at a
speed of 0.8m/s if the person’s momentum is
52.0kg x m/s?



p= mv
m= p
v
m= (52.0kg x m/s) = 65kg
0.8m/s
Force and Changing Momentum

Recall that acceleration is the difference
between the initial and final velocity, divided
by the time.


a= vf – vi
t
Also, from Newton’s second law, the net force
on an object equals its mass times its
acceleration.

F= ma
Force and Changing Momentum
Continued…


By combining these two relationships,
Newton’s third law can be written in this way:
In this equation mvf is the final momentum
and mvi is the initial momentum.
The Law of Conservation of
Momentum
The momentum of an object doesn’t change
unless its mass, velocity, or both change.
 Momentum, however, can be transferred from
one object to another.
 The law of conservation of momentum states
that if a group of objects exerts forces only
on each other, their total momentum doesn’t
change.

When Objects Collide

The results of a collision depend on the
momentum of each object.
Did We Reach Our Learning Goals
For Section 3?
1.
State Newton’s third law of motion.

2.
Identify action and reaction forces.

3.
Action and reaction forces act on different objects.
Calculate momentum.

4.
For every action force, there is an equal and opposite
reaction force.
p= mv
Recognize when momentum is conserved.

If objects exert forces only on each other, their total
momentum is conserved. In a collision, momentum is
transferred from one object to another.