Forces and Motion

In Ancient Times, around 400 BC, a
philosopher named Aristotle, thought that
the rate objects fell depended on their mass.
 Example: he thought a baseball would fall faster
than a marble

In the late 1500’s a young Italian
scientist named Galileo Galilei
questioned this idea.
 He thought that the mass of an object did
not matter.
 To prove this, he dropped two different
cannonballs off of the Leaning Tower of
Pisa in Italy 

Acceleration depends on both force and mass

A heavier object experiences a greater
gravitational force than a lighter object does

But a heavier object is also harder to accelerate
because it has more mass

The extra mass of the heavier object exactly
balances the additional gravitational force so
they fall at the same rate

Acceleration is the rate at which velocity
changes over time

All objects accelerate toward Earth at a rate
of 9.8 m/s2.
 So for every second an object falls, the object’s
downward velocity increases by 9.8m/s

You can calculate the change in velocity (∆v) of a
falling object by using the following equation:

∆v = g × t
 In this equation, g is the acceleration due to gravity on
Earth (9.8 m/s2)
 t is the time the object takes to fall (in seconds)
 The change in velocity is the difference between the final
velocity and the starting velocity
A stone at rest is dropped from a cliff, and the
stone hits the ground after a time of 3
seconds. What is the stone’s velocity when it
hit the ground?
∆v = g × t
= 9.8 m/s2 × 3 s
= 29.4 m/s

To rearrange the equation to find time, divide
by the acceleration due to gravity:
t = ∆v
g

A penny at rest is dropped from the top of a
tall stairwell. What is the penny’s velocity
after it has fallen for 2 seconds?

The same penny hits the ground in 4.5
seconds. What is the penny’s velocity as it
hits the ground?

A marble at rest is dropped from a tall
building. The marble hits the ground with a
velocity of 98 m/s. How long was the marble
in the air?

An acorn at rest falls from an oak tree. The
acorn hits the ground with a velocity of 14.7
m/s. How long did it take the acorn to land?

Air resistance: the
force that opposes
the motion of objects
through air
 Amount depends on
size, shape, and speed
of object
 As speed increases, air
resistance increases
until it is equal to the
downward force of
gravity

Terminal Velocity: the constant velocity of a
falling object when the force of air resistance
is equal in magnitude and opposite in
direction to the force of gravity
http://www.youtube.com/wa
tch?v=1ukf2vntU44

Free Fall: the motion of a body of
when only the force of gravity is
acting on the body
 Can only occur if there is NO AIR!!!!!
 This is only in space and in a vacuum.
 Astronauts are not weightless, but
they are in Free Fall due to the lack of
air

Orbiting: when an object is traveling around
another object in space. (See figure 7 on
page 40)

Centripetal Force: The unbalanced force that
causes objects to move in a circular path
 Gravity provides the centripetal force that keeps
objects in orbit
http://www.youtube.com/watch?v=yyDRI6iQ9Fw

Has Two components:
1. Horizontal motion – parallel to the ground
2. Vertical motion – perpendicular to the ground

These components are independent of one
another, so they have no effect on each other

When the two motions are combined, they
form a curved path
Examples of projectile motion:

Frog leaping

Water sprayed by a sprinkler

Arrow shot by an archer

Newton’s First Law of Motion  An object
at rest remains at rest, and an object in
motion remains in motion as a constant
speed and in a straight line unless acted upon
by an outside force

An object at rest is not moving. These
objects will not move until a push or pull is
exerted on them.

A moving object stops eventually because of
the opposing force of friction.

Inertia: the tendency of an object to resist
being moved or, if the object is moving, to
resist a change in speed or direction until an
outside force acts on the object
 Newton’s First Law is sometimes called the Law of
Inertia.
 Mass is a measure of inertia

Newton’s Second Law of Motion  The
acceleration of an object depends on the mass of
the object and the amount of force applied

Acceleration depends on Mass: the acceleration
of an object decreases as its mass increases and
vice versa

Acceleration Depends on Force: acceleration
increases as the force of the object increases and
vice versa; acceleration of an object is always in
the same direction as the force applied
a = F/m
Or
F = ma

What is the acceleration of a 3 kg mass if a
force of 14.4 N is used to move the mass?
(Note: 1 N is equal to 1 kg · m/s2)

a = F/m
Replace F and m with the values given in the
problem, and solve
a = 14.4/3 = 4.8 m/s2



What is the acceleration of a 7 kg mass if a
force of 68.6 N is used to move it toward
Earth?

What force is necessary to accelerate a 1,250
kg car at a rate of 40 m/s2?

Zookeepers carry a stretcher that holds a
sleeping lion. The total mass of the lion and
the stretcher is 175 kg. The lion’s forward
acceleration is 2 m/s2. What is the force
necessary to produce this acceleration?

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.

Simply stated, all forces act in pairs; they are action
and reaction forces.

Example: You sit on a chair. Your weight pushing
down on the chair is an action force. The reaction
force is the force exerted by the chair that pushes up
on your body. The force is equal to your weight.

These forces do not always equal though or nothing
would ever move!!

When the action and reaction forces are unbalanced,
there is movement.

Momentum: a quantity defined as the
product of the mass and velocity of an object
 The more momentum an object has the harder it
is to stop the object or change its direction
http://www.pbs.org/opb/circus/classroom/circusphysics/activity-guide-linear-momentum/

Calculating momentum (p):

p = mv
 m = the mass of the object in kilograms
 v = the object’s velocity in meters per second
 units of momentum will be kg∙m/s

What is the momentum of an ostrich with a
mass of 120 kg that runs with a velocity of 16 m/s
north?

Write the equation: p = mv

Replace the m and v with the values given in the
problem and solve:

p = 120 x 16

p = 1,920 kg· m/s north

What is the momentum of a 6 kg bowling ball
that is moving at 10 m/s down the alley
toward the pins?

An 85 kg man is jogging with a velocity of 2.6
m/s to the north. Nearby, a 65 kg person is
skateboarding and is traveling with a velocity
of 3 m/s north. Which person has a greater
momentum? Show your calculations.

Like velocity, momentum has a direction and
its direction is always the same as the
direction of the object’s velocity

The Law of Conservation of Momentum:
states that any time objects collide, the total
amount of momentum stays the same
 is true for any collision if no other forces act on the
colliding objects
 law applies whether the objects stick together or
bounce off each other after they collide

Objects sticking together:
 after objects stick together they move together as
one object (like a dog catching a ball)
 the mass of the combined objects is equal to the
masses of the two objects added together
 When mass changes, velocity must change also

Objects Bouncing off Each other:
 Momentum is usually transferred from one object
to another
 The transfer causes the objects to move in
different directions at different speeds; however
the total momentum of all the objects will remain
the same before and after the collision

When action and reaction forces are equal
and opposite, momentum is neither gained
nor lost.