Forces and Motion
Chapter 3
By Mr. Leavings
And just what are we going
to LEARN?
 Explain the meaning of Force
Show how force is required to change the motion of an
object
 Explain and discuss Newton’s three laws, the first
dealing with inertia, the second with force, third with
equal but opposite reactions
Describe how changing the mass of a car affects its
acceleration
 Demonstrate how friction can affect motion
 Identify action-reaction pairs of forces
Force, Mass and Acceleration
Physics Teacher: "Isaac Newton was sitting
under a tree when an apple fell on his head
and he discovered gravity. Isn't that
wonderful?"
Student: "Yes sir, if he had been sitting in
class looking at books like us, he wouldn't
have discovered anything."
THE LAWS
Law
1st
2nd
3rd
Statement
In your own
words:
An object at rest will remain at
rest unless acted on by an
unbalanced force. An object in
motion will continue with constant
speed and direction, unless acted
on by an unbalanced force.
Objects keep doing what
they are doing unless
something intervenes.
The acceleration of an object is
directly proportional to the force
acting on it and inversely
proportional to its mass.
If net force, then
acceleration. Heavier
objects are harder to
move.
Whenever one object exerts a
force on another, the second
object exerts an equal and
opposite force on the first.
Action, reaction.
Force, Mass and Acceleration
If I asked you to move a cart containing a
large, heavy box, would you:
a) Push it
b) Pull it
c) Yell at it till it went where you wanted
Every object continues at a state of rest,
or of motion, unless a FORCE is applied to
change the system.
Force, Mass and Acceleration
Force: an action that has the ability to change
motion.
Force is described in two units:
Pounds and Newtons (there are 4.448 Newtons
in 1 pound)
Newton = 1 kg x m
sec2
Newton’s 1st Law
An object at rest will remain at rest unless
acted on by an unbalanced force. An
object in motion will continue with
constant speed and direction, unless
acted on by an unbalanced force.
Newton’s 1st Law
Demo: Ring and the
Flask
 Challenge: get the
object into the
flask.
 Rules: Only touch
the hoop. Quickest
time wins.

Newton’s 1st Law

Force
◦ Any action that has the ability to change
motion.
◦ i.e. a push or pull
◦ Forces don’t always change motion
◦ Units of force: pounds, newtons
 1lb = 4.448 N
Newton’s 1st Law
The Difference Between Force and Mass
◦ force: newtons
◦ mass: grams, kilograms
 Force is a push or pull
 Mass is the amount of “stuff” in an
object.
 Mass is the same everywhere in the
universe, force depends on what is acting
on the mass.

Newton’s 1st Law

Inertia is the
tendency of an
object to resist
changes in its
velocity: whether
in motion or
motionless.
These pumpkins will not move unless
acted on by an unbalanced force.
Newton’s 2nd Law
Newton's second law relates to the
applied force on an object.
The acceleration of an object is
directly proportional force acting
upon it and inversely proportional to
the mass of the object.
Newton’s 2nd Law
Newton’s 2nd Law
It says that:
• Force causes acceleration
• Mass resists acceleration
• The acceleration you get
is equal to the ratio of
force over mass
Newton’s 2nd Law
Form of Newton’s
second law
If you want to
know…
And you know….
a = F/m
the acceleration (a)
the mass (m) and force
(F)
F = ma
the force (F)
the mass (m) and the
acceleration (a)
m = F/a
the mass (m)
the force (F) and the
mass (m)
Newton’s 2nd Law
An example:
A car rolls down a ramp and you measure
a force of 2 Newtons pulling the car. The
car has a mass of 500 g (0.5kg). Calculate
the acceleration of the car.
What do we Know?
M = 0.5 kg
F=2N
A=?
Newton’s 2nd Law
Another example:
An airplane with a mass of 5000 kg needs
to accelerate at 5 m/s2 to take off before
it reaches the end of its runway. How much
force is needed from the engine?
What do we Know?
M = 5000 kg
F=?
A = 5 m/s2
Newton’s 2nd Law
Even another example:
An snail slimes along with a force of 0.05
Newtons (N). If its acceleration is 0.1
m/s2, what is the mass of the slug?
What do we Know?
M=?
F = 0.05 N
A = 0.1 m/s2
Balanced and Unbalanced
Forces
Net Force: The motion of an object depends
on the total of all forces acting on it.
To figure out Net Force we have to
assign directions for forces to be either
positive or negative.
Positive
Negative
Balanced and Unbalanced
Forces
Positive
500 N
Positive
490 N
Negative
10 N
The above forces are
not in equilibrium and
the car moves forward.
If the forces were
equal the car would not
move.
Balanced and Unbalanced
Forces
example:
An person is pushing on a car to keep it from
moving with a force of 3 N. The car has a mass of
500 kg. The driver steps on the gas causing the
car to accelerate at 2 m/s2. What happens?
What do we Know?
Fn = 3 N
Fp = ?
M = 500 kg
A = 2 m/s2
Positive ?
Negative
3N
Balanced and Unbalanced
Forces
Newton’s 2nd Law is really describing the
NET FORCE. Acceleration can only
happen if the net force is not zero.
Balanced and Unbalanced
Forces
Force Diagrams show all the different
forces acting on an object.
 They can also show magnitudes by changing
the arrow size, or by including numbers.

FN
FG
Balanced and Unbalanced
Forces
Force of Gravity (FG): Pulls an object
straight down
 Normal Force (FN): Force on an object
from support (like a table) that is
perpendicular to the support

FN
FG
Balanced and Unbalanced
Forces
Force of Friction (Ff): Force that acts
against another force if there is motion.
 Tension Force (FT): Force acting on an
object if it is suspended from something.
 Applied Force (Fapp): Any force acting on
an object other than those already
mentioned.

Balanced and Unbalanced
Forces
This diagram shows
four forces acting
upon an object.
There aren’t always
four forces, For
example, there could
be one, two, or three
forces.
Ff
FN
FG
Fapp
Balanced and Unbalanced
Forces
A man drags with his daughter inside
with a rightward acceleration. Draw a
force diagram of the sled.
FN
Ff
Fapp
FG
Balanced and Unbalanced
Forces
A spider is hanging from its thread in a tree.
Draw the force diagram for the spider.
FT
FG
The tensile force (FT)
of the thread is
exerting a force on
the spider upwards –
this keeps it in place.
Balanced and Unbalanced
Forces
On a flat, horizontal plane, the force of
gravity always equals the normal force.
FN = 50 N
FNet = 0 N
FG = 50 N
Balanced and Unbalanced
Forces
A cupcake is being pulled along a table with a
force of 25 N, and a frictional force of 10
N. What is the overall motion?
FN = 50 N
Fapp = 25 N
No motion up or down.
Motion to left.
Ff = 10 N
FG = 50 N
Weight and Gravity
Gravity: a force that pulls every mass
toward every other mass.
Since Earth is the
biggest mass around,
gravity pulls everything
toward the center of
the earth.
Weight and Gravity
Gravity depends on mass!
The force of gravity depends on how
much mass you have. If you have more
mass, gravity pulls on you with more
force.
Fw
<
Fw
Weight and Gravity
On earth the force due to
gravity is 9.8 Newtons.
Notice this number is the
same as accel due to
gravity fro 1 kg!
On Mars that force is
adjusted lower since that
planet is smaller and the
force due to gravity is only
3.8 Newtons. BUT YOUR
MASS REMAINS THE
SAME!
Weight and Gravity
Weight: force created by gravity on
objects.
Mass (kg)
Fw = mg
Weight Force
(N)
Acceleration due
to gravity (9.8
m/s2)
Weight and Gravity
Form of Weight
equation to use
If you want to
know…
And you know….
Fw = mg
the weight (Fw)
the mass (m) and
gravity (g)
m = Fw/g
the mass (m)
the weight (Fw) and
the gravity (g)
g = Fw/m
the gravity (g)
the weight (Fw) and
the mass (m)
Weight and Gravity
Lets do an example:
around 1587 Galileo
dropped two balls from
the leaning tower of
Pisa to see which would
fall faster.
a. Calculate the weight
of each ball
b. Calculate the
acceleration of each
ball’s fall
Ball 1:
1kg
Part a)
Fw1 = mg = (1kg)(9.8m/s2)
Fw1 = 9.8 N
Fw2 = mg = (5kg)(9.8m/s2)
Fw2 = 49 N
Part b)
A1 = Fw1/m = (9.8N)/1kg
A1 = 9.8 m/s2
A2 = Fw2/m = (49N)/5kg
A1 = 9.8 m/s2
Ball 2:
5kg
Weight and Gravity
Lets do another example:
An elephant is sitting in a Zoo (on earth), it has
a mass of 5400 kg. What is the Normal force
that is acting upon the elephant?
What do we know?
M = 5400kg
G = 9.8 m/s2
Fw = ?
FN
Fw = (5400kg)x(9.8 m/s2)
Fw = 52,920 N
Fw = Fg = Fn
FG
Law of Universal Gravitation
Why does the Moon orbit the
earth?
The same gravity that
gives you weight is what holds
Earth and the Moon together.
If you could simply drop the
Moon it would fall to earth,
this does not happen because
the Moon is moving fast in a
direction perpendicular to
Earth’s gravity. The force of
gravity bends the Moons path
toward the Earth giving it a
nearly circular orbit.
Law of Universal Gravitation
Law of Universal Gravitation: a force of
attraction that exists between any two objects
that have mass.
Mass 2
Mass 1
Force
of
Gravity
F= G
Gravitation constant:
6.67 x 10-11 Nm2/kg2
m1 m2
_________
d2
Distance between
mass 1 and mass 2
Law of Universal Gravitation
Example:
The mass of Jupiter's third largest
moon, Io, is 8.9 x 1022 kg. The radius of
Io is 1,815 km. Use the equation for
universal gravitation to calculate your
weight if you were on the surface of Io
and had a mass of 50 kg.
Law of Universal Gravitation
m1 m2
_________
F= G
F=
d2
-11Nm2/kg2)(8.9x1022kg)(50kg)
(6.67x
10
____________________________
(1,815,000m)2
F = 90.1N
Friction
What is friction?
Term used to describe forces that result
from relative motion between objects (like
the wheel and axel of a car)
Frictional forces ALWAYS work against the
motion that produces them.
Friction
Kinds of Friction
Air Friction: The air moving around
moving objects creates an opposing force.
Sliding Friction: When two surfaces rub
against each other, caused by
irregularities in the surfaces
Viscous Friction: Objects that move in
water or other fluids.
Rolling Friction: Caused by one object
rolling over another, like car tires on a
road.
Friction
Remember our Net Force
diagrams? We have already seen
friction in action.
Fapp = 25 N
Fnet = 15 N
to the left
Ff = 10 N
Sliding Friction!
Momentum Defined
p = mv
p = momentum
m = mass
v = velocity
Momentum of a Bus
Bus: m = 9000 kg; v = 100 m /s
Calculate the momentum of the bus.
What is known?
m = 9000 kg
v = 100 m/s
What is missing?
momentum  p = ?
Equation
p = m·v
Solve
p = (9000 kg)(100 m/s) = 900,000 kg·m/s
Conservation of Momentum
Momentum in a system is ALWAYS
conserved.
 The total momentum two or more
objects have prior to a collision is equal
to the total momentum after the
collision.

Conservation of Momentum
The total momentum of the objects is the same before and after the collision.
Positive is defined as the right direction.
before:
pT
= m1 v1 - m2 v2
v2
v1
m1
m2
m1 v1 - m2 v2 = - m1 va + m2 vb
after:
pT
= - m1 va + m2 vb
va
vb
m1
m2
Directions after a collision
Some collisions cause the objects to go in opposite directions.
Other collisions cause the objects to go in similar directions.
v1
m1
v2
m2
m1
va
vb
m2
Elastic vs. Inelastic
Elastic collisions occur when the object “bounce” off each other and no energy is lost
to changes in shape.
Inelastic collision occur when the objects get “stuck” to each other, or energy is lost
to changes in shape.
v1
m1
v2
m2
vb
m1
m2
Sample Problem
35 g
7 kg
700 m/s
v=0
A rifle fires a bullet into a giant slab of butter on a frictionless surface. The bullet
penetrates the butter, but while passing through it, the bullet pushes the butter to
the left, and the butter pushes the bullet just as hard to the right, slowing the bullet
down. If the butter skids off at 4 cm/s after the bullet passes through it, what is the
final speed of the bullet?
(The mass of the rifle matters not.)
35 g
v=?
4 cm/s
7 kg
continued on next slide
Sample Problem
(cont.)
Let’s choose left to be the + direction & use conservation of momentum, converting all
units to meters and kilograms.
35 g
p before = 7 (0) + (0.035) (700)
7 kg
= 24.5 kg · m /s
v=0
35 g
v=?
p before = p after
v
700 m/s
4 cm/s
7 kg
24.5 = 0.28 + 0.035 v
p after = 7 (0.04) + 0.035 v
= 0.28 + 0.035 v
v = 692 m/s
came out positive. This means we chose the correct direction of the
bullet in the “after” picture.
Sample Problem
35 g
7 kg
700 m/s
v=0
Same as the last problem except this time it’s a block of wood rather than butter,
and the bullet does not pass all the way through it. How fast do they move
together after impact?
v
7. 035 kg
(0.035) (700) = 7.035 v
v = 3.48 m/s
Note: Once again we’re assuming a frictionless surface, otherwise there would be
a frictional force on the wood in addition to that of the bullet, and the “system”
would have to include the table as well.