Unit 3: Forces
EQ: How do forces affect motion?
The Meaning of Force
• Force: a push or pull upon an object resulting
from the object’s interaction with another
object.
• Force is a vector quantity.
• For simplicity sake, all forces (interactions)
between objects can be placed into two
categories:
– Contact Forces
– Action-at-a Distance Forces
• Contact Forces: those types of forces that result
when two interacting objects are perceived to be
physically contacting each other.
• Action-at-a-Distance Forces: those types of forces
that result even when the two interacting objects are
not in physical contact with each other, yet are able
to exert a push or pull despite their physical
separation.
• Newton: the amount of force required to give a 1-kg
mass an acceleration of 1 m/s2. The standard unit of
measurement for force.
1 Newton (N) = 1 kg ∙ m/s2
Types of Forces
Contact Forces
Action-at-a-Distance Forces
• Frictional Force
• Gravitational Force
• Tension Force
• Electrical Force
• Normal Force
• Magnetic Force
• Air Resistance Force
• Applied Force
• Spring Force
Type of Force
Applied Force
Description
A force that is applied to an object by a person or
another object.
Symbol
Fapp
Fgrav
= mg
m= mass in kg
g= 9.8 N/kg
Gravitational Force
The force with which the earth, moon, or other
massively large object attracts another object
towards itself. Gravity is directed downward toward
the center of the earth. The weight of an object.
Normal Force
The support force exerted upon an object that is in
contact with another stable object. (Ex. Book on a
desk)
Fnorm
Friction Force
The force exerted by a surface as an object moves
across it or makes an effort to move across it.
(Sliding, static)
Ffrict
Air Resistance Force
A special type of force that acts upon objects as they
travel through the air. It opposes the motion of the
object.
Fair
Tension Force
The force that is transmitted through a string, rope,
cable or wire when it is pulled tight by forces acting
from opposite ends. (Tug-of-War)
Ftens
Spring Force
The force exerted by a compressed or stretched
spring upon any object that is attached to it.
Fspring
Types of Friction
1) Sliding Friction: results when an object slides
across a surface. (Ex: pushing a box across a
floor)
2) Static Friction: results when the surfaces of two
objects are at rest relative to one another and a
force exists on one of the objects to set it into
motion relative to the other object. (Ex: pushing
a couch across a carpeted floor - what you must
overcome in order to get the couch to move)
3) Fluid Friction: results when a solid object
moves through a fluid. (Ex: bird flying
through the air, fish moving through water)
4) Rolling Friction: results when an object rolls
across a surface. (Ex: bicycle wheel rolling
over the road)
Mass vs. Weight
• The force of gravity acting upon an object is
sometimes referred to as the weight of the
object. It is related to the pull of gravity on
the object and is altered by location.
• The mass of an object refers to the amount of
matter that is contained by the object. Mass is
never altered by location, the pull of gravity,
speed, or even the existence of other forces.
Check Your Understanding
1) Different masses are hung on a spring scale calibrated in
Newtons. (Fgrav = mg)
a) The force exerted by gravity on 1 kg = 9.8N.
b) The force exerted by gravity on 5 kg = _____N.
c) The force exerted by gravity on _____kg = 98N.
d) The force exerted by gravity on 70 kg = _____N.
2) When a person diets, is their goal to lose mass or to lose
weight? Explain.
Drawing Free-Body Diagrams
• Free-Body Diagrams: diagrams used to show
the relative magnitude and direction of all
forces acting upon an object in a given
situation.
• The size of the arrow in a free-body diagram
reflects the magnitude of the force while the
tip of the arrow shows the direction that the
force is acting.
Fnorm
Ffrict
Fapp
Fgrav
Guided Practice
1) A book is at rest on a tabletop. Diagram the forces
acting on the book.
2) A girl is suspended motionless from the ceiling by two
ropes. Diagram the forces acting on the combination of
girl and bar.
3) An egg is free-falling from a nest in a tree. Neglect air
resistance. Diagram the forces acting on the egg as it is
falling.
4) A flying squirrel is gliding (no wing flaps) from a tree to
the ground at constant velocity. Consider air resistance.
Diagram the forces acting on the squirrel.
Graded Practice
1) A rightward force is applied to a book in order to move
it across a desk with a rightward acceleration. Consider
frictional forces. Neglect air resistance. Diagram the
forces acting on the book.
2) A rightward force is applied to a book in order to move
it across a desk at constant velocity. Consider frictional
forces. Neglect air resistance. Diagram the forces acting
on the book.
3) A college student rests a backpack upon his shoulder.
The pack is suspended motionless by one strap from
one shoulder. Diagram the vertical forces acting on the
backpack.
4) A skydiver is descending with a constant velocity.
Consider air resistance. Diagram the forces acting
upon the skydiver.
5) A force is applied to the right to drag a sled across
loosely packed snow with a rightward acceleration.
Neglect air resistance. Diagram the forces acting on
the sled.
6) A football is moving upwards towards its peak after
having been booted by the punter. Neglect air
resistance. Diagram the forces acting upon the
football as it rises upward towards its peak.
7) A car is coasting to the right and slowing down.
Neglect air resistance. Diagram the forces acting
upon the car.
Determining Net Force
• Net Force: the vector sum of all the forces
that act upon an object.
5
5
+
= 10
5
-5
+
=0
5
10
15
+
=
-10
5
-5
+
=
-10
5
-15
+
=
10
+
-5
=
5
Guided Practice
1200 N
50 N
600 N
20 N
50 N
800 N
800 N
Fnet = 400N up
Fnet = 200N down
Fnet = 20N left
Does a Net Force Exist?
Graded Practice 1
3N
3N
5N
5N
A
3N
5N
B
3N
40N
20N
C
D
20N
25N
Graded Practice 2
300N
B
Fnet = 0 N
Fnet = 60N, left
A
50N
80N
200N
D
E
F
C
20N
G
Fnet = 900N, up
200N
H
Fnet = 30N, right
Forces Practice Worksheet 1
Design an Experiment Activity
Formative Assessment 1
Sir Isaac Newton Biography
https://www.youtube.com/watc
h?v=YPRV1h3CGQk
Newton’s First Law of Motion
• Isaac Newton, a 17th century scientist, put forth a
variety of laws that explain why objects move (or
don’t move) as they do.
• These laws are known as Newton’s Three Laws of
Motion.
• Newton’s First Law of Motion: an object at rest stays
at rest and an object in motion stays in motion with
the same speed and in the same direction unless
acted upon by an unbalanced force.
• Sometimes referred to as the law of inertia.
Forces are Balanced
Objects at Rest
Objects in Motion
(v = 0 m/s)
(v ≠ 0 m/s)
a = 0 m/s2
a = 0 m/s2
Stay in Motion
Stay at Rest
(same speed and
direction)
Balanced vs. Unbalanced Forces
• Balanced Forces: Equal in magnitude,
opposite in direction. Also known as
equilibrium.
• Unbalanced Forces: Forces not in equilibrium.
• Inertia: the resistance to a change in motion.
• Everyday Examples of Newton’s First Law:
1) A car stopping suddenly. The force of the road on
the locked wheels provides the unbalanced force to
change the car’s state of motion, yet there is no
unbalanced force to change your own state of
motion. Thus, you continue in motion, sliding along
the seat in forward motion. What stops you from
continuing through the windshield?
• Your seat belt!
• The seat belt provides the unbalanced force that
brings you from a state of motion to a state of
rest.
2) Blood rushes from your head to your feet while
quickly stopping when riding on a descending
elevator.
3) A brick is painlessly broken over the hand of a
physics teacher by slamming it with a hammer.
(Don’t try this at home!)
4) To dislodge ketchup from the bottom of the
ketchup bottle, it is often turned upside down and
thrusted downward at high speeds and then
abruptly halted.
5) Headrests are placed in cars to prevent whiplash
injuries during rear-end collisions.
6) While riding a skateboard (or wagon or bicycle),
you fly forward off the board when hitting a curb or
rock or other object that abruptly halts the motion
of the skateboard.
Inertia and Mass
• Before Newton, it was believed that it was the
natural tendency of an object to come to rest.
Eventually moving objects would stop moving; a
force was necessary to keep an object in motion.
• Galileo, a premier scientist in the 17th century,
developed the concept of inertia. He reasoned that
moving objects eventually stop because of a force
called friction. In experiments using a pair of inclined
planes facing each other, Galileo observed that a ball
would roll down one plane and up the opposite
plane to approximately the same height. If smoother
planes were used, the ball would roll up the
opposite plane even closer to the original height.
• Galileo reasoned that any difference between
initial and final heights was due to the presence
of friction. He postulated that if friction could be
entirely eliminated, then the ball would reach
exactly the same height each time.
• He further observed that regardless of the angle
in which the planes were oriented, the final
height was almost always equal to the initial
height.
• If the opposite incline were elevated at nearly a
0-degree angle, then the ball would roll almost
forever in an effort to reach the original height.
• Isaac Newton built on Galileo’s thoughts
about motion. His first law declares that a
force is not needed to keep an object in
motion, rather one is needed to get it to stop.
• In the absence of friction, an object would
continue in motion with the same speed and
direction – forever!
• All objects resist change in motion – but some
have more of a tendency to resist change
more than others.
• The tendency of an object to resist changes in
its state of motion varies with mass.
• The more mass an object has, the more inertia
it has.
• https://www.youtube.com/watch?v=T1ux9D7
-O38
Check Your Understanding
1) Imagine a place in the cosmos far from all
gravitational and frictional influences.
Suppose that you could visit that place and
throw a rock. The rock will
a) gradually stop
b) continue in motion in the same
direction at constant speed
2) A 2-kg object is moving horizontally with a
speed of 4 m/s. How much net force is
required to keep the object moving at this
speed and in this direction?
3) Mac and Tosh are arguing in the cafeteria.
Mac says that if he flings the Jell-O with a
greater speed it will have a greater inertia.
Tosh argues that inertia does not depend
upon speed, but rather upon mass. Who do
you agree with?
4) Supposing you were in space in a weightless
environment, would it require a force to set
an object in motion?
5) Fred spends most Sunday afternoons at rest on
the sofa, watching pro football games and
consuming large quantities of food. What affect
(if any) does this practice have upon his inertia?
Explain.
6) Ben Tooclose is being chased through the woods
by a bull moose that he was attempting to
photograph. The enormous mass of the bull
moose is intimidating. Yet, if Ben makes a zigzag
pattern through the woods, he will be able to
use the large mass of the moose to his own
advantage. Explain this in terms of inertia and
Newton’s first law of motion.
7) Two bricks are resting on the edge of the lab
table. Shirley Sheshort stands on her toes
and spots the two bricks. She acquires an
intense desire to know which of the two
bricks is most massive. Since Shirley is
vertically challenged, she is unable to reach
high enough to lift the bricks, she can
however reach high enough to give the bricks
a push. Discuss how the process of pushing
the bricks will allow Shirley to determine
which of the two bricks is most massive.
What difference will Shirley observe and how
can this observation lead to the necessary
conclusion?
Answers
1) B
2) 0-N An object in motion will remain in motion unless acted
upon by an unbalanced force.
3) Tosh. Inertia depends solely on mass.
4) Yes! Even in space, an object has mass which means it has
inertia. A force must be used to set an object in motion.
5) If Fred continues this habit, his mass will increase thus
causing his inertia to increase.
6) The moose has a large mass which means it has a large
inertia. This large inertia requires more force to change the
moose’s state of motion.
7) The brick with the greater mass will have more resistance to
motion and will require a larger force to set into motion.
Newton’s Second Law of Motion
• According to Newton, an object will only
accelerate if there is a net or unbalanced force
acting upon it.
• The presence of an unbalanced force will
accelerate an object – changing its speed, its
direction, or both.
• Newton’s second law of motion pertains to
the behavior of objects for which all existing
forces are not balanced.
• Newton’s Second Law of Motion: The
acceleration of an object as produced by a net
force is directly proportional to the magnitude
of the net force, in the same direction as the
net force, and inversely proportional to the
mass of the object.
a = Fnet ÷ m
• The above equation is often rearranged to a
more familiar form:
Fnet = ma
• As the force acting upon an object is
increased, the acceleration of the object is
increased.
• As the mass of an object is increased, the
acceleration of the object is decreased.
• The acceleration is directly proportional to the
net force; the net force equals mass times
acceleration; the acceleration is in the same
direction as the net force; an acceleration is
produced by a net force.
• So, what am I trying to get across?
• It is not just any ole force that is used in the
equation, it is the NET FORCE!
• Reminder: The net force is the vector sum of
all the forces acting upon an object.
Practice
Net Force (N)
Mass (kg)
10
2
20
2
20
4
2
10
Acceleration (m/s2)
5
10
• The numerical information in the preceding table
demonstrates some important qualitative
relationships between force, mass, and acceleration.
• Comparing the values in rows 1 and 2, it can be seen
that a doubling of the net force results in a doubling
of the acceleration (if mass is held constant).
• Comparing the values in rows 2 and3, it can be seen
that a doubling of the mass results in a halving of the
acceleration (if the force is held constant).
• The direction of the net force is in the same direction
as the acceleration.
Check Your Understanding
1) Determine the accelerations that result when a 12N
net force is applied to a 3 kg object then to a 6 kg
object.
2) A net force of 15N is exerted on an encyclopedia to
cause it to accelerate at a rate of 5 m/s2. Determine
the mass of the encyclopedia.
3) Suppose that a sled is accelerating at a rate of 2 m/s2.
If the net force is tripled and the mass is doubled,
then what is the new acceleration of the sled?
4) Suppose that a sled is accelerating at a rate of 2 m/s2.
If the net force is tripled and the mass is halved, then
what is the new acceleration of the sled?
Answers
1)
2)
3)
4)
4 m/s2; 2 m/s2
3.0 kg
3 m/s2
12 m/s2
Motion Misconceptions
• Sustaining motion requires a force.
• Two students are discussing their physics
homework prior to class. They are discussing
an object that is being acted upon by two
individual forces (both in a vertical direction);
the free-body diagram for the particular
object is shown below.
F
= 20N
norm
Fgrav = 20N
• During the discussion, Anna Litical suggests to
Noah Formula that the object under
discussion could be moving. In fact, Anna
suggests that if friction and air resistance
could be ignored, the object could be moving
in a horizontal direction.
• Noah objects, arguing that the object could
not have any horizontal motion if there are
only vertical forces acting upon it. Noah claims
that the object must be at rest, perhaps on a
table or floor. After all, says Noah, an object
experiencing a balance of forces will be at
rest. Who do you agree with?
Answer
• Anna is correct.
• Noah Formula may know his formulas but he
does not know (or does not believe) Newton's
laws. If the forces acting on an object are
balanced and the object is in motion, then it
will continue in motion with the same velocity.
Remember: forces do not cause motion.
Forces cause accelerations.
Finding Acceleration Guided Practice
a = Fnet/m
1) An applied force of 50N is used to accelerate an
object to the right across a frictional surface. The
object encounters 10N of friction. Use the diagram to
determine the normal force, the mass, and the
acceleration of the object. (Neglect air resistance)
Fnorm = _______
Ffrict = 10N
Fapp = 50N
Fgrav = 80N
2) An applied force of 20N is used to accelerate
an object to the right across a frictional
surface. The object encounters 10N of
friction. Use the diagram to determine the
normal force, the net force, the mass, and
the acceleration of the object. (Neglect air
resistance)
Fnorm = ________
Ffrict = 10N
Fapp = 20N
Fgrav = 100N
Guided Practice
1) Imagine you throw a baseball that weighs 0.1kg
with a force of 100N. What is the acceleration of
the baseball?
2) An arrow leaves the bow with a force of 500N. The
mass of the arrow is 250kg. What is its
acceleration?
3) A dog has a mass of 20kg. If the dog is pushed
across the ice with a force of 40N, what is its
acceleration?
Graded Practice
1) Suppose a student pushes a cart of groceries
with a 40kg mass. How much force does he use
if the cart accelerates 2.5 m/s2?
2) A bag of charcoal has a mass of 10kg. Two bags
were added to the cart of groceries mentioned
in problem 1. If the student pushes with a force
of 90N, what is the acceleration of the cart?
3) If the acceleration of the cart with the added
mass of the two bags of charcoal is increased to
2.5 m/s2, how much additional force must be
applied to the cart?
Answers
1) 100N
2) 1.5 m/s2
3) 60N
Forces Practice Worksheet 2
Answers
1) 6000N
2) 30N
3) 5000N
4) 2.5 m/s2
5) 10 m/s2
6) 2500 kg
7) 20 m/s2
8) 4N
9) 50 m/s2
10) 50 kg
Formative Assessment 2
Weight and Second Law Math Practice
Net Force Practice
Force Diagram Practice Worksheet
Terminal Velocity
• The free-body diagrams below show the forces acting
upon an 85-kg skydiver.
350N
833N
700N
833N
833N
833N
• As the skydiver falls, he picks up speed. The increase in speed
leads to an increase in the amount of air resistance.
Eventually the air resistance becomes large enough to
balance the force of gravity. At this instance, the net force
becomes 0N and the skydiver will quit accelerating. He has
reached terminal velocity.
Newton’s Third Law of Motion
• Newton’s Third Law of Motion: For every
action, there is an equal and opposite
reaction.
• Forces always come in pairs – action-reaction.
• The size of the forces are equal.
• The direction of the forces are opposite.
Examples of Interaction Force Pairs
• Fish Swimming:
A fish uses its fins to push water backwards as the
water pushes the fish forward.
• Birds Flying:
The wings of the bird push downward and the air
is pushing the bird upwards.
• Car Moving:
As the wheels of the car spin, they grip the road
and push the road backward as the road pushes
the car forward.
Check Your Understanding
1) For years, space travel was believed to be
impossible because there was nothing that
rockets could push off of in space in order to
provide the propulsion necessary to accelerate.
This inability of a rocket to provide propulsion is
because…
a) …space is void of air so the rockets have nothing to push
off of.
b) …gravity is absent in space.
c) …space is void of air and so there is no air resistance in
space
d) …nonsense! Rockets do accelerate in space and have
been able to do so for a long time.
2) Many people are familiar with the fact that a
rifle recoils when fired. This recoil is the result of
action-reaction force pairs. A gunpowder
explosion creates hot gases that expand
outward allowing the rifle to push forward on
the bullet. Consistent with Newton’s Third Law
of Motion, the bullet pushes backwards upon
the rifle. The acceleration of the recoiling rifle
is…
a) …greater than the acceleration of the bullet.
b) …smaller than the acceleration of the bullet.
c) …the same size as the acceleration of the bullet.
3) In the top picture, Kent Budgett is pulling upon a rope
that is attached to a wall. In the bottom picture, Kent is
pulling upon a rope that is attached to an elephant. In
each case, the force scale reads 500N. Kent is pulling…
a) …with more force when the rope is attached to the
wall.
b) …with more force when the rope is attached to the
elephant.
c) …the same force in each case.
Answers
1) Answer: D
It is a common misconception that rockets are unable
to accelerate in space. The fact is that rockets do
accelerate. There is indeed nothing for rockets to push
off of in space - at least nothing which is external to the
rocket. But that's no problem for rockets. Rockets are
able to accelerate due to the fact that they burn fuel
and push the exhaust gases in a direction opposite of
the direction which they wish to accelerate.
2) Answer: B
The force on the rifle equals the force on the bullet.
Yet, acceleration depends on both force and mass.
The bullet has a greater acceleration due to the fact
that it has a smaller mass. Remember: acceleration
and mass are inversely proportional.
3) Answer: C
Kent is pulling with 500 N of force in each case. The
rope transmits the force from Kent to the wall (or to
the elephant) and vice versa. Since the force of Kent
pulling on the wall and the wall pulling on Kent are
action-reaction force pairs, they must have equal
magnitudes. Inanimate objects such as walls can
push and pull.
Identifying Action-Reaction Forces
• Identify at least six pairs of action-reaction
pairs in the following diagram.
Answers
1) The elephant's feet push backward on the ground; the
ground pushes forward on its feet.
2) The right end of the right rope pulls leftward on the
elephant's body; its body pulls rightward on the right end
of the right rope.
3) The left end of the right rope pulls rightward on the man;
the man pulls leftward on the left end of the right rope.
4) The right end of the left rope pulls leftward on the man;
the man pulls rightward on the right end of the left rope.
5) The tractor pulls leftward on the left end of the left rope;
the left end of the left rope pulls rightward on the tractor.
6) The tractor’s wheels push backward on the ground; the
ground pushes forward on the wheels.
What Makes a Bug Go Splat?
Splat! A bug has just flown into the windshield
of an oncoming car. The car must have hit the
bug much harder than the bug hit the car,
right?
• Buzz: In order for the bug to fly through the
air, a force has to push the bug forward.
Identify this force. How does the bug produce
it? (Hint. Think back to how a swimmer moves
through the water)
Air pushes the bug forward. The bug produces
this force by pushing backward on the air with
its wings, and the reaction force is that the air
pushes forward on the bug.
• The bug was at rest on a tree when it saw the
car and decided to fly toward it. If the bug has
a mass of 0.05 kg and accelerates at 2 m/s2,
what’s the net force on the bug?
0.05 kg x 2 m/s2 = 0.1 N
• Vroom: The driver hates killing bugs. When
she saw one coming toward the windshield,
she braked suddenly and hoped it would get
out of the way. (Sadly, it did not.) When she
hit the brakes, she felt that she was thrown
forward. Use one of Newton’s laws to explain
why.
Newton’s first law says that objects in motion
stay in motion. The car stopped but she kept
moving forward.
• Splat: The unfortunate bug hits the windshield
with a force of 1 N. If you call this the action
force, what is the reaction force? Does the car
hit the bug any harder than the bug hits the
car? Use one of Newton’s laws to explain why
or why not.
The windshield hits the bug with a 1 N force.
No; Newton’s third law states that for every
force, there is an equal and opposite force.
• Compare the forces on the bug and the car
again. Use another one of Newton’s laws to
explain why the bug goes splat and the car
keeps going, without noticeably slowing
down.
Newton’s second law; The same force acts on
both, but the bug has a much smaller mass, so
it accelerates much more.
Newton’s first law; The bug is not massive
enough to stop the car or change it’s motion.
Assess Your Understanding
1) A dog pulls on his leash with a 10 N force to
the left, but doesn’t move. Identify the
reaction force.
The leash pulls on the dog with a 10 N force
to the right.
2) Using all three of Newton’s laws, explain how
objects react to forces.
Sample: Newton’s first law states objects
change their motion when force is applied.
Newton’s second law says the acceleration
depends on the strength of the force and the
mass of the object. Newton’s third law says
that whenever a force acts on an object, that
object applies an equal and opposite force
back.
Momentum
• The sports announcer says, “Going into the allstar break, the St. Louis Cardinals have the
momentum.” The headlines declare “St. Louis
Rams Gaining Momentum.” The coach pumps
up his team at half-time saying, “You have the
momentum; the critical need it that you use
that momentum and bury them in the third
quarter.”
• Momentum is a commonly used term in
sports. A team that has the momentum is on
the move and is going to take some effort to
stop.
• Momentum, however, is a physics term
referring to the quantity of motion that an
object has. If an object is in motion, then it
has momentum.
• Momentum: mass in motion (vector quantity)
• Momentum is dependent upon two things:
how much stuff is moving (mass) and how fast
the stuff is moving (velocity).
Momentum = mass ∙ velocity
p = mv
Units: kg ∙ m/s
• An object at rest does not have momentum.
Guided Practice
1) A lioness has a mass of 180 kg and a velocity of 16
m/s to the right. What is her momentum?
180kg x 16 m/s = 2880 kg∙m/s to the right
2) The warthog has a mass of 100 kg. What does the
warthog’s speed have to be for it to have the same
momentum as the lioness?
28.8 m/s
Graded Practice
1) Find the momentum of the following:
a) A 60 kg halfback is moving eastward at 9 m/s.
b) A 1000 kg car is moving northward at 20 m/s.
c) A 40 kg freshman is moving southward at 2 m/s.
2) A car possesses 20,000 units of momentum.
What be the car’s new momentum if…
a) …its velocity was doubled?
b) …its velocity was tripled?
c) …its mass was doubled (by adding more
passengers and a greater load)?
d) …both it’s velocity and mass were doubled?
3) A halfback (m= 60 kg), a tight end (m= 90 kg),
and a lineman (m= 120 kg) are running down
the football field. Consider their ticker tape
patterns below.
Compare the velocities of these three players.
How many times greater are the velocity of the
halfback and the velocity of the tight end than
the velocity of the lineman? Which player has
the greatest momentum and why?
Answers
1) a) 540 kg∙m/s
b) 20,000 kg∙m/s
c) 80 kg∙m/s
2) a) 40,000 kg∙m/s
b) 60,000 kg∙m/s
c) 40,000 kg∙m/s
d) 80,000 kg∙m/s
3) Tight End: covers twice the distance in the same amount of
time (v = 6 m/s)
Halfback: covers three times the distance in the same
amount of time (v = 9 m/s)
The tightend and the halfback both have a momentum of
540 kg∙m/s, while the lineman only has a momentum of
360 kg∙m/s
Law of Conservation of Momentum
• In the absence of an outside force (friction),
the total momentum of objects that interact
does not change.
• The total momentum of any group of objects
remains the same, or is conserved, unless
outside forces act on the objects.
Non-sticky Collisions
• When two objects of the same mass (100 kg)
collide and don’t stick together and outside
forces are negligible, the objects trade
velocities. The car that is going faster before
the collision will end up slowing down, and
the car that is going slower before the collision
will end up speeding up. Therefore, the
momentums are the same.
Car 1:
Car 2:
m = 100 kg
m = 100 kg
v = 4 m/s
v = 2 m/s
M = 400 kg∙m/s
M = 200 kg∙m/s
Total M = 600 kg∙m/s
After Collision:
v = 2 m/s
v = 4 m/s
M = 200 kg∙m/s
M = 400 kg∙m/s
Total M = 600 kg∙m/s
Sticky Collisions
• Sometimes objects end up sticking together
during a collision. Two cars, which have the
same mass, got tangled together after they
collided. Since one car was at rest and had a
momentum of zero, only the other car had
any momentum before the collision. After
they collided and stuck together, the cars
shared that momentum. The total
momentum of the two cars stayed the same.
Check Your Understanding
1) How can a heavy moving van have the same
momentum as a small motorcycle?
Momentum equals mass times velocity, so
the truck would need to be moving more
slowly than the motorcycle.
2) What is the momentum of a 750 kg car
traveling at a velocity of 25 m/s?
750 kg x 25 m/s = 18750 kg∙m/s
3) The total momentum of two marbles before
a collision is 0.06 kg∙m/s. No outside forces
act on the marbles. What is the total
momentum of the marbles after the
collision?
0.06 kg∙m/s
Inertia v. Momentum
• How are inertia and momentum related?
• Inertia is the measure of how much resistance
matter has to acceleration. The more inertia
something has, the less it wants to respond to
forces and accelerate. This statement is
mathematically stated a = F/m. (Newton’s Second
Law) The more force, the more acceleration. The
more inertia, the less acceleration.
• Momentum is the product of inertia (m) and
velocity (v). p=ma. The more inertia something
has, the more momentum it has, when in motion.
Predictions for the Year 3000