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PPT Activity
Momentum
Developer Notes
1.
Goals
1. Students should know that momentum is massvelocity.
2. Students should know and be able to manipulate Ft = ∆(mv).
3. Students should know that momentum is conserved in collisions.
Concepts & Skills Introduced
Area
physics
physics
physics
Concept
momentum = mv
impulse and momentum, Ft = m∆v
conservation of momentum
Time Required
min
Warm-up Question
1. What do you think momentum is? Describe momentum.
2. If you were able to apply a small net force on an aircraft carrier, including the wind, waves,
currents, etc., and you kept that force applied constantly, how fast would the aircraft carrier
eventually go?
Answer: the speed of light
Presentation
Do warm-up question 1. Don't ask for definitions, just what they think it is, related words, etc.
Then lead a discussion, which should follow the pattern below. You can have the students work
to make group descriptions, then discuss it in class. Put the list on the board, then check the
words that come up most often.
Everyone uses the term momentum, but what is it? How is it defined in physics? The word
momentum is often used to mean that something is moving and it will be hard to make it stop or
change directions. What does that sound like to you? Hard to stop or change directions means a
lot of inertia, or mass. Moving means velocity. So something with a lot of momentum has a lot
of mass and velocity.
Another way to look at it: What do you think of when something is going to hit you? Usually,
how big and how fast. (Also how sharp!) How is mass related to impact, directly or indirectly?
How is velocity related to impact, directly or indirectly? Impact  mass, and impact  velocity,
so impact  massvelocity. That's momentum.
Maybe do warm-up 2 here.
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PPT Activity
Momentum
Here's how it's done in physics: Remember Newton's 2nd Law of Motion, Fnet=ma? Will it make
a difference how long you apply the force? Descartes (Need to check this.) took the equation
from Newton's 2nd Law, F = ma, and looked at what would happen if the force was applied for a
period of time. Ft = ?. Applying the force for a longer time will result in the same acceleration,
but a greater final speed.
Along the same lines, Ft = mat. What does at become? Remember a = ∆v/t? Rearrange it to
form at = ∆v. The units are (m/s2)s. The seconds cancel, leaving m/s, or velocity. So, Ft =
m∆v, or Ft = ∆mv.
This can also be derived from two equations relating to acceleration. a = F/m and a = ∆v/t. Put
together, you get F/m = ∆v/t. Rearranged, its Ft = m∆v. Same thing.
So there are a bunch of different ways to achieve the same thing. Momentum is defined as mass
times velocity. A change in momentum is achieved by applying a force (surprise!) for a time that's called impulse.
Ft = ∆mv
Impulse = the change in momentum
Later, in the energy unit, we'll take a look at how long you apply a force using distance instead of
time.
What is momentum good for? It is a measure of the effect something will have. Remember from
Newton's 3rd Law, action-reaction, that an object can only apply as much force as the other
object gives back. In the same way, when two objects hit, they touch for the same amount of
time. So, when two objects hit, they apply the same amount of force to each other for the same
amount of time. F1t1 = F2t2. That means that ∆m1v1 = ∆m2v2. If two objects collide, they have
the same change in momentum. It can't be any other way.
If two objects collide and the always have the same (but opposite) change in momentum, what
does that mean? The momentum before and after the collision is the same! Momentum is
conserved! Conservation means that there is the same amount before and after. Scientists love
conservation. It means that they can look at a situation, and if it violates a law of conservation,
they know there is something wrong with their observations or calculations. Conservation of
momentum is one such law.
We have defined force, time, mass, and velocity. Now combine them in a new way to get more
information, another way to look at things.
Activity
 Make sure the surfaces are flat and level. Make sure the carts roll easily. You can check the
carts by racing them down a ramp. You may need to lube the wheels.
 Make sure the weights are against the rear wall of the carts so that the weights don't slide as
the carts are pushed apart.
Demos/POEs
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Momentum
1. Calculate the mass of a cart + weight from a demo of two carts pushing apart (like the lab),
given the mass of one cart + weight and the distance each cart goes. Could make it tougher
by giving the mass of the cart.
2. Teeter-totter with two carts pushing apart (like the lab). Will the teeter-totter stay balanced?
3. Add mass to a cart that is already rolling. What will happen to its speed?
4. Drop two balls, a tennis ball on top of a playground ball. Drop them together so they are
touching like a snowman. What will happen after they hit the floor? Afterwards, show each
ball bouncing on its own, then re-demonstrate the two together. The playground ball bounces
much lower when they're together.
5. Demonstrate two croquet ball colliding at various angles (like pool or billiards).
6. Bounce a croquet ball off a bowling ball. The croquet ball should come off with more speed.
7. Have the students line up four pennies and shoot another straight into the end. Just one pops
out.
8. Ball bearing collision off a ramp.
Assessment
Writing Prompts
1.
Relevance
Summary
Exercises
1. Look at the equation Ft = ∆(mv). If force increases, what must happen to keep the equation
balanced? t must go down, or m must go up, or v must go up. The first line of the table is
filled in. Fill in the rest.
IF
F
t 
m
v
THEN
t
F
F
F
OR
m
m
t
t
OR
v
v
v
m
2. Two identical carts are initially at rest, and a spring between them is released. If cart A has
twice the mass of cart B, what will cart A's velocity be relative to B's?
Answer: Cart a will have 1/2 the velocity of cart B.
3. Using the equation for momentum, explain why padding in a car helps to protect you during
accidents.
Answer: Your momentum changes during an accident. The padding extends the time so that
the force is less.
4. Using the equation for impulse and momentum, explain why jumpers bend their knees when
they land.
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PPT Activity
Momentum
Your momentum changes to zero when you land. Bending your knees increases the time so
that the force of landing is less.
5. If a car traveling down the highway runs into a bug,
a. which one exerts more force on the other? Answer: The forces are equal and
opposite.
b. which one hits the other for a longer time? Answer: The times are the same.
c. which experiences the greater change in momentum? Answer: The change in
momentum must be the same if the force and time are the same.
d. which experiences the greater change in velocity? Answer: The bug experiences
the greater change in velocity. The car slows down a little.
e. which experiences the greater acceleration? Answer: This is the same as d.
6. Which has more momentum, a 1,200 N lineman running at 6 m/s, or an 800 N lineman
running at 9 m/s? Answer: the same, 720 kgm/s.
7. If a 100 N net force is applied for 10 s to a stationary 5 kg mass, what will its speed be? What
will its momentum be? 100 N10 s = 5 kgx m/s. x = 200 m/s.
8. Two sumo wrestlers start their bout. One of the wrestlers weighs 1,500 N, and the other
weighs 2,000 N. They both lunge forward with the same speed. Which one exerts the larger
force? Which one ends up going backward? They exert equal and opposite forces. The lighter
one goes backward.
9. An 80 kg defensive back runs straight into a 100 kg runner and tackles him. The defensive
back is running 10 m/s and the runner is running 8 m/s. Which one exerts the larger force?
Which one ends up going backward? Answer: The forces are equal and opposite. Neither
goes backward, they stop where they hit.
10. Auntie and Wendell go to the skating rink. Auntie has a mass of 60 kg and Wendell has a
mass of 20 kg. Wendell is standing still by the side of the rink. Auntie skates by at 2 m/s and
picks him up. What is the speed of Auntie + Wendell after she picks him up?
Answer: Momentum is conserved. Auntie before is 60 kg2 m/s, and Wendell before is 0.
Afterwards, 60 kg2 m/s = 80 kgx m/s. x = 1.5 m/s.
11. A 10 kg fish gets hungry, so he swims up behind a 2 kg fish and swallows it. Before lunch,
the big fish was going 4 m/s, and the little fish was going 2 m/s in the same direction. How
fast is the big fish (+ little fish) going after lunch?
Answer: Momentum is conserved. Momentum before is 10 kg  4 m/s + 2 kg  2 m/s = 44
kgm/s. Momentum after is 12 kg  x m/s = 44 kgm/s. x = 3.67 m/s.
Challenge/ extension
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PPT Activity
Momentum
Background / History
Everyone uses the term momentum, but what is it? How is it defined in physics? If you were
playing football, and someone was about to tackle you, what are the two main things you'd think
about? Probably how big they are and how fast they're moving.
The word momentum is often used to mean that something is moving and it will be hard to make
it stop or change direction. Does that sound like anything we've studied? How about Newton's 1st
Law of Motion? If something is hard to stop or make change direction, that means it has a lot of
inertia, or mass. And if it is moving, that means it has velocity.
Momentum is the combination of mass and velocity, or
momentum = mv.
Remember Newton's 2nd Law of Motion, F = ma? Will it make a difference how long you apply
the force? Applying the force for a longer time will result in the same acceleration, but the
acceleration will continue longer, resulting in a greater final speed.
Look at the equation again. Multiply the force times time, and do the same thing to both sides
Ft = mat
What does at become? Remember a = ∆v/t? Rearrange it to form at = ∆v. The units are (m/s2)s.
The seconds cancel, leaving m/s, or velocity. So, Ft = m∆v, or
Ft = ∆(mv)
This can also be derived from two equations relating to acceleration. a = F/m and a = ∆v/t. Put
together, you get F/m = ∆v/t. Rearranged, its Ft = m∆v. Same thing.
So there are a bunch of different ways to achieve the same result. Momentum is defined as mass
times velocity. A change in momentum is achieved by applying a force (surprise!) for a time that's called impulse.
Ft = ∆(mv)
Impulse = the change in momentum
Later, in the energy unit, we'll take a look at how long you apply a force using distance instead of
time.
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PPT Activity
Momentum
Problem
Investigate momentum.
Materials
1
mass cart with spring
1
mass cart with no spring
2
bricks? kg masses?
1.5 m string
1
meter stick
1
scale
Procedure
1. Work in groups of three.
2. Your teacher will demonstrate the material setup. Answer the first section of summary
questions after the demonstration.
3. Set up the equipment in your group.
4. Take data on at least three different combinations of carts, noting each cart's total mass and
how far it travels.
Summary
1. We're investigating momentum, which is mv, but you recorded the distances the carts
traveled. How does that compare to their velocities?
Diagram each stage and draw the force vectors affecting the carts' motion.
2. Stage 1 - Describe the initial state of the carts.
3. Stage 2 - Describe what is happening after the spring is released, but while it is still in
contact with both carts.
4. Stage 3 - Describe what happens when the spring is no longer touching both carts, up until
the string reaches its limit.
5. In this experiment, what is the independent variable?
6. What is the dependent variable?
7. What are the main controls?
8. Which cart goes further, the one with more mass or less mass?
9. For each combination, what is the total momentum in stage 1?
10. For each combination, what is the total momentum in stage 3 (remember that velocity is a
vector, so direction matters)?
11. Find a pattern in your data, based on the formula for momentum.
12. Can you make a general rule that you think might apply in all cases?
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Momentum
Exercises
1. Look at the equation Ft = ∆(mv). If force increases, what must happen to keep the equation
balanced? t must go down, or m must go up, or v must go up. The first line of the table is
filled in. Fill in the rest.
IF
F
t 
m
v
THEN
t
F
F
F
OR
m
m
t
t
OR
v
v
v
m
2. Two identical carts are initially at rest, and a spring between them is released. If cart A has
twice the mass of cart B, what will cart A's velocity be relative to B's?
3. Using the equation for momentum, explain why padding in a car helps to protect you during
accidents.
4. Using the equation for impulse and momentum, explain why jumpers bend their knees when
they land.
5. If a car traveling down the highway runs into a bug,
a. which one exerts more force on the other?
b. which one hits the other for a longer time?
c. which experiences the greater change in momentum?
d. which experiences the greater change in velocity?
e. which experiences the greater acceleration?
6. Which has more momentum, a 1,200 N lineman running at 6 m/s, or an 800 N lineman
running at 9 m/s?
7. If a 100 N net force is applied for 10 s to a stationary 5 kg mass, what will its speed be? What
will its momentum be?
8. Two sumo wrestlers start their bout. One of the wrestlers weighs 1,500 N, and the other
weighs 2,000 N. They both lunge forward with the same speed. Which one exerts the larger
force? Which one ends up going backward?
9. An 80 kg defensive back runs straight into a 100 kg runner and tackles him. The defensive
back is running 10 m/s and the runner is running 8 m/s. Which one exerts the larger force?
Which one ends up going backward?
10. Auntie and Wendell go to the skating rink. Auntie has a mass of 60 kg and Wendell has a
mass of 20 kg. Wendell is standing still by the side of the rink. Auntie skates by at 2 m/s and
picks him up. What is the speed of Auntie + Wendell after she picks him up?
11. A 10 kg fish gets hungry, so he swims up behind a 2 kg fish and swallows it. Before lunch,
the big fish was going 4 m/s, and the little fish was going 2 m/s in the same direction. How
fast is the big fish (+ little fish) going after lunch?
Challenge/ extension
1.
Vocabulary
4. Momentum - The mass of an object times its velocity, mv.
5. Impulse - How long a force is applied, Ft.
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Momentum
6. Formula for impulse and momentum - Ft = ∆(mv)
7. Conservation of momentum - the sum of momentum before a collision is equal to the sum of
momentum after a collision. ∑mvbefore = ∑mvafter.
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