Momentum Basics - GCISD

Name: _____________________ Momentum Basics
Period: _____________________

1. A 14 N force is applied for 0.33 seconds. Calculate the impulse.

48kg 10m/s 2. A 48 kg object is moving 12 m/s down. It hits the ground and bounces up moving 10 m/s.
A. Which velocity is negative?
12m/s 48kg B. Calculate the initial momentum of the object.

C. Calculate the final momentum of the object.

D. Remembering that “change of” is always final – initial,
what is the change of momentum of the object?

Before 10 N After 3. A 6 kg object starts at rest. It is then pushed by a 10 N force for 8 seconds.
v = 0 m/s 8 sec v = _____ A. How much initial momentum does the object have?
6 kg B. Calculate the impulse that acted on the object.
6 kg I= pafter =
C. Since impulse equals a change of momentum, how much momentum
pbefore = did it gain?

D. How much momentum does it have afterwards?

E. Under the diagram, calculate the final velocity of the object.

cstephenmurray.com Copyright © 2009, C. Stephen Murray

Name: _____________________ Momentum Basics
Period: _____________________

1. A 14 N force is applied for 0.33 seconds. Calculate the impulse.

48kg 10m/s 2. A 48 kg object is moving 12 m/s down. It hits the ground and bounces up moving 10 m/s.
A. Which velocity is negative?
12m/s 48kg B. Calculate the initial momentum of the object.

C. Calculate the final momentum of the object.

D. Remembering that “change of” is always final – initial,
what is the change of momentum of the object?

Before 10 N After 3. A 6 kg object starts at rest. It is then pushed by a 10 N force for 8 seconds.
v = 0 m/s 8 sec v = _____ A. How much initial momentum does the object have?
6 kg B. Calculate the impulse that acted on the object.
6 kg I= pafter =
C. Since impulse equals a change of momentum, how much momentum
pbefore = did it gain?

D. How much momentum does it have afterwards?

E. Under the diagram, calculate the final velocity of the object.

cstephenmurray.com Copyright © 2011, C. Stephen Murray

Name: _____________________
Period: _____________________

Before 6N After 4. A 3 kg object is at rest. It is pushed on by a 6 N force for 1 minute.
v = 0 m/s 1 min v = _____ A. What time are you going to use for impulse?
3 kg B. Calculate the impulse.
3 kg I= pafter =
C. Calculate the final velocity of the object.
pbefore =

Before 50 N After Before 5N After
v = 0 m/s 2 sec v = _____ v = 0 m/s 40 sec v = _____
2 kg 2 kg
2 kg I= pafter = 2 kg I= pafter =

pbefore = pbefore =

5. A 50 N force pushes on a 2kg object for 2 seconds. On another 2 kg object a 5 N force pushes for 40 seconds.

A. Calculate the impulse of the 50 N force. B. Calculate the impulse of the 5 N force.

C. Which one gave a bigger impulse? D. Which one gave a greater change of momentum?

E. Under the diagrams, calculate the final velocities of each.

F. So, which gives a bigger impulse: the big force or the small force?

cstephenmurray.com Copyright © 2009, C. Stephen Murray

Name: _____________________
Period: _____________________

Before 6N After 4. A 3 kg object is at rest. It is pushed on by a 6 N force for 1 minute.
v = 0 m/s 1 min v = _____ A. What time are you going to use for impulse?
3 kg B. Calculate the impulse.
3 kg
C. Calculate the final velocity of the object.
pbefore = I = pafter =

Before 50 N After Before 5N After
v = 0 m/s 2 sec v = _____ v = 0 m/s 40 sec v = _____
2 kg 2 kg
2 kg I= pafter = 2 kg I= pafter =

pbefore = pbefore =

5. A 50 N force pushes on a 2kg object for 2 seconds. On another 2 kg object a 5 N force pushes for 40 seconds.

A. Calculate the impulse of the 50 N force. B. Calculate the impulse of the 5 N force.

C. Which one gave a bigger impulse? D. Which one gave a greater change of momentum?

E. Under the diagrams, calculate the final velocities of each.

F. So, which gives a bigger impulse: the big force or the small force?

cstephenmurray.com Copyright © 2011, C. Stephen Murray

Name: _____________________
Period: _____________________

cstephenmurray.com Copyright © 2011, C. Stephen Murray

Name: _____________________ Momentum Basics Examples
Period: _____________________

Before you are able to do more advance Conservation of Momentum problems,
you must master the following concepts.

Calculating Momentum:

p = mv

Remember that momentum can be negative or zero, if not moving.

Ex 1: A 5 kg object going 2 m/s to the left. p = 5(-2) = -10 kgm/s.
Ex 2 : A 10 kg object going 3 m/s to the right. p = 10(3) = 30 kgm/s.

Calculating Net Momentum:

pnet =Σp = p1 + p2 + p2... (Find the momentum of each individual object and add them together.)

Remember that momentum can be zero and that net momentum can be positive, negative, or zero.

Ex 1: A 2 kg object going 3 m/s left and a 3 kg object going 1 m/s left. pnet = 2(-3) + 3(-1) = -6 -3 = -9 kgm/s.
Ex 2: A 3 kg object going 6 m/s left and a 2 kg object going 9 m/s right. pnet = 3(-6) + 2(9) = -18 + 18 = 0 kgm/s

Calculating Change of Velocity:

∆v = vfinal – vinitial (Change of Velocity = vfinal – vinitial)

Remember negatives and that a negative times a negative is a positive.
Ex 1: A 2 kg mass going 2m/s left ends up going 6m/s left. Change of velocity = -6 - (-2) = -6 + 2 = -4 m/s
Ex 2: A 3 kg mass going 4 m/s ends up going 3 m/s the other way. Change of velocity = -3 - 4 = -7 m/s
Note: "The other way means negative, if started positive. OR, if you assume it starts going left: 3 -(-4) = 7 m/s.

Calculating Change of Momentum:

∆p = pfinal – pinitial = m(vfinal – vinitial) (Either way)

Remember negatives and that a negative times a negative is a positive.
Ex 1: A 4 kg mass going 10 m/s stops. 0 - 4(10) = -40 kgm/s OR 4(0-10) = 4(-10) = -40 kgm/s
Ex 2: A 4 kg mass going 6 m/s right ends up going 2 m/s left. 4(-2 - (6)) = 4(-8) = -32 kgm/s
Ex 3: A 2 kg mass going 4 m/s to the left ends up going 3 m/s to the right. 2(3 - (-4)) = 2(3 + 4) = 2(7) = 14 kgm/s

Impulse (I):

I = F∆t = ∆p OR F∆t = m∆v OR F∆t = m(vfinal - vinitial) (just written differently)

Just like a force does work to change the energy of an object, a force acting during a time (an impulse) creates a change
of momentum. In both of these cases a force speeds up or slows down an object. Remember: the same impulse (∆p)
can be done several ways: a large force over a small time can create the same change of momentum as a small force
acting over a large time. (Think about this mathematically: 24 kgm/s = (2N) x 12 sec OR = 8 N x 3 seconds, etc.)

cstephenmurray.com Copyright © 2011, C. Stephen Murray

Name: _____________________ The Law of Conservation of Momentum
Period: _____________________

Transfer of Momentum Momentum can be transferred when objects collide. The objects exert equal and
opposite forces on each other, causing both objects to change velocity.

The ball on the left transfers its When a car is hit from behind it lunges forward because
momentum thru the three middle momentum is transferred from the car in the back.

balls to the ball on the right. The
balls in the middle do not move.

Before After

Momentum is Conserved In any interaction (objects colliding or pushing off from each other) momentum
is conserved: the total amount of momentum doesn’t change. It is just redistributed!

before 1 kg 1 kg collision 1 kg 1 kg after 1 kg 1 kg

v = 3 m/s v = 1 m/s Equal and opposite forces v = 1 m/s v = 3 m/s
are applied on each other.
p = 3 kgm/s + p = 1 kgm/s p = 1 kgm/s + p = 3 kgm/s

pnet = 4 kgm/s Momentum is conserved! pnet = 4 kgm/s

Law of Conservation “If there are no external forces, the net Law of Conservation of Momentum
of Momentum momentum of a system remains constant.
Σpbefore ± I = Σpafter
We know that an impulse can change momentum, so it must be included in our
equation. But only an external impulse must be included—one that changes the
momentum of the system.

The equal and opposite forces of Any external force changes the Combined Objects
a collision cancel each other out, total momentum and must be
so they don’t need to be included. Sometimes objects combine or split.
included as an impulse. When combined, the mass = m1 + m2 = m1+2.
collision
external force Example 2: A 5 g bullet is shot into a resting 2 kg
No External Impulse block. How fast are the two going afterwards?
F

Positive External Impulse

Example 1: A 2 kg mass going 1 m/s is pulled by an 8 N 5 g; before after
force for 4 sec. How fast is the mass going afterwards? 400 m/s mafter = v = ?
m = 2 kg m1+2
Before After v = 0 m/s = 2.005 kg
m= m=
2 kg +W 2 kg There are two objects before (ΣpB = p1 + p2), no external
8N forces (I = 0), and one combined object after (ΣpA = p1+2).
4 sec

v = 1 m/s v=? Σpbefore ± I = Σpafter Combined mass
m1v1B + m2v2B + 0 = (m1+ m2)vA
There is only one object, so Σpbefore = mv .02/2.005 = vA
and there is an external impulse. .005(400)+ 2(0) = (2.005)vA vA = .01 m/s
.02 + 0 = 1.005vA
Σpbefore ± I = Σpafter 2(1)+ 8(4) = 2(vA) 34 = 2vA
mvB + Ft = mvA 2 + 32 = 2vA vA = 17 m/s

Thrown, Launched, Thrown objects start at rest, so v = 0 and Σpbefore = 0. Since momentum is conserved, Σpafter must
or Pushed Objects still = 0. So the objects must be moving in opposite directions, with equal amounts of momentum.

Rockets The rocket because the fuel
(and balloons) goes up goes down.
Notice that
mball = 1 kg mskater = 40 kg the more move by conservation
vb = -20 m/s vS = 0.5 m/s
massive object of momentum, too. Gases
moves slower.
are expelled at a very fast velocity,

Σpbefore = 0 Σpafter = 0 = pball + pskater pushing the rocket the opposite direction.

cstephenmurray.com Copyright © 2011, C. Stephen Murray

Name: _____________________

Period: _____________________

1. p1 + 2 A. Velocity of the second object after 6. pB + I = pA A. Two moving objects collide and stop.
2. m1 a collision.
3. v2A 7. p1B + p2B = p1A + p2A B. An object is pushed and speeds up.
4. m1 + 2 B. Velocity of two combined objects.
5. v1 + 2 8. p1B + p2B = p(1+2)A C. Two objects at rest push off.
C. Mass of two objects that are stuck
together. 9. p(1+2)B = p1A + p2A D. Two objects collide and stick.

D. Momentum of two combined objects. 10. p1B + p2B = 0 E. A moving object breaks apart.

E. Mass of the first object. 11. 0 = p1A + p2A F. Two objects collide and don’t connect.

12. An object going 3 m/s is pushed by a force for 2 seconds. 16. A moving object is stopped by a force.

Conservation of p Equation: ___________________ . Conservation of p Equation: ___________________

13. A cannon shoots a cannonball. 17. A person jumps into a boat that is at rest to begin with.

Conservation of p Equation: ___________________ Conservation of p Equation: ___________________
14. Two pool balls collide and bounce off of each other. 18. Two ice skaters push off from each other.

Conservation of p Equation: ___________________ Conservation of p Equation: ___________________
15. An object at rest is pushed by a force. 19. A moving object explodes into two pieces.

Conservation of p Equation: ___________________ Conservation of p Equation: ___________________

20. A 6 kg object going 3 m/s hits a 4 kg object at rest. If the 24. When is momentum not conserved?
6 kg object is going 1 m/s afterwards, what is the 4 kg
object’s final velocity? 25. A person shoots a bullet from a gun.
A) What happens to the gun and shoulder holding the gun?

21. A 10 kg object going 3 m/s is pushed by a 12 N force for B) How much does the shooter move?
4 seconds. Find its final velocity.
C) If the bullet hits a person-size target, how much will the
target move?

D) In the movies a bullet causes a person to “fly
backwards” violently. Explain why this is impossible.

22. A 1,000 kg cannon shoots a 2 kg cannonball 500 m/s to the 26. How does a rocket move?
right. How fast does the cannon move? 27. As a person jumps up, what happens to the earth?

23. A 60 kg person running 1.5 m/s jumps into a 12 kg boat 28. A 6 kg object moving 10 m/s to the right splits into two
that is at rest. How fast is the boat and person moving equal pieces. If afterwards, one of the pieces is moving
afterwards? 4 m/s to the right, how fast is the other piece moving?

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Name: _____________________
Period: _____________________

V = −1 m/s Must go down.
cstephenmurray.com Copyright © 2011, C. Stephen Murray