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Momentum
What is Momentum?
1. What is the momentum for a 1200 kg car traveling at 24 m/s?
2. Calculate the momentum for the following:
a. A 100 kg linebacker traveling at 7 m/s
b. A 1200 kg car traveling at 0.5 m/s
c. A proton traveling at half the speed of light (use the reference table)
d. A 5,000 kg bus at rest
Which has the greatest momentum?
Which has the greatest inertia?
3. How fast would a 0.001 kg fly have to travel to have the same momentum as a 5,000 kg bus going 2 m/s?
4. A 1500 kg car accelerates from 15 m/s to 30 m/s in 12 seconds.
a. What is the initial momentum of the car?
b. What is the final momentum of the car?
c. What is the change in momentum?
What is Impulse?
Examples of increasing time to reduce force for an impulse:
5. A car comes to rest with a force of 10,000 N over 2 seconds.
a. What was the magnitude of the impulse?
b. What was the change in momentum of the car?
c. What was the final and initial momentum of the car?
6. A 1000 kg car is traveling 20 m/s and comes to rest in 10 seconds.
a. What is the change in momentum of the car?
b. What is the impulse?
c. What is the force bringing the car to rest?
7. A 1,200­kilogram car traveling at 12 meters per second hits a tree and is brought to rest in 0.10 second. What is the magnitude of the average force acting on the car to bring it to rest?
8. Which situation will produce the greatest change of momentum for a 1.0­kilogram cart?
1. accelerating it from rest to 3.0 m/s
2. accelerating it from 2.0 m/s to 4.0 m/s
3. applying a net force of 5.0 N for 2.0 s
4. applying a net force of 10.0 N for 0.5 s
9. A 1000­kilogram car traveling due east at 15 meters per second is hit from behind and receives a forward impulse of 6000 newton­seconds. Determine the magnitude of the car’s change in momentum due to this impulse.
Recall Newton’s 3rd Law of motion: Every force has an equal and opposite force.
A 50 kg ice skater pushes on a 100 kg ice skater with a force of 100 N
What happens to the 50 kg ice skater?
What is the force on the 50 kg ice skater?
Which ice skater moves faster? Why?
Since both ice skaters experience the same force for the same amount of time, they experience equal and opposite impulses, or change in momentum. So the total change in momentum for both ice skaters is 0.
Conservation of Momentum
In the absence of external forces on a system, the total momentum of the system
Any momentum lost by one object
External Forces and Closed Systems
10. A 200 kg cannon shoots a 10 kg ball with a speed of 50 m/s
Is momentum conserved for the cannonball?
Is momentum conserved for the cannon/cannonball system when the ball is fired? What will happen to the cannon?
11. Now the cannon is placed against a wall so it can’t roll backwards, and fires the cannonball.
Is momentum conserved for the cannonball?
Is momentum conserved for the cannon/cannonball system?
For what system is momentum conserved?
When do I use conservation of momentum?
You use the principle of conservation of momentum when looking at explosions/recoil or collisions.
Explosions and Recoil
When an object separates into pieces
12. A 200 kg cannon (initially at rest) shoots a 3 kg cannonball at 50 m/s. Determine the velocity of the cannon after firing.
pbefore = pafter
(203 kg)(0 m/s) =
Where did 203 kg come from?
(200 kg)v + (3 kg)(50 m/s)
13. A 1.2­kilogram block and a 1.8­kilogram block are initially at rest on a frictionless, horizontal surface. When a compressed spring between the blocks is released, the 1.8­
kilogram block moves to the right at 2.0 meters per second, as shown. What is the speed of the 1.2­kilogram block after the spring is released?
pbefore = pafter
14. A 10 kg gun fires a 0.1 kg bullet with a force of 10,000 N to a speed of 300 m/s. What is the force the bullet applies to the gun? 15. A 90 kg astronaut and his 2 kg wrench are accidentally floating away from the space station at 2 m/s. How fast must he throw his wrench so that he can stop floating away?
In the absence of external forces on a system, the total momentum of the system remains constant
Any momentum lost by one object is gained by others. pbefore = pafter
16. A cue­ball is rolling towards the 8­ball with constant velocity of 2 m/s. Is momentum conserved for the cue ball? (Neglect friction). What is another way to describe this behavior?
17. The cue ball strikes the 8 ball and comes to a stop. Is momentum conserved for the cue ball? If not, for what system is it conserved? (Neglect friction)
Conservation of Momentum – Collisions
We will look at 2 types of collisions. Elastic (“bouncy”) collisions and inelastic (“sticky”) collisions.
Elastic “Bouncy” Collisions
18. A cue­ball traveling at 2.5 m/s with mass 0.5 kg strikes an 8­ball at rest with the same mass. The cue ball comes to rest after the collision.
pbefore mvcue­ball + mv8­ball
= pafter
=
mvcue­ball + mv8­ball
19. A 0.5 kg cue ball traveling at 2.5 m/s strikes the 2­ball (same mass) traveling at 1.5 m/s. After the collision, the cue ball has a velocity of 1.5 m/s. a. What is the total momentum of the system before and after the collision?
b. How fast is the 2­ball moving after the collision?
Inelastic “Sticky” Collisions
20. A 3000 kg freight car traveling at 12 m/s collides with a 2000 kg freight car at rest. They stick together. Determine the velocity of the cars after the collision
pbefore = pafter
mvfreight car 1 + mvfreight car 2
=
mvboth stuck together
21. A 6 kg fish swims toward and swallows a 2 kg fish at rest. If the larger fish swims at 1 m/s, what is its velocity immediately after lunch?
pbefore = pafter
22. A 6 kg fish swims at 1 m/s toward a 2 kg fish, and eats it. After lunch, the fish is at rest.
a. What is the mass of the fish now?
b. How fast was the 2 kg fish moving before being eaten?
23. Ball A of mass 5.0 kilograms moving at 20 meters per second collides with ball B of unknown mass moving at 10 meters per second in the same direction. After the collision, ball A moves at 10 meters per second and ball B at 15 meters per second, both still in the same direction. What is the mass of ball B?
24. On a snow­covered road, a car with a mass of 1.1×103 kilograms collides head­on with a van having a mass of 2.5×103 kilograms traveling at 6.0 meters per second. As a result of the collision, the vehicles lock together and immediately come to rest. Calculate the speed of the car immediately before the collision.
Setting Up Conservation of Momentum Problems
pbefore = pafter
Explosions/Recoil
25. Bender and his swag are flying through space. Bender throws his swag to bring himself to a stop
26. A motionless cannon (m1) fires a cannonball (m2), they both leave at speed v1 and v2 respectively.
Elastic “Bouncy” Collisions
27. A 5kg mass going v1 hits a 3kg mass at rest. After the collision the 5kg mass is at rest. How fast v2 does the 3 kg mass go?.
Inelastic “Sticky” Collisions
28. A freight train (m1) traveling at speed v1 collides with a freight car (m2) at rest, the two stick together and travel with speed v2.
29. A 5000 kg bus collides with a 1500 kg car traveling at 8 m/s. After the collision, the two stick together and come to a halt. How fast was the bus traveling?
30. A 2000.­kilogram empty cart moving with a speed of 4.0 meters per second is about to collide with a stationary loaded cart having a total mass of 5000. kilograms, as shown. After the collision, the carts lock and move together. Calculate the speed of the combined carts after the collision.
31. The A­team is trying to fly a 9000 kg tank. If the cannon can shoot projectiles at 700 m/s, how massive does a shell have to be to give the tank a velocity of 4 m/s?
32. A 5.0 kilogram block is sliding east at 4 meters per second when it collides with a 3.0 kilogram block at rest. The two blocks collide with no sticking and the 5.0 kilogram block comes to a stop after the collision. What is the speed of the 3.0 kilogram block after the collision?
33. A 2000 kilogram car and a 5000 kilogram truck collide and come to a stop. The car was initially moving with a velocity of 4 meters per second east. Determine the velocity of the truck before the collision.
34. A bullet traveling at 250 meters per second is brought to rest by an impulse of 4 newton·seconds. What is the mass of the bullet?
35. A 1,200­kilogram car traveling at 4 meters per second hits a tree and is brought to rest in 0.10 second. What is the magnitude of the average force acting on the car to bring it to rest?
36. A 4­kilogram gun initially at rest is free to move. When a 0.015­kilogram bullet leaves the gun with a speed of 500 meters per second, what is the speed of the gun?
37. A 0.4 kg rubber ball travels towards the wall at 15 m/s and bounces back at 12 m/s. Calculate the total change in momentum of the ball