Chapter 6 Collision Notes AP Physics 1 2016

Momentum and Collisions Homework Worksheet Name______Hour______

1. A pitcher claims he can throw a 0.145 kg baseball with as much momentum as a 3g bullet moving with a speed of 1500 m/s a. What must the baseball’s speed be if the pitcher’s claim is valid?

b. Which has greater kinetic energy, the ball or the bullet (calculate both to find out)?

2. A 0.140kg baseball is thrown straight up into the air with an initial speed of 17m/s. a. After 2 seconds, what is the speed of the baseball?

b. What is the change of velocity from t=0 to t=2 seconds? (v =v-v0)

c. Calculate mv (mass*change of velocity) for the baseball from 0 to 2 seconds.

d. What force is the only force acting on the baseball (physics word)? This is the net force.

e. Calculate Fnett (net force * time) for t=0 to t=2 seconds. Compare this to your answer from part “c”. Chapter 6 Collision Notes AP Physics 1 2016

3. A crate weighing 80N slides across a rough horizontal surface having k=0.10. The initial speed of the crate is v0=4m/s. a. Draw a freebody diagram for the crate and write your Newton’s 2nd Law equations.

b. Calculate the acceleration for the crate.

c. Write your conservation of energy equation for the crate slowing down.

d. How much time does it take for the crate to slide to a stop?

e. Calculate the Fnet acting on the crate.

f. Calculate Fnett (net force * time) for the time it was slowing down for.

g. What is the change of velocity from initial to when it stops? (v =v-v0)

h. Calculate mv (mass*change of velocity) for the crate from initial to when it stops. Compare this to your answer from part “f”. Chapter 6 Collision Notes AP Physics 1 2016 Chapter 6 Collision Notes AP Physics 1 2016

Momentum and Collisions 1. What is momentum? What is Equation Units Vector? What does How do I find momentum? positive magnitude given tell me? components?

2. What is impulse? Equation Units Vector? What does positive tell me?

3. Why is it incorrect to say that impulse equals momentum?

4. A cart runs into a fixed barrier. The mass of the cart, its velocity just before impact with the barrier, and its velocity right after collision are given. Rank the impulse for each cart from the greatest change to the least change in momentum.

5. Use Newton’s 2nd law to derive the impulse - Δ momentum theorem. Chapter 6 Collision Notes AP Physics 1 2016

Fnet= ma is nothing new!! Just writing it a new way. a. What kind of situations can this theorem be applied to? i. A box sliding down an incline plane ii. Projectile motion iii. A hockey puck slowing down on ice iv. A Mack truck colliding with a compact car v. Atwood vi. All of the above vii. None of the above

b. When looking at a collision of two objects, how do the forces on the two objects compare?

c. When looking at a collision of two objects, how do you know what mass to use for the change of momentum side of the equation?

d. Do we need to pay attention to direction of the velocities and force?

6. Suppose a ping-pong ball and a bowling ball are rolling toward you. Both have the same momentum, and you exert the same force to stop each. How do their velocities compare? How do the time intervals to stop them compare?

7. You can’t throw a raw egg against a wall without breaking it, but you can throw it at the same speed into a sagging sheet without breaking it. Explain. 8. In terms of impulse and momentum, why are air bags in automobiles a good idea? Why do cars crumple in collisions? Chapter 6 Collision Notes AP Physics 1 2016

9. Why is falling on carpet less dangerous than falling on concrete?

10. If a boxer is able to make the impact time five times longer by “riding” with the punch, how much will the force of impact be reduced?

11. Alice, who has a mass of 60.0 kg, is riding at 25 m/s in her sports car when she must suddenly slam on the brakes to avoid hitting a dog crossing the road. She is wearing her seatbelt, which brings her body to a stop in 0.4 s. a. What average force did the seatbelt exert on her?

b. If she had not been wearing her seatbelt, the windshield would stopped her head in 1.0x10-3s, what average force would the windshield have exerted on her?

c. How many times greater is the stopping force of the windshield than the seatbelt? Chapter 6 Collision Notes AP Physics 1 2016

12. If 270 million people in the United States jumped up in the air simultaneously, pushing off Earth with an average force of 800 N each for a time of 0.10s, what would the velocity of the 5.98 x1024kg Earth be?

13. A 115 kg full back is running at 4.0 m/s to the east and is stopped in 0.75 s by a head on tackle by a tackler running due west. a. Calculate the original momentum of the fullback.

b. Calculate the impulse exerted on the fullback.

c. Calculate the impulse exerted on the tackler

d. Calculate the average force exerted on the tackler.

e. If the 115 kg full back had a velocity of 2m/s to the west after being tackled, calculate the impulse exerted on the fullback. Chapter 6 Collision Notes AP Physics 1 2016

And Now for a Complete Change of Direction 14. Suppose you roll a bowling ball into a pillow and the ball stops. Now suppose you roll it against a spring and it bounces back with an equal and opposite momentum. a. Which object exerts a greater impulse, the pillow or the spring? Why?

b. If the time it takes the pillow to stop the ball is the same as the time of contact of the ball with the spring, how do the average forces exerted on the ball compare?

15. A karate chop can produce dramatic effects by breaking boards and cement blocks. Why does the karate expert (Arlo) not pull back when striking so that his hand is made to bounce back?

16. Alice attempts to knock down a large wooden bowling pin by throwing a sphere at it. She has two spheres of equal size and mass, one made of rubber and the other of putty. The rubber sphere bounces back, while the sphere of putty sticks to the pin. Which sphere is most likely to topple the bowling pin? Chapter 6 Collision Notes AP Physics 1 2016

17. A 0.2 kg billiard sphere traveling at a speed of 15 m/s strikes the side rail of the table at an angle of 60 degrees. If the sphere rebounds at the same speed and angle a. What is the initial momentum?

b. What is the final momentum?

c. What is the change in momentum?

d. What is the impulse given the wall? Chapter 6 Collision Notes AP Physics 1 2016

18. What if the force varies?

Example: The forces shown in the force-time diagram act on a 1.5 kg particle.

a. Find the impulse for the interval t=0 to t=3.0s

b. Find the impulse for the interval t=0 to t=5.0s

c. If the forces act on a 1.5 kg particle that is initially at rest, find the particle’s speed at t=3.0s and at t=5.0s.

19. Why do you bend your legs when landing from a jump? Chapter 6 Collision Notes AP Physics 1 2016

20. Newton’s second law states that if no net force is exerted on a system, no acceleration occurs. Does it follow that no change in momentum occurs?

21. When is momentum conserved?

22. In terms of momentum conservation, why does a cannon recoil when fired? What difference in recoil would you expect in firing a solid ball versus firing a hollow ball from the same cannon?

23. It is said that in ancient times a rich man with a bag of gold coins froze to death stranded on the surface of a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

24. A 5kg fish swimming 1 m/s swallows an absent minded 1 kg fish at rest. What is the speed of the large fish immediately after lunch?

a. What would its speed be if the small fish were swimming toward it at 4 m/s before lunch?

c. What is the energy lost during this last collision? Chapter 6 Collision Notes AP Physics 1 2016

25. A 4 kg mess kit sliding on a frictionless surface explodes into two 2 kg parts, one moving at 3 m/s, due north, and the other at 5 m/s, 30 degrees north of east. What is the original speed of the mess kit?

Two Types of Collisions- Elastic and Inelastic 26. What are the characteristics of Elastic collisions?

Derive Elastic Equation…. Remember this is only for Elastic collisions!

27. A 0.450 kg block, moving with a speed of 3 m/s, has a head-on collision with a 0.9 kg block initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each block after the collision? Chapter 6 Collision Notes AP Physics 1 2016

28. A 0.280kg sphere makes an elastic head-on collision with a second sphere initially at rest. The second sphere moves off with half the original speed of the first sphere. What is the mass of the second sphere?

29. What are the characteristics of an Inelastic collision?

30. Completely or Perfectly inelastic collisions are a subset of Inelastic collisions. What are the mathematical benefits of considering these types of collisions vs an Inelastic collisions?

31. Given a problem that doesn’t state the type of collision, what assumptions can we make? What wording do you look for in a problem to identify the type of collision being presented? Chapter 6 Collision Notes AP Physics 1 2016

32. Arlo, whose mass is 80 kg, swings from a 3 m vine that is horizontal when he starts. At the bottom of his arc, he picks up 60 kg Alice in a perfectly inelastic collision. a. What is Arlo’s velocity at the bottom of the arc before colliding with Alice?

b. What is Arlo’s and Alice’s velocity after the collision?

c. What is the height of the highest tree limb they can reach on their upward swing?

33. A 1600 kg (empty) train rolls with a speed of 2.5 m/s under a loading bin, and a mass of 3500kg is deposited in the train. What is the train’s speed immediately after loading? Chapter 6 Collision Notes AP Physics 1 2016

34. An eagle of mass 4.3 kg moving with speed 10.2 m/s is on a collision course with a second eagle of mass 5.6 kg moving at 7.8 m/s in a direction at right angles to the first. After they collide, they hold onto one another. a. In what direction, and with what speed, are they moving after the collision?

b. How much energy transfers to non-mechanical forms?

34. A 5.0 kg body moving in the +x direction at 5.5 m/s collides with a 3.0 kg body moving in the –x direction at 4.0 m/s. Find the final velocity of each mass if a. The bodies stick together. Chapter 6 Collision Notes AP Physics 1 2016

b. What if the collision is elastic? What would the objects do and find their final velocities?

35. A billiard ball moving at 5 m/s strikes a stationary ball of the same mass. After the collision, the first ball moves at 4.33 m/s at an angle of 30 degrees with respect to the original line of motion. a. Find the velocity (magnitude and direction) of the second ball after the collision?

b. Was this an inelastic collision or an elastic collision?