Name (printed) ______First Day Stamp

INTRODUCTION TO MOMENTUM AND IMPULSE

1. Momentum depends on mass as well as velocity. Find the momentum of a 50-kg person walking at 2.0 m/s and the momentum of a 10-g bullet moving at 1,000 m/s. Person Bullet

BIG IDEA #1:

2. Now find the kinetic energy of the person and the bullet. Person Bullet

BIG IDEA #2:

3. To change the momentum of an object, you must apply …

4. A 0.25 kg soccer ball is rolling at 8.0 m/s toward a player. The player kicks the ball back in the opposite direction, giving it a speed of 16 m/s. What is the average force, during the kick, between the player’s foot and the ball if the kick lasts -2 3.0 x 10 s?

5. 6. Raw eggs are fragile. They break easily. Can you think of a way to throw one as hard as possible without it breaking? Be specific.

7. Egg tosses are fun, especially when the distance between the participants is large. In one egg toss, a 0.60 kg egg is moving at 15 m/s. The egg can only take 24 N of force before breaking. How much time must the catch last in order for the egg not to break?

BIG IDEA #3:

8. The photograph to the right shows a Pelton water wheel attached to an electric generator. Notice that the water wheel blades are more like little bowls rather than being traditionally flat. This causes the water to be splashed upward after striking the blades. Considering impulse and change in momentum, why would this be advantageous?

BIG IDEA #4:

1 SUMMARY QUESTIONS IMPULSE AND MOMENTUM

1. _____ Which of the following has the largest momentum relative to the Earth? a. a tightrope walker crossing Niagara Falls c. a pickup truck speeding along a highway b. a Mack truck parked in a parking lot d. a dog running down the street

2. _____ Compared to falling on a wooden floor, a wine glass may not break when it falls to a carpeted floor because of the a. smaller impulse b. longer time to stop. c. both of these d. neither of these.

3. _____ Compared to the force that brings a small car to a stop, the force required to bring a heavy truck traveling at the same speed to a stop a. is less b. is more c. may be less and may be more.

4. _____ Why is it safer to hit your head on a padded dashboard than on an unpadded dashboard? a. The change in momentum is smaller c. The impulse is smaller b. The impulse time is longer d. The acceleration is higher

5. _____ A 15.0 N force acts on a 2.0 kg mass for 5.0 seconds. How much does the momentum of the object change? a. 6 kg-m/s b. 38 kg-m/s c. 75 kg-m/s d. 150 kg-m/s

6. _____ A mass of 2 kg is at rest on a frictionless horizontal surface. A constant force of 2 N is applied to the mass for 3 s and is then removed. What is the speed of the mass after 6 s? a. 1 m/s b. 3 m/s c. 6 m/s d. 12 m/s e. 24 m/s

7. _____ A 0.25-kg soccer ball is rolling at 6.0 m/s toward a player. The player kicks the ball back in the opposite direction and gives it a velocity of 14 m/s. If the kick lasts 0.020 s, what is the average force during the interaction between the player’s foot and the ball? a. 75 N b. 100 N c. 175 N d. 250 N

Move ahead STOP! IF YOU MOVE BEYOND THIS POINT WITHOUT 2 GETTING CHECKED THERE WILL BE A PENALTY. QUESTIONS AND PROBLEMS IMPULSE AND MOMENTUM

Do the following questions and problems from the Giancoli book in the space below and on the following page. Pages 187 – 192 Questions 7, 9; Problems 2, 3, 15, 18, 19

Move ahead STOP! IF YOU MOVE BEYOND THIS POINT WITHOUT 3 GETTING CHECKED THERE WILL BE A PENALTY. INTRODUCTION TO CONSERVATION OF MOMENTUM 1.

2. A 2.0 kg mass moving with a speed of 0.50 m/s collides head-on with a 1.5 kg mass moving at 0.30 m/s in the opposite direction. After the collision, the 2.0 kg mass stops. What is the velocity of the other mass after the collision?

Demo #______: Exploding Cans (What is the big takeaway?)

Demo #______: Air / Water Rocket (What is the big takeaway?)

Demo #______: Tennis Ball Cannon (Calculate the speed of the tennis ball using Conservation of Momentum.)

3. A 4.0 kg cart moving at 2.0 m/s suddenly explodes into two pieces with a 1.0 kg piece being propelled forward at 10 m/s (with respect to the ground). What is the velocity of the other piece?

4 SUMMARY QUESTIONS CONSERVATION OF MOMENTUM

1. _____ A firecracker is placed in the midst of a motionless cluster of billiard balls on a table. When the firecracker explodes, the balls scatter in all directions. The total momentum of the balls immediately after the explosion is a. more than before the explosion c. the same as before the explosion b. less than before the explosion d. cannot tell from this information

2. _____ A firecracker is placed in the midst of a motionless cluster of billiard balls on a table. When the firecracker explodes, the balls scatter in all directions. The total kinetic energy of the balls immediately after the explosion is a. more than before the explosion c. the same as before the explosion b. less than before the explosion d. cannot tell from this information

3. _____ Two objects collide and one is initially at rest. After the collision, it is possible for: a. both to be moving d. either “a” or “b” b. one to be moving e. either “a” or “c” c. both to be at rest f. either “a,” “b,” or “c”

4. _____ A rifle recoils from firing a bullet. The speed of the rifle’s recoil is small because the a. force against the rifle is smaller than against the bullet. c. rifle has much more mass than the bullet. b. momentum is mainly concentrated in the bullet. d. momentum of the rifle is smaller.

5. _____ Mighty Matt weighs 800 N and is running down the football field at 4 m/s. Speedy Gonzales weighs only 400 N but runs at 8 m/s, while Ponderous Poncho weighs 1600 N and runs only 2 m/s. In an attempt at a tackle who will be more effective in stopping Matt? a. Speedy Gonzales b. Ponderous Poncho c. Both the same

6. _____ In which collision will Mighty Matt be hurt more? a. Speedy Gonzales b. Ponderous Poncho c. Both the same

7. _____ A rifle recoils from firing a bullet. The speed of the rifle’s recoil is small because the a. force against the rifle is smaller than against the bullet. c. rifle has much more mass than the bullet. b. momentum is mainly concentrated in the bullet d. momentum of the rifle is smaller.

8. _____A 5-kg fish swimming at a speed of 1 m/s swallows an absent-minded 1-kg fish swimming toward it at 4 m/s. The speed of the larger fish after lunch is a. 1 m/s b. 1 m/s c. 1 m/s d. 1 m/s 9 6 5 2

9. _____€ A 3-kg fish swimming at a€ speed of 3 m/s swallows an absent-minded 1-kg fish swimming moving away from it at 2 m/s. The speed of the larger fish after lunch is 11 9 7 3 a. 4 m/s b. 4 m/s c. 4 m/s d. 4 m/s

€ € € € Move ahead STOP! IF YOU MOVE BEYOND THIS POINT WITHOUT 5 GETTING CHECKED THERE WILL BE A PENALTY. LAB COLLISIONS IN ONE DIMENSION

INTRODUCTION The equipment pictured below can be used to produce collisions between two marbles. A flexible ruler is mounted into a curved metal frame. A steel marble is released in the groove of the ruler at its highest point and collides with another marble, which is set on a pedestal at the end of the ruler. The pedestal is positioned such that the marble on the pedestal is projected horizontally.

PURPOSE To test the Law of Conservation of Momentum in one-dimensional collisions. PROCEDURE

1. Measure the masses of the steel and glass marbles.

2. Measure the distance the steel ball travels horizontally from the ruler when released from the upper end of the ruler and has no collision.

3. Position the glass marble on the pedestal so that it will be projected horizontally when struck by the steel marble (and in the same direction as the steel marble is moving). Measure the distance that each of the marbles travels horizontally from the end of the ruler when the steel marble is released from the upper end of the ruler and allowed to collide with the glass marble. The distances can be made more easily by allowing the marbles to strike carbon paper. DATA

Mass of steel marble (kg): ______Mass of glass marble (kg): ______

Distance of steel ball (m) with no collision

Average distance of steel marble without collision (m): ______

Distance of steel ball (m) with collision

Average distance of steel marble with collision (m): ______

Distance of glass ball (m) with collision

Average distance of glass marble with collision (m): ______

6 QUESTIONS/CALCULATIONS (SHOW ALL WORK CAREFULLY)

1. Use the ideas of horizontal projectile motion to calculate how long the marbles take to drop to the floor.

2. Using the distances recorded in the Data section, calculate the following:

a. Velocity of steel marble with no collision:

b. Velocity of steel marble after collision:

c. Velocity of glass marble after collision:

3. Using the velocities calculated above, calculate the following momenta:

a. Momentum of steel marble with no collision:

b. Momentum of steel marble after collision:

c. Momentum of glass marble after collision:

4. Calculate the percentage difference between the momentum of the steel marble before the collision to the sum of the momenta of the steel and glass marbles after the collision.

5. Let’s assume that the steel marble you used had actually gone 10% farther than it did before the collision, but after the collision it had gone the same distance it had in the experiment. How far would the glass marble have gone?

Move ahead STOP! IF YOU MOVE BEYOND THIS POINT WITHOUT 7 GETTING CHECKED THERE WILL BE A PENALTY. QUESTIONS AND PROBLEMS CONSERVATION OF MOMENTUM

Do the following questions and problems from the Giancoli book in the space below. Pages 187 – 192 Questions 3, 4, 5; Problems 4, 6, 8, 12, 77

Move ahead STOP! IF YOU MOVE BEYOND THIS POINT WITHOUT 8 GETTING CHECKED THERE WILL BE A PENALTY. LAB THE BALLISTIC PENDULUM

This classic case of combining both the law of INTRODUCTION conservation of energy and the law of conservation of It might seem like you would need a “high tech” momentum is now possible as a lab using the steel method to measure the speed of a bullet, but you can ball shot from the mini projectile launcher into a do it easily with a simple distance measurement and pendulum catcher. Let’s break down the process – two simple mass measurements. It’s been done step by step: routinely for over a century with the ballistic pendulum (see Figure 1). This device is nothing more than a block of wood suspended by strings so Action Reason that it is free to swing back and forth and is large Measure the maximum Needed in order to enough to capture and fully contain a high-speed height of the ballistic calculate the increase in bullet. It is quite accurate, safe, and is a very elegant pendulum after it has gravitational potential example of the power of both the law of conservation been struck by the bullet. energy of the ballistic of energy and the law of conservation of momentum. pendulum. To use the ballistic pendulum, a bullet is fired into Calculate the increase in It will be the same as the the block of wood and the block moves forward (see gravitational potential kinetic energy of ballistic Figure 2) and up (see Figure 3). Because no energy of the ballistic pendulum after it has momentum is lost in collisions, the momentum of the pendulum after it has been struck by the bullet. block and bullet after the collision is equal to the been struck by the bullet. Conservation of momentum of the bullet before the collision. Energy is applied Additionally, because of energy conservation, the here. gravitational potential energy of the block at its highest point is equal to its kinetic energy at the Determine the speed of Needed to calculate the lowest point, (after the bullet has entered the block). the ballistic pendulum momentum of the You can use the height that the block rises (easily just after it has been ballistic pendulum just measured with a meter stick) to calculate the increase struck by the bullet. after it has been struck in gravitational potential energy for the block and by the bullet. bullet at their highest point. Then you can use this to Calculate the momentum It will be the same as the find the speed of the block and its momentum at their of the ballistic pendulum momentum of the bullet lowest point. Finally, you can use the momentum of just after it has been just before it strikes the the block after it is hit to find the original speed of struck by the bullet. ballistic pendulum. the bullet. Now that is impressive! I did this as a Conservation of demonstration at Tam for many years until it was Momentum is deemed too dangerous (in 2006). applied here. Calculate the speed of This is the goal of the the bullet from its process. momentum.

Figure 2: Pendulum moving forward after receiving the projectile.

Figure 1: Ballistic Pendulum 9 Figure 3: Pendulum rising after receiving the projectile.

PURPOSE

To use the laws of Conservation of Energy and Conservation of Momentum to calculate the speed of a projectile. PROCEDURE (PART 1)

Fire the projectile launcher vertically into the air several times, measuring the maximum height of the metal ball with a ruler each time. This should be done on the long range setting (three clicks). DATA (PART 1)

Maximum Height of Ball (m)

Average maximum height of the ball: ______

QUESTIONS/CALCULATIONS (PART 1) (SHOW ALL WORK CAREFULLY)

1. Use the maximum height of the ball to calculate its initial speed. This will be the known projectile speed that will be used for comparison in the second part of the lab.

PROCEDURE (PART 2)

1. Determine the mass of the ball and the catcher and the height of the bottom of the catcher above the lab table.

2. Attach a thread from the ball catcher to the Velcro assembly on the base of the launcher.

3. With the launcher on the long-range setting, fire a test shot to see how far the thread gets pulled out. Pull two centimeters of thread back through the Velcro, leaving the rest of the thread slack. This reduces the effect of friction throughout the trials.

4. Fire the ball into the pendulum. After the shot, pull the pendulum back until it is taut and measure the change in height for the pendulum.

5. Repeat five times. DATA (PART 2)

Mass of ball (kg): ______Mass of catcher (kg): ______Height above floor (m): ______

Height change of Catcher (m)

Average change in height of the catcher: ______

10 QUESTIONS/CALCULATIONS (PART 2) (SHOW ALL WORK CAREFULLY)

1. Use your data and the steps discussed on page 5 to determine the speed of the steel ball as it left the launcher. There are several steps here. Please indicate each step and explain why it is necessary.

2. Calculate the percent difference between the speed of the steel ball found in part 1 and its speed found in Part 2.

3. Calculate the KE of the steel ball before it strikes the catcher. Then use the KE of the catcher and ball after the ball strikes it to calculate the percentage KE lost in the collision. Explain where lost kinetic energy went. (Hint: it’s not GPE, and it’s more specific than “heat.”)

Post-Lab Problems 1. Let’s say you have a 1.50-kg block resting on top of a gun barrel that is pointing straight up in the air. You shoot the gun and the 8.00-gram bullet comes out at 900 m/s and immediately enters the block. It exits the block at 300 m/s straight upward. How high does the block rise?

2. A ballistic pendulum is used to find the speed of a bullet. The bullet has a mass of 10.0 grams and the suspended block of wood that it is fired into has a mass of 1.20 kg. The block rises 0.750 m after the bullet makes contact and sticks. How fast was the bullet moving before it hit the block?

11 Move ahead STOP! IF YOU MOVE BEYOND THIS POINT WITHOUT GETTING CHECKED THERE WILL BE A PENALTY. QUESTIONS AND PROBLEMS COMBINING ENERGY AND MOMENTUM

Do the following problems from the Giancoli book in the space provided below. Pages 190 – 192 Problems 32, 35, 70, 71

12 Move ahead STOP! IF YOU MOVE BEYOND THIS POINT WITHOUT GETTING CHECKED THERE WILL BE A PENALTY. INTRODUCTION TO CONSERVATION OF ANGULAR MOMENTUM

1. There are strong similarities between linear and angular momentum. However, there is a very big difference between the two in terms of the inertia component in each. What is that difference?

2. Considering your response to Question 1 above, what is the interesting consequence related to angular velocity of a spinning system?

3. What is the non-intuitive method for determining the direction of the angular momentum vector?

4. What is the direction of the angular momentum vector in each of the following instances?

a. The wheels of a bicycle being ridden.

b. The Earth.

c. The second hand on a clock.

d. A football thrown by a right-handed quarterback.

e. Your head as you rotate it to look at someone interesting to your left.

5. Explain what gives spinning things so much stability.

6. Divers will often go into a tuck position when they are doing a dive that involves one or more rotations. This increases their angular velocity. What is the tucked angular velocity of a diver who starts out straight and rotating about his center at 0.50 rev/s? The diver is 1.6 m tall and has a mass of 50 kg. Assume that in the straight position the diver is like a uniform rod and in the tucked position he is like a sphere with a diameter half his height.

SUMMARY QUESTIONS CONSERVATION OF MOMENTUM

1. _____ Suppose the ice cap at the South Pole melted and the water was distributed uniformly over the Earth’s oceans. What would happen to the Earth’s angular velocity? a. increase b. decrease c. remain the same

2. _____ A woman is sitting on the spinning seat of a piano stool with her arms extended. What happens to her angular velocity as she folds her arms? a. increases b. stays the same c. decreases

3. _____ A woman is sitting on the spinning seat of a piano stool with her arms folded. What happens to her angular momentum as she extends her arms? a. increases b. stays the same c. decreases

4. _____ If you were in the center of a rotating playground merry-go-round platform and then decided to run to the edge of the platform, the rotational speed of the platform would: a. speed up b. slow down c. stay the same

13 Move ahead STOP! IF YOU MOVE BEYOND THIS POINT WITHOUT GETTING CHECKED THERE WILL BE A PENALTY. QUESTIONS AND PROBLEMS CONSERVATION OF ANGULAR MOMENTUM

Do the following questions and problems from the Giancoli book in the space provided below. Pages 218 - 225 Questions 15, 22, 23 Problems 53, 54, 56, 62

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