Lesson Plans

Physics: Principles with Applications 5th Revised Edition ©2002

by Douglas Giancoli

Week 9

Chapter 7: Linear Momentum

College Board Performance Objectives:

• Distinguish by definition between elastic, inelastic and completely inelastic collisions.
• Relate energy changes in elastic and completely inelastic collisions.
• Understand that momentum and kinetic energy are conserved in elastic collisions.
• Apply the Law of Conservation of Linear Momentum to problems involving colliding bodies.
• Use energy and momentum principles to discuss what occurs after an elastic collision has stopped.
• Predict the velocities of two colliding bodies after impact when the masses and initial velocities are given.
• Apply the Law of Conservation to solve recoil problems.
• Predict the scattering angles after a two-dimensional elastic collision.
• Understand the distinction between the center of mass and center of gravity of a system.
• Calculate the location of the center of mass in simple systems.

College Board Lab Objectives:

• Design an experiment to demonstrate the validity of the Law of Conservation of Linear Momentum.
• Design and conduct an experiment to study two-dimensional scattering collisions.
• Experimentally determine the center of mass of a rigid body.

Suggested Labs:

• Conservation of Linear Momentum on the Air Track
• Ballistic Pendulum
• Momentum and Collisions in Two Dimensions on the Air Table
• Two-Dimensional Collisions

Resources:

• Chapter 7: Linear Momentum — pp. 187–201
• Student Study Guide — pp. 7-1–7-13
• Instructor's Solution Manual — pp. 94–112
• Test Items File — pp. 114–133

Pacing Guide:

• Conservation of Energy and Momentum in Collisions—days 1, 2, and 3
• Elastic Collisions in One Dimension—days 1, 2, and 3
• Inelastic Collisions—days 2, 3, and 4
• Collisions in Two or Three Dimensions—days 3 and 4
• Center of Mass—days 3 and 4
• Lab—day 5
• Block Scheduling
  The conservation of energy and momentum in collisions, elastic, and inelastic collisions require two blocks. Emphasize elastic, inelastic, completely inelastic collisions, and the energy relationships with each. Two-dimensional collisions and center of mass should be done in the remaining time.

Key Words:

Critical Thinking Questions:

1. Two masses of 2.00 kg and 5.00 kg traveling in opposite directions undergo a head-on collision. The 2.00 kg mass has a speed of 6.00 m/s and the other has a speed of 10.0 m/s. Consider the collision to be elastic. Calculate the velocities of the masses just after collision and determine the percentage of kinetic energy remaining in the system. Explain.
2. Again consider the two masses of 2.00 kg and 5.00 kg traveling in opposite directions undergoing a head-on collision. This time the collision is inelastic with a coefficient of restitution of 0.7. Calculate the velocities of the masses just after collision and determine the percentage of kinetic energy remaining in the system. Explain.
3. Once again consider the two masses of 2.00 kg and 5.00 kg traveling in opposite directions undergoing a head-on collision. The collision in this case is completely inelastic. Calculate the velocities of the masses just after collision and determine the percentage of kinetic energy remaining in the system. Explain.
4. State reasons for the differences in the velocities and kinetic energies in questions 1 through 3.
5. A 200 g ball is dropped from a height of 1.50 m onto a surface. If the coefficient of restitution is 0.75, what is the time between the first and second bounce?
6. A 5.00 kg mass moving at 3.00 m/s on a frictionless surface undergoes an elastic collision with a 4.00 kg body. Subsequently, the 4.00 kg body makes an elastic collision with another body of 3.00 kg initially at rest. What is the velocity of the 3.00 kg body just after the collision?

Troubleshooting Tips/Error Traps:

• Remind students that momentum and impulse are vectors where kinetic energy is a scalar. The kinetic energy change in a collision is work done during the collision.
• Students will commonly make sign errors in identifying initial and final velocities in collisions. Reinforce that velocities have magnitude and direction.
• Students may experience difficulty in distinguishing between elastic, inelastic, and completely inelastic collisions. Carefully designed teacher examples help. Emphasize kinetic energy changes with each example.

End of Chapter Activity:

1. If the velocity of a body is doubled, its momentum is multiplied by a factor of
   1. 4
   2. 2
   3. 1
   4. 0.5
   5. 0.25
2. A 40.0 kg mass traveling along the +x-axis with a speed of 3.00 m/s undergoes a head-on collision with a 20.0 kg mass which is at rest. If the collision is completely inelastic, what is the velocity of the composite mass immediately after collision?
   1. 2.00 m/s
   2. –2.00 m/s
   3. 6.00 m/s
   4. 20.0m/s
   5. 0.500 m/s
3. A 4.00 kg mass traveling along the +x-axis at 10.0 m/s undergoes a perfectly elastic head-on collision with an equal mass but traveling with a velocity of –6.00 m/s. Immediately after this collision the first mass has a velocity of
   1. 2.00 m/s
   2. 6.00 m/s
   3. –6.00 m/s
   4. 10.0 m/s
   5. –10.0 m/s
4. A 1.00 MT cannon fires a 10 kg shell with a velocity of 380 m/s. What is the recoil velocity of the cannon?
   1. 3.8 m/s
   2. –3.8 m/s
   3. 5.4 m/s
   4. –5.4 m/s
   5. 7.4 m/s
5. A pool ball of mass 0.30 kg traveling at 4.0 m/s strikes an identical pool ball that is at rest. After collision the first pool ball is observed to be scattered at an angle of 30°. What is the scattering angle of the second ball?
   1. 30°
   2. 45°
   3. –30°
   4. 60°
   5. –60°
6. Of all of the following, momentum is conserved for
   1. totally inelastic collisions
   2. partially elastic collisions
   3. perfectly elastic collisions
   4. explosions
   5. all of these
7. A boy and a girl on ice skates face one another. The boy has a mass of 30 kg and the girl has a mass of 20 kg. The boy pushes the girl backward with a speed of 3.0 m/s. Ignoring friction, what is the recoil speed of the boy?
   1. 2.0 m/s
   2. 3.0 m/s
   3. zero
   4. 4.0 m/s
   5. 5.0 m/s
8. The earth and moon are separated by 3.84x10⁸ m. The earth has a mass of 5.89x10²⁴ kg and the moon has a mass of 7.36x10²² kg. Where is the center-of-mass for the earth-moon system relative to the center of the earth?
   1. 3.8x10⁶ m
   2. 4.7x10⁶ m
   3. 7.4x10⁶ m
   4. 1.0x10⁸ m
   5. 2.1x10⁸ m
9. Three identical 10.0 kg masses are positioned along the x-axis with positions of 1.0 m, 5.0 m, and 6.0 m from the origin. What is the location of the center-of-mass of the system?
   1. 1.0 m
   2. 2.0 m
   3. 3.4 m
   4. 4.0 m
   5. 5.6 m
10. A 0.015 kg bullet is fired into a ballistic pendulum initially at rest. The center-of-mass of the pendulum rises a vertical distance of 10.0 cm. The initial velocity of the bullet was
    1. 100 m/s
    2. 275 m/s
    3. 375 m/s
    4. 425 m/s
    5. 525 m/s
    
    

answers: 1 (c), 2 (a), 3 (c), 4 (b), 5 (d), 6 (e), 7 (a), 8 (b), 9 (d), 10 (c)

Suggested Problem Assignments: