Lesson Plans

Physics 1st Edition ©2002

by James S. Walker

Week 8

Chapter 8: Potential Energy and Conservative Forces

College Board Performance Objectives:

• Define potential energy.
• Define gravitational potential energy.
• Write an equation that will determine the gravitational potential energy of a known mass or weight relative to a given location in space.
• State and write the Law of Conservation of Mechanical Energy. Include kinetic, spring potential, gravitational potential energies, and work due to friction.
• Discuss the meaning of the expression conservative force.
• Understand the significance of a conservative force.
• Discuss the meaning of the expression nonconservative force.
• Understand that the gravitational field is a conservative field.
• Understand that the spring force is a conservative force.
• Understand the relationship between work, energy, and power.

College Board Lab Objectives:

• Determine the potential energy of a compressed or elongated spring.
• Show that the change in gravitational potential energy of a mass-spring system is equal to the change in spring potential energy.

Suggested Labs:

• Conservation of Elastic and Gravitational Potential Energy

Resources:

• Student Edition — pp. 198–225
• Student Study Guide — pp. 121–137
• Instructor's Solution Manual Volume 1 — pp. 86–100
• Instructor's Solution Manual CD — Chapter 08.doc
• Instructor's Resource Guide — pp. 37–39
• Test Items File — pp. 88–102
• Media Portfolio CD — Lecture Resources Chapter 8

Pacing Guide:

• Conservative and Nonconservative Forces—days 1, 2 and 3
• Potential Energy and the Work Done by Conservative Forces—days 1, 2, and 3
• Conservation of Mechanical Energy—days 2, 3 and 4
• Work Done by Nonconservative Forces—days 2, 3, and 4
• Potential Energy Curves and Equipotentials—days 3 and 4
• Lab—day 5
• Block Scheduling
  Conservative and Nonconservative Forces, Potential Energy and the Work Done by Conservative Forces, and Conservation of Mechanical Energy require two blocks. Emphasize, with examples, the importance of the Law of Conservation of Mechanical Energy in conservative and non-conservative systems. Use the remaining time to define and discuss Work Done by Nonconservative Forces and Potential Energy Curves and Equipotentials.

Key Words:

Critical Thinking Questions:

1. A crate of mass m is projected up a rough inclined plane inclined at an angle of with an initial velocity v_o. Using the Law of Conservation of Mechanical Energy, show that the maximum distance s the crate travels up the plane is given by:
   
2. In the diagram on p. 231 of the textbook, figure 8-29, let the relative height of the block of mass m be 3R. Using the Law of Conservation of Mechanical Energy, show that the acceleration of the block at the top of the loop is 2g.
3. A spring gun, with k = 1000.0 N/m, held at an angle of 30.0° to the horizontal shoots a 25.0 g sphere. Using energy considerations, what is the maximum altitude reached by the sphere when the spring is compressed 10.0 cm?
4. A 1.2 kg ball rolls off a table 1.0 m high with a velocity of 2.5 m/s. (a) What is the kinetic energy of the ball at impact? (b) How far from the foot of the table will the ball strike the floor?
5. A 40.0 g pine cone on a branch 5.6 m above a snow drift drops. The pine cone sinks 1.3 m into the snow before coming to rest. What average frictional force stopped the pine cone?
6. Solve problem 60 on p. 230 in the textbook.
7. Solve problem 70 on p. 231 in the textbook.

Answers: 1. proof; 2. proof; 3. 5.1 m; 4. (a) 15.5 J and (b) 1.1 m; 5. 2.1 N; 6. 1.1 m; 7. 9.7 cm

Troubleshooting Tips/Error Traps:

• Emphasize that in dealing with the Law of Conservation of Mechanical Energy only the initial and final results will enter into student calculations.
• Some students have difficulty in fixing the proper signs to the forces in springs. Remind them that Hooke's Law is a law of restitution.
• Stress that friction is a degrading force and that work done by friction is negative.
• Give the students a series of parallel problems that can be done via Kinematics and Newton's Second Law and via Law of Conservation of Mechanical. Encourage them to solve the problems both ways.

End of Chapter Activity:

1. The total mechanical energy in a system is conserved only if the
   1. potential energy in the system is zero.
   2. kinetic energy is a constant.
   3. forces are conservative forces.
   4. forces are non-conservative forces.
   5. system is at rest.
2. The work done by friction is always
   1. positive because friction is a conservative force.
   2. negative because friction is a non-conservative force.
   3. positive or negative since friction is non-conservative.
   4. zero because friction is a non-conservative force.
   5. zero because friction is a conservative force.
3. If the height of a particle of mass m at rest above the ground is doubled, its gravitational potential energy is multiplied by a factor of
   1. one-fourth.
   2. one-half.
   3. one.
   4. two.
   5. four.
4. Two unequal masses hang from the ends of a massless cord that passes over a frictionless pulley. The masses are released from rest. Which of the following statements is true about the kinetic energy K and the potential energy U of the system?
   1. U = 0 and K = 0
   2. U = 0 and K > 0
   3. U < 0 and K > 0
   4. U > 0 and K < 0
   5. U < 0 and K = 0
5. A 2.0 kg body has a gravitational potential energy of 6.4 kJ at some height H above ground level. If the body is released from rest, what is its velocity on impact with the ground?
   1. –80 m/s
   2. +80 m/s
   3. –32 m/s
   4. +32 m/s
   5. –160 m/s
6. The basic principle of conservation of energy states that if no work is done on a closed system by a non-conservative force the
   1. kinetic energy is always a constant.
   2. gravitational potential energy is always a constant.
   3. elastic potential energy is always a constant.
   4. total energy is a constant.
   5. total energy is non-constant.
7. A pendulum bob of mass m = 0.3 kg is pulled to one side elevating its center of mass by 0.70 m. The bob is then released from rest. As the bob passes through equilibrium position it has a speed of
   1. 1.4 m/s.
   2. 2.1 m/s.
   3. 2.9 m/s.
   4. 3.2 m/s.
   5. 3.7 m/s.
8. A 750 gram body is released from rest in a fluid and has a speed of 5.0 m/s after falling 2.0 m. How much work is done by the resistive force of the fluid during the fall?
   1. –2.6 J
   2. –4.4 J
   3. –5.3 J
   4. –6.1 J
   5. –6.5 J
9. In a dimensional system, a force is conservative if it is a
   1. function of time and position.
   2. function of time.
   3. function of position.
   4. linear function of time.
   5. quadratic function of position.
10. Conservative forces behave in such a way as to guarantee that when a particle returns to a particular position it will have
    1. no change in kinetic energy.
    2. an increase in kinetic energy.
    3. a decrease in kinetic energy.
    4. an undeterminable kinetic energy.
    5. no relationship to kinetic energy.

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

Suggested Conceptual Questions:

Suggested Problem Assignments: