TUTORIL 4: CONSERVTION OF ENERGY Instructors: Kazumi Tolich and Sheh Lit Chang
2 Relating work and changes in energy: experiments 1 and 2 Two experiments are conducted with identical blocks on a level, frictionless surface. Each block is pushed through the same distance by the same force. In experiment 1 both blocks end at rest and in 2 both blocks have a final speef v f2. System 1: Two blocks and spring in experiment 1. System 2: Two blocks in experiment 2.
3 Relating work and changes in energy: Checkpoint 1 1. Determine whether the quantities in the table are positive, negative, or zero for each system. System 1 System 2 W net ext ΔK ΔU ΔE tot 2. With which of the following students, if any, do you agree? Student 1 The net work done on a system is always equal to the change in kinetic energy of that system. Student 2 The total energy of a system can change if something is doing work on that system. The net work done on a system by external forces is equal to the change in total energy of the system. Student 3 In the absence of friction, the total energy of a system must remain constant. In other words, K i + U i = K f + U f or ΔK + ΔU = 0
Relating work and changes in energy: experiments 1, 2, and 3 4 Experiment 3 is similar to experiment 1, but the spring in experiment 3 is weaker than in experiment 1 (k 3 < k 1 ). t the enf experiment 3, each block has a speef v f3. System 3 consists of the two blocks and the spring in experiment 3. ll three experiments are shown together below. Experiment 1 Experiment 2 Experiment 3 t = t 1 Each hand pushes with a constant force of magnitude F o t = t 3 Each hand pushes with a constant force of magnitude F o t = t 5 Each hand pushes with a constant force of magnitude F o k 1 k 3 t = t 2 t = t 4 t = t 6 v f 1 = 0 v f 2 > 0 v f 3 > 0
5 Relating work and changes in energy: Checkpoint 2 Consider systems 1 3. 3. Rank these systems according to the net work done on each system by external forces, from smallest to largest. If the net work done on any system is zero, state so explicitly. 4. Rank these systems according to the change in total energy of the system, from smallest to largest. If the change in total energy of any system is zero, state so explicitly.
6 Relating work and changes in energy: Checkpoint 3 5. Rank these systems according to the change in kinetic energy of the system, from smallest to largest. If the change in kinetic energy of any system is zero, state so explicitly. 6. Rank these systems according to the change in potential energy of the system, from smallest to largest. If the change in potential energy of any system is zero, state so explicitly.
Work and energy in systems 7 block of mass m on a level, frictionless surface is attached to an ideal massless spring of constant k, as shown at right. t time t i, the block is released from rest, and at time t f the spring is at its equilibrium position. We will account for the change in kinetic energy of the block, ΔK block by considering 2 different systems: System, which consists of the block alone System S, which consists of the spring and the block
8 Work and energy in systems: Discussion questions 7. Sketch a free-body diagram for system and system S during the interval from t i to t f (after the hand releases the block). 8. For each force on your diagrams, determine whether it does positive, negative, or zero work. 9. For each system, determine whether the net external work is positive, negative, or zero.
Work and energy in systems: Checkpoint 4 9 10. Two students are considering the work done on the two systems: Student 1: I think that the spring does positive work on the block, and the wall does positive work on the spring-block system. Student 2: ut the point where the wall exerts a force on the spring-block system doesn t move, so how can the wall do work? The displacement is zero. With which student, if either, do you agree?
Work and energy in systems: Checkpoint 5 10 11. For each system, determine whether ΔU over the interval from t i to t f is positive, negative, or zero. 12. Two students are considering an energy analysis of system (the block alone): Student 1: The spring does work on system, so system s spring potential energy changes. Student 2: I agree that the spring does work on system, but there aren t any springs in system, so how could it have spring potential energy? It s just a block. With which student, if either, do you agree?
11 Work and energy in systems: Discussion questions 13. For which system, if either, is the total energy unchangever the interval from t i to t f? Explain how you can use the principle of conservation of energy to account for the change in kinetic energy of the block in this system. 14. For the system for which the total energy changes, explain how you can account for the change in kinetic energy of the block in that system.