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Learning Introductory Physics with Activities

Paul J. Emigh, Rebecka Tumblin, Kathryn Hadley, Danielle Skinner

Section 24.1 Objects and Energy

Subsubsection Activities: Energy Analysis

Explanation 24.1.1. Warm-up: Mechanical Energy.

When is the total mechanical energy of a system conserved? Describe how you know.
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Answer.
Recall the Work-Energy Theorem theorem. If the net work done by external forces on an object is zero, then total mechanical energy (kinetic and potential) is conserved. As tempting as it can be to say that energy is always conserved, the conservation of energy is highly dependent on your choice of system.
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Explanation 24.1.2. Two Apples.

Consider the two experiments described below. In each case, consider the system consisting of the apple and the Earth.
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Experiment 1: You are initially holding an apple at rest a distance \(h\) above the ground, and you lower the apple and place it at rest on the ground.
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Experiment 2: You are initially holding an apple at rest a distance \(h\) above the ground, and you drop the apple so that it is moving at speed \(v_f\) right before it hits the ground.
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Which of the following statements is true about work and energy for these two experiments?
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  1. The work done by external forces is positive for both systems.
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  2. The change in total energy is positive for both systems.
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  3. The change in kinetic energy is positive for both systems.
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  4. The change in potential energy is negative for both systems.
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Explain your reasoning for each statement.
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Solution.
Watch the video below and compare your answers.
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Explanation 24.1.3. Two Charges.

Suppose you have two positive point charges separated by some distance. A few minutes later, you find that the distance between the two point charges has increased.
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Do you think the potential energy of the system of both charges increased, decreased, or stayed the same? Explain your reasoning.
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