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AP Physics 1 7.4 SHM Mechanical Energy Overview

Analyze simple harmonic motion through the exchange of kinetic and potential energy while total mechanical energy remains constant.

Syllabus
Effective Fall 2025
Course
AP Physics 1: Algebra-Based

Exam points

  • Use conservation of mechanical energy to compare kinetic and potential energy at positions in an SHM cycle.

Covered syllabus points

7.4.A—Describe the mechanical energy of a system exhibiting SHM

7.4 Energy of Simple Harmonic Oscillators question 1

[Maximum number: 4]

(7 points, suggested time 13 minutes)
A cart on a horizontal surface is attached to a spring. The other end of the spring is attached to a wall. The cart is initially held at rest, as shown in Figure 1. When the cart is released, the system consisting of the cart and spring oscillates between the positions x=+L and x=-L. Figure 2 shows the kinetic energy of the cart-spring system as a function of the system's potential energy. Frictional forces are negligible.

Question (a)

(a)

On the graph of kinetic energy K versus potential energy U shown in Figure 2, the values for the x-intercept and y-intercept are the same. Briefly explain why this is true, using physics principles.

Figure 3

Figure 3

When the cart is at +L and momentarily at rest, a block is dropped onto the cart, as shown in Figure 3. The block sticks to the cart, and the block-cart-spring system continues to oscillate between -L and +L. The masses of the cart and the block are m0m_{0} and 3m03 m_{0}, respectively.

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Question (b)

(b)

The dashed line in Figure 4 shows the kinetic energy K versus potential energy U of the block-cart-spring system after the block is dropped onto the cart. This graph is identical to the graph shown in Figure 2 for the cart-spring system before the block is dropped onto the cart.

Figure 4

Figure 4

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Question (i)

(i)

Briefly explain why the two graphs must be the same, using physics principles.

[ 1 ]

Question (ii)

(ii)

After the block is dropped onto the cart, consider a system that consists only of the cart and the spring. On Figure 4, sketch a solid line that shows the kinetic energy of the system that consists of the cart and the spring but not the block after the block is dropped onto the cart.

Figure for Question (ii) — AP Physics 1: Algebra-Based
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