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AP Physics 1: Algebra-Based 7.4 A Describe the Mechanical Energy of a System Exhibiting Shm Questions

Track the constant total energy of an SHM system as kinetic and potential energy exchange across positions, times and oscillator configurations.

Syllabus
Effective Fall 2024
Course
AP Physics 1: Algebra-Based

Exam points

  • calculate total spring–object energy from stiffness, amplitude, maximum speed or cycle distance
  • find kinetic or potential energy at a stated displacement such as half the amplitude
  • identify maximum and minimum kinetic or potential energy at equilibrium and turning points
  • interpret or sketch kinetic, potential and total-energy graphs versus time or position
  • use motion-graph symmetry to justify equal kinetic and potential energies at different times
  • compare total energy and maximum speed when mass, amplitude or spring configuration changes
  • apply the selected system boundary when a block joins a cart–spring oscillator
  • use energy conservation to compare a pendulum's release and return angles

AP Physics 1: Algebra-Based 7.4 A Describe the Mechanical Energy of a System Exhibiting Shm Questions 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.

[ 1 ]

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

[ 3 ]

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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