Free response · Unit 7 Beta

Energy of a block on a spring

Translation Between Representations · 12 points

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The question

Name: ______________________   Date: ____________   Energy of a block on a spring (12 points)

Diagram

A block on a horizontal spring

Mx = −Ax = 0x = +A/2x = +A

A block of mass M is attached to a spring of spring constant k on a level, frictionless surface. The block is pulled to x = +A and released from rest at time t = 0. It then oscillates in simple harmonic motion about x = 0. The system is the block and the spring.

  1. (a) On the bar charts, draw shaded bars to show the kinetic energy K of the block and the elastic potential energy Us of the system when the block is at x = +A, at x = +A/2 and at x = 0. Use the same scale for all three charts. A zero line is drawn for each. [3 points]

  2. (b) Derive an expression for the speed of the block when it is at x = +A/2. Express your answer in terms of M, k, A and physical constants, as appropriate. Your equation should be consistent with your bar chart for x = +A/2. [3 points]

  3. (c) On the axes, sketch and label graphs of the kinetic energy K, the potential energy Us and the total mechanical energy E of the system as functions of the block's position x, from x = −A to x = +A. [3 points]

  4. (d) Explain how your bar charts in part (a), your equation in part (b) and your graph in part (c) are consistent with each other. [3 points]