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Physics / Chapter 7: Kinetic Energy and Work / Section 7-8

Power — Question 9

Section 7-8 · Physics pages 1008–1009

Question 9 Power can vanish at an instant while force remains nonzero A 1 kg block attached to a horizontal spring of k = 100 N/m moves without friction. At one turning point its extension is +0.20 m. Later it crosses the relaxed position. x relaxed: 0 block turning: .20 m subsequent motion m = 1 kg; k = 100 N/m Compare the force and speed separately at the turning point and relaxed crossing. (a) Find spring force and spring power exactly at the turning point. (b) Find speed, spring force, and spring power at the relaxed position. (c) Explain why zero instantaneous power does not imply either rest or zero acceleration.
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Question 9 - Solution Power can vanish at an instant while force remains nonzero x relaxed: 0 block turning: .20 m subsequent motion m = 1 kg; k = 100 N/m (a) At a turning point velocity is zero. The governing relation is Ps = −kxv, a = −kx m Fs = −kx = −20 N, but Ps = Fsv = 0. Acceleration is −20 m/s2, so the block begins moving back. (b) At the relaxed position force is zero. Spring work from the turning point is 1 2(100)(.20)2 = 2 J. Thus speed is 2 m/s, while force and power are both zero. (c) A product can vanish for different reasons. At the turning point v=0 but acceleration is nonzero. At the relaxed position force is zero but speed is nonzero. Instantaneous power describes the instantaneous energy rate, not the motion or force separately.

Question 9

Power can vanish at an instant while force remains nonzero

A 1 kg block attached to a horizontal spring of k=100k=100 N/m moves without friction. At one turning point its extension is +0.20 m. Later it crosses the relaxed position.

Diagram shown in the original SVG worksheet.

  1. Find spring force and spring power exactly at the turning point.

  2. Find speed, spring force, and spring power at the relaxed position.

  3. Explain why zero instantaneous power does not imply either rest or zero acceleration.

Question 9 - Solution

Power can vanish at an instant while force remains nonzero

Diagram shown in the original SVG worksheet.

(a) At a turning point velocity is zero.

The governing relation is Ps=−kxv,a=−kxm\boxed{P_s=-kxv,\qquad a=-\frac{kx}{m}}

Fs=−kx=−20N,F_s=-kx=-20\ \mathrm N, but Ps=Fsv=0.P_s=F_sv=0. Acceleration is −20m/s2-20\ \mathrm{m/s^2}, so the block begins moving back.

(b) At the relaxed position force is zero.

Spring work from the turning point is 12(100)(.20)2=2J.\tfrac12(100)(.20)^2=2\ \mathrm J. Thus speed is 2 m/s, while force and power are both zero.

(c) A product can vanish for different reasons.

At the turning point v=0 but acceleration is nonzero. At the relaxed position force is zero but speed is nonzero. Instantaneous power describes the instantaneous energy rate, not the motion or force separately.

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