   Chapter 13, Problem 5CQ

Chapter
Section
Textbook Problem

If the spring shown in Figure CQ13.3 is com pressed rather than stretched so that x = −x0, determine (a) the ratio of the new force to the original force, Fn/F0, and (b) the ratio of the new to the original elastic potential energy, PEsn/PEs0. (Hint: Force is a vector.)

(a)

To determine
The ratio of the original force to the new force.

Explanation

Given info: In the original position the displacement of the spring from equilibrium position is x0 and the force on the spring is F0 . In the new position the displacement from the equilibrium position is x0 since the spring is compressed and the force is Fn .

The Hooke's law states that in simple harmonic motion the net force is proportional to the displacement from the equilibrium point and is always directed toward the equilibrium point.

Fr=kx

• Fr

(b)

To determine
The ratio of the new potential energy to the original potential energy.

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