## Mastering Physics Solutions: Exercise 5.42

Exercise 5.42

Part A = 4.2*10-2

Solution Below:

A horizontal spring, resting on a frictionless tabletop, is stretched 18 cm from its unstretched configuration and a 1.00kg mass is attached to it. The system is released from rest. A fraction of a second later, the spring finds itself compressed 3.7 cm from its unstretched configuration.

Part A

How does its final potential energy compare to its initial potential energy? (Give your answer as a ratio, final to initial.)

Spring potential energy is given by the formula U = 1/2kx2. So we can set up a ratio by solving for the final and initial spring potential energies and then dividing. Remember that stretching or compressing doesn’t matter – the sign will disappear when the x is squared.

The final spring potential energy (3.7cm compressed):

Uf = 1/2kxf2
Uf = 1/2k(0.037)2
Uf = 0.0006845k

And the initial spring potential energy (1.8cm stretched):

Ui = 1/2kxf2
Ui = 1/2k(-0.18)2
Ui = 0.0162k

Now set up the ratio Uf / Ui:

Uf / Ui = 0.0006845k / 0.0162k
Uf / Ui = 0.042k / k
Uf / Ui = 0.042

Mastering physics likes things like this in scientific notation, so:

Uf / Ui = 4.2 * 10-2

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### 2 Responses to Mastering Physics Solutions: Exercise 5.42

1. pb says:

Ui should = .0162 in the section solving for Ui. It is correct at the end Uf / Ui

• Mastering Physics Solutions says:

Good catch! Sorry about that one!