Exercise 5.42

Solution Below:

Part A

Express your answer using two significant figures.

Spring potential energy is given by the formula U = 1/2kx^{2}. 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):

U_{f} = 1/2kx_{f}^{2}

U_{f} = 1/2k(0.037)^{2}

U_{f} = 0.0006845k

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

U_{i} = 1/2kx_{f}^{2}

U_{i} = 1/2k(-0.18)^{2}

U_{i} = 0.0162k

Now set up the ratio U_{f} / U_{i}:

U_{f} / U_{i} = 0.0006845k / 0.0162k

U_{f} / U_{i} = 0.042k / k

U_{f} / U_{i} = 0.042

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

U_{f} / U_{i} = 4.2 * 10^{-2}

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

Good catch! Sorry about that one!