# Potential Energy with springs

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1. May 13, 2015

### lion_

1. The problem statement, all variables and given/known data
A spring constant of $3200 N/m$ is initially streched until the elastic potential energy is $1.44$ J ($U=0$ for no stretch). What is the change in elastic potential energy if the initial stretch is changed to (a) a stretch of $2.0$ cm, (b) a compression of $2.0$ cm, (c) a compression of $4.0$ cm.

2. Relevant equations
$\Delta U=U_f-U_i$
$U=\frac{1}{2}kx^2$

3. The attempt at a solution

(a) $\Delta U=U_f-U_i=\frac{1}{2}(3200)(0.02)^2-1.44=-0.8 J$

(b) $\Delta U=U_f-U_i=-\frac{1}{2}(3200)(0.02)^2-1.44=-2.08 J$

(c) $\Delta U=U_f-U_i=-\frac{1}{2}(3200)(0.04)^2-1.44=-4J$

The first answer (a) is correct but the last 2 they get (b) $-0.8J$ and (c) $1.1J$ respectively. How?

2. May 13, 2015

### PhanthomJay

You should check your math.....

3. May 13, 2015

### lion_

If the spring is compressed, isn't potential energy for the spring negative?

4. May 13, 2015

### PhanthomJay

square a negative and you get a ????