The Change in Elastic Potential Energy with Different Spring Stretches

[lion_]

Homework Statement

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.

Homework Equations

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

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?

 

[PhanthomJay]

Homework Statement

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.

Homework Equations

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

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?

You should check your math...

 

[lion_]

You should check your math...

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

 

[PhanthomJay]

square a negative and you get a ?