# Homework Help: Conservation of energy up a ramp.

1. Feb 25, 2013

### macaholic

1. The problem statement, all variables and given/known data
Suppose there is a block attached to a spring with spring constant $k$. The block is pushed so that it compresses the spring a distance $x_1$. The block is released and slides without friction up a ramp, coming to a maximum height $h_1$ above the ground. Suppose we compressed the spring twice as far, what maximum height does the block now reach?

2. Relevant equations
$SPE = \frac{k x^2}{2}$
$GPE = m g h$

3. The attempt at a solution
Conservation of energy, for the first situation then the second:
$SPE=GPE$
$\frac{k x_1^2}{2} = mgh_1$
$h_1=\frac{k x_1^2}{2mg}$

$SPE=GPE$
$\frac{k (2 x_1)^2}{2} = mgh_2$
$h_2=\frac{k 4x_1^2}{2mg}$

$\frac{h_2}{h_1} =\frac{k 4 x_1^2}{2mg} * \frac{2mg}{k x_1^2} = 4$

However the answerI have (this is from a course I took a long time ago) says it goes $\sqrt{2}$ times as high. Did I do something stupid here?

2. Feb 25, 2013