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macaholic
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Homework Statement
Suppose there is a block attached to a spring with spring constant [itex]k[/itex]. The block is pushed so that it compresses the spring a distance [itex]x_1[/itex]. The block is released and slides without friction up a ramp, coming to a maximum height [itex]h_1[/itex] above the ground. Suppose we compressed the spring twice as far, what maximum height does the block now reach?
Homework Equations
[itex]SPE = \frac{k x^2}{2}[/itex]
[itex]GPE = m g h[/itex]
The Attempt at a Solution
Conservation of energy, for the first situation then the second:
[itex]SPE=GPE[/itex]
[itex]\frac{k x_1^2}{2} = mgh_1[/itex]
[itex] h_1=\frac{k x_1^2}{2mg}[/itex]
[itex]SPE=GPE[/itex]
[itex]\frac{k (2 x_1)^2}{2} = mgh_2[/itex]
[itex] h_2=\frac{k 4x_1^2}{2mg}[/itex]
[itex]\frac{h_2}{h_1} =\frac{k 4 x_1^2}{2mg} * \frac{2mg}{k x_1^2} = 4[/itex]
However the answerI have (this is from a course I took a long time ago) says it goes [itex]\sqrt{2}[/itex] times as high. Did I do something stupid here?