# 1. A 2 kg mass and a 4 kg mass are placed at the top of a ramp. When released, they slide down and compress two identical springs. A student states that one spring will be compressed twice as much as the other. Is the student correct? Explain.

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#### Explanation

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#### Explanation:

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1
Oct 22, 2017

Student is incorrect

#### Explanation:

Potential energy at height “h” is mgh

Ratio of their potential energy $= \frac{{m}_{1} g h}{{m}_{2} g h} = {m}_{1} / {m}_{2} = \frac{2 k g}{4 k g} = \frac{1}{2}$

Potential energy gained by spring $= \frac{k {x}^{2}}{2}$

Ratio of potential energy gained by spring $= \frac{\frac{k {x}_{1}^{2}}{2}}{\frac{k {x}_{2}^{2}}{2}} = {\left({x}_{1} / {x}_{2}\right)}^{2}$

Energy is conserved. So,
Ratio of their potential energy = Ratio of potential energy gained by spring
$\frac{1}{2} = {\left({x}_{1} / {x}_{2}\right)}^{2}$

x_2 = sqrt(2) × x_1

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