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Workign with a compressed spring - Toy Gun

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"The launching mechanism of a toy gun consists of a spring of unknown spring constant. If the spring is compressed a distance of 0.139 m and the gun is fired vertically, the gun can launch a 25.1g projectile from rest to a maximum height of 24.5 m above the starting point of the projectile. Neglecting all resistive forces, determine the spring constant."

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If you compress a spring to some extent, the work done by your body will be stored in the spring as the potential energy of the spring. When the spring is released, the energy is also released as some other form.

The potential energy of the spring PE = (1/2)*k * (x-x0)^2

where k is the force constant and (x-x0) is the compresion. Thus in our case, the energy stored is

PE = 0.5 * k * 0.139 = ...

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