# Spring and energy problem

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A ball of mass m = 1.80 kg is released from rest at a height h = 0.650 m above a light vertical spring of force constant k as shown in caption (a) of the figure. The ball strikes the top of the spring and compresses it a distance d = 0.090 m where it comes to rest (see caption (b)).  Assume no energy losses in the spring and the collision. Find the force constant k using energy considerations. Hint: Choose the final position of the mass as yg = 0. Note that an uncompressed spring has zero potential energy.

asked Oct 27, 2014 in General

## 1 Answer

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Assume h is measured from the top of the spring, then the total vertical displacement is h+d. The change of gravitational potential energy is then mg(h+d). When it stopped by the spring, the potential energy in the spring is equal to mg(h+d). Therefore, we have $mg(h+d)=\frac 12 kd^2$.  Solve for k.
answered Oct 27, 2014 by (21,750 points)