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Compressions of a Spring When a Box is Pushed Down a Hill Toward It

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The solution explains the steps taken to calculate the compressions of a box sliding down a frictionless hill to collide with a spring clearly and comprehensively.

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m = 14 kg, k = 180 N/m, d = 4 m, angle theta = 30 deg.; g = 9.8 m/s^2

a) max. Compression:
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Let the max. compression be x meters.

Let us compute x more accurately by NOT assuming that x<<4.

Taking the final totally compressed level as the reference for height (and hence for P.E. calculations)

So original height = h = (x+4)*Sin (30 deg.)

We will use the conservation of energy principles to ...

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