A block is sliding along a frictionless roller coaster. It starts at height h ab

Question

A block is sliding along a frictionless roller coaster. It starts at height h above the ground with some unknown initial speed vo. It travels downwards to a trough at depth h/3 below the ground level with a speed of vt before climbing a hill of height 5h/4. The block is able to just get to the top of this hill. (its final speed is 0). The block then slides down back to ground level, starting at rest at the top of the second hill. When coming to ground level the block is stopped by a spring with spring constant k. Find the compression of the spring.

Explanation / Answer

energy is not lost during the motion , we can apply conservation of energy . 0.5*m*(v0)^2 + mgh = 5mgh/4 , 0.5*m*(v0)^2 = mgh/4 , v0 = sqrt(gh/2) , 5mgh/4 = 0.5*k*x^2 , x= sqrt(5mgh/8k).

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