I am confused about how we use the spring equations to calculate what the readin

Question

I am confused about how we use the spring equations to calculate what the reading on a scale would be. For example, if some objects falls on a scale and we have the object's mass, height from which it falls, and the spring constant of the scale, how do we calculate what the scale reads when it's most compressed?

(I thought this is done by calculating the force acting on the scale, so I thought of calculating mgh and that would be the reading; however, I don't seem to be coming up with right answers. How does the spring constant factor in?)

Explanation / Answer

You should use the energy equation. Here is the process for what happening. 1.) Block starts at a height 'h' above the scale with a potentail energy of mgh 2.) The block falls and right before impact it has .5mv^2 Joules of energy. 3.) The block hits the scale and compresses the spring to an energy of .5kx^2 All of these energies will be equal. mgh = .5mv^2 = .5kx^2 x = sqrt(2*mgh/k)

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