Problem 8: An object of mass 1000 g falls from a height of 30 m on the sand below. If it penetrates 4 cm into the sand, what opposing force is exerted on it by the sand? Neglect air friction.

Solution

The object at 30 m height possesses P.E. This potential energy is converted to K.E as it falls down and when it hits the sand the kinetic energy is converted to work done.

The work on the sand is equal to fh, where f is the force exerted by the sand to stop the object and h = 4 cm.

We can correctly assume that the work done is equal to the P.E of the object at 30 m height.

Given Mass of the object = 1000 g = 1 kg, Height, h = 30 m

Distance covered in sand, S = 4 cm = 0.04 m

Find Force exerted by the sand, f

Therefore, mgh = fS OR f = (mgh)/S

Put the values,

f = (1 × 9.8 × 30)/0.04 = 294/0.04 = 7350 N (Answer)

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