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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.


  • 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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