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)