A spherical ball of mass 2 kg falls from a height of 10 m and is brought to rest after penetrating 10 cm into sand. The average force exerted by sand on the ball is _______ N. (Take g = 10 m/s ^2 )

Step-by-step solution

Using the work-energy theorem, the total work done on the ball is equal to its change in kinetic energy. Since the ball starts from rest and finally comes to rest, the change in kinetic energy is zero. W_ gravity + W_ sand = K = 0 The work done by gravity is over the total distance h + d , and the work done by the resistive force of the sand F is over the distance d . mg(h + d) - Fd = 0 F = mg(h + d) d Given m = 2 kg, g = 10 m/s ^2 , h = 10 m, and d = 10 cm = 0.1 m: F = 2 10 (10 + 0.1) 0.1 F = 20 10.1 0.1 F = 20 10