Q1.
Raise the ball over the sand bed to a height of about 1 m and drop it (Fig. 7.17). Is a depression created in the sand? Why does the ball create a depression?
Answer
Yes, a bowl-shaped depression forms. The ball creates it because it arrives with kinetic energy and uses that energy to do work on the sand, pushing the grains aside.
Raising the ball through h = 1 m stores potential energy U = mgh
Falling freely, all of it becomes kinetic energy just above the sand:
½mv2 = mgh, so v = √(2gh) = √(2 × 10 × 1) ≈ 4.5 m s–1
In the sand, the resistive force F acts through depth d and stops the ball:
F × d = mgh → d = mgh / F
Falling freely, all of it becomes kinetic energy just above the sand:
½mv2 = mgh, so v = √(2gh) = √(2 × 10 × 1) ≈ 4.5 m s–1
In the sand, the resistive force F acts through depth d and stops the ball:
F × d = mgh → d = mgh / F
Why it happens: the sand pushes back on the ball (negative work on the ball) and the ball pushes the grains outward and downward (positive work on the sand). The ball keeps moving until the sand has absorbed all its kinetic energy — and the deeper it goes, the more work the sand has done.
Try This: repeat on a hard cemented floor. There is no depression at all, because the floor cannot be deformed — the energy goes instead into a loud sound and into the bounce of the ball.