An iron nail is dropped from a height h from the level of a sand bed. If it penetrates through a distance x in the sand before coming to rest, the average force exerted by the sand on the nail is,
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The nail hits the sand with a speed V o after falling through a height h
⇒ ⇒ 
… (1)
The nail stops after sometime say t, penetrating through a distance, x into the sand. Since its velocity decreases gradually the sand exerts a retarding upward force, R (say). The net force acting on the nail is given as
Σ Σ F y = R – mg = ma
⇒ ⇒ R = m (g + a) … (2)
Where a = deceleration of the nail. Since the nail penetrates a distance x
0 − − V 2 0 = − − 2a x … (3)
Putting V 0 from (1) and ‘a’ from (2) in (3), we obtain
⇒ ⇒ 
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