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, then the average force exerted by the sand on the nail is

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The nail has fallen through a total vertical distance of $(h + x)$ . Hence loss in its potential energy $= mg (h + x)$ . If average retarding force exerted by sand on the nail is $f$ , then work done $W = - Fx$

For equilibrium, $mg (h + x) = Fx$ or $F = mg \frac{h + x}{x} = mg (\frac{h}{x} + 1)$ .

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