First slide

Work

Question

An open knife edge of mass 'm' is dropped from a height 'h' on a wooden floor. If the blade penetrates upto the depth 'd' into the wood, the average resistance offered by the wood to the knife edge is

Moderate

A

$mg$
B

$mg (1 - \frac{h}{d})$
C

$mg (1 + \frac{h}{d})$
D

$mg {(1 + \frac{h}{d})}^{2}$

Solution

Let the blade stops at depth d into the wood.
$v^{2} = u^{2} + 2 aS$
$\Rightarrow 0 = {(\sqrt{2 gh})}^{2} + 2 (g - a) d$
by solving $a = (1 + \frac{h}{d}) g$
So the resistance offered by the wood $= mg (1 + \frac{h}{d})$

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