A knife of mass m is dropped from a height h | vedclass

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(C) Let $F$ be the average resistive force exerted by the wood. Using the work-energy theorem,the total work done on the knife by all forces equals th

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$mg(1 + h/d)$

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(C) Let $F$ be the average resistive force exerted by the wood. Using the work-energy theorem,the total work done on the knife by all forces equals the change in its kinetic energy.The forces acting on the knife during its penetration into the wood are gravity ($mg$ downwards) and the resistive force ($F$ upwards).The total distance moved by the knife from the point of release to the final stop is $(h + d)$.Work done by gravity = $mg(h + d)$Work done by resistive force = $-Fd$According to the work-energy theorem:$W_{	ext{total}} = \Delta K$$mg(h + d) - Fd = 0 - 0$$mg(h + d) = Fd$$F = \frac{mg(h + d)}{d}$$F = mg(1 + \frac{h}{d})$

$A$ knife of mass $m$ is dropped from a height $h$ onto a wooden floor. If the blade penetrates a distance $d$ into the wood,what is the average resistance offered by the wood to the knife?

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