A hammer of mass 0.5kg is to drive a nail of mass 50g into a piece of wood horizontally. If the hammer moves with a velocity of 4.4m/s and the resisting force of the wood is 100N. How far will the nail he driven into wood? Assuming the hammer doesn't rebound from the nail.

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Solution

Dear Student

Mass of nail: ð‘š=50 g = 0.05 kg

Mass of hammer: ð‘€=0.5kg

Velocity of hammer before striking nail: ð‘¢ = 4.4ms⁻¹

Velocities of hammer and nail after hammer strikes nail are the same: v

$M u_{h} + m u_{n} = (M + m) v v = \frac{M u_{h} + m u_{n}}{(M + m)} = \frac{0.5 \times 4.4 + m \times 0}{0.5 + 0.05} v = \frac{2.20}{0.55} = 4 m / s$
a = F/m = 100 / 0.05 = 10000/5 = 2000 $v^{2} = u^{2} + 2 a s 4^{2} = 0 + 2 a s s = \frac{16}{2 a} = \frac{8}{a} = \frac{8}{2000} = \frac{1}{250} s = 0.004 m = 0.4 c m$ m/s²
$v^{2} = u^{2} + 2 a s 4^{2} = 0 + 2 a s s = \frac{16}{2 \times 2000} = \frac{1}{250} = 0.004 m = 0.4 c m$

Regards

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