First slide

Second law

Question

A hammer of mass M strikes a nail of mass m with velocity of u m/s and drives it a metre into a fixed block of wood. The average resistance of wood to the penetration of nail is

Easy

A

$[\frac{M}{m + M}] \frac{u^{2}}{2 a}$
B

$[\frac{M^{2}}{(m + M)^{2}}] \frac{u^{2}}{2 a}$
C

$[\frac{M^{2}}{(m + M)}] \frac{u^{2}}{2 a}$
D

$[\frac{M + m}{m}] \frac{u^{2}}{2 a}$

Solution

Applying the conservation of momentum
mu = (M + m)V₀
$v_{0} = (\frac{M}{m + M}) u$
The acceleration A can be obtained using the formula $(v^{2} = u^{2} + 2 as)$ . Here, we have
$0 = v_{0}^{2} - 2 Aa or A = v_{0}^{2} / 2 a$
$∴ A = {(\frac{M}{m + M})}^{2} \frac{u^{2}}{2 a}$
Resistance = (M + m) A
$= [\frac{M^{2}}{(m + M)}] \frac{u^{2}}{2 a}$ .

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