First slide

Second law

Question

A hammer of mass 1 kg strikes on the head of a nail with a velocity of 2 ms^–1. It drives the nail 0.01 m into a wooden block. Find the force applied by the hammer and the time of impact.

Difficult

A

200 N ; 10^–2 sec.
B

100 N ; 10^–3 sec.
C

300 N ; 10^–2 sec.
D

400 N ; 10^–3 sec.

Solution

a = Retardation of the nail
$\therefore$ For the nail, 0 = u² - 2as $\Rightarrow a = \frac{{{u^2}}}{{2s}} = \frac{{{{(2)}^2}}}{{2 \times 0.01}}m/{s^2}$ $\Rightarrow a = 200\,m/{s^2}$
$\therefore$ F = Force applied by the hammer on the nail = Average resistance force applied by wood on the nail
= ma = 1 x 200N = 200N
Now, v = Final velocity of the hammer = 0, u = Initial velocity of the hammer = 2m/s
$\therefore$ V = u - at ⇒ 0 = 2 - 200.t ⇒ t = 10^-2s.

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