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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.

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200 N; 10^{- 2} \sec

100 N; 10^{- 3} \sec

400 N; 10^{- 3} \sec

300 N; 10^{- 2} \sec

answer is A.

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Detailed Solution

Hammer strikes with velocity

u = 2 m/s, s = 0.01 m = 10^{- 2} m

$v^{2} - u^{2} = 2 as$

$a = \frac{v^{2} - u^{2}}{2 s}$

$= \frac{0 - {(2)}^{2}}{2 \times 10^{- 2}}$

$= \frac{- 4}{2} \times 100$

$= - 200 {m/s}^{2}$

Force $F = ma = 1 \times (200) = 200 N$

Time of impact $t = \frac{v - u}{t} = \frac{0 - 2}{- 200} = \frac{1}{100} = 10^{- 2} s$

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