A hammer of mass 1 kg hits a nail at a speed of 10 m. `s^(-1)` . For this, the nail penetrates 2 cm through a wooden plank. Calculate (i) impulse due to the hammer, (ii) the applied force and (iii) the time of contact between the hammer and the nail.

Explanation

Impulse due to the hammer
= change in momentum of the hammer
= m(v - u) = 1 `xx ( 10 - 0) = 10 kg cdot m cdot s^(-1)`.
The nail penetrates 2 cm through the wooden plank. Let the time for which the hammer is in contact with the nail be t s.
`therefore` Distance moved = average velocity `xx` time
or, `(2)/(100) = (10 + 0)/(2) xx t [ "average velocity" = (u + v)/(2) = (10 + 0)/(2)]`
or, ` t = 4 xx 10^(-3)s`
If the applied force is F, then F `cdot` t = 10
or, `F = (10)/(4 xx 10^(-3)) = (10000)/(4) = 2500 N`.