Question

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

Answer 1

Let the force applied on the nail = F

displacement of nail (s)= 0.01m

here, all the kinetic energy of the hammer is used to do the work.

So work done = KE of hammer

=> Fs= 1/2 mv^2

=> F × 0.01 = 1/2 × 1 × 2^2

=> 0.01F = 2

=> F = 2/0.01 = 200N

So force is 200N.
__________________________

We know that force = rate of change of momentum of hammer

=> 200 = mv/t
(where t is time of impact)

=> 200 = 1×2/t

=> t = 2/200

=> t = 0.01 second

time of impact = 0.01 sec

Answer 2

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Suppose the force applied on the nail = F

Displacement of nail (n)

= 0.01m

Hence,

kinetic energy of the hammer is used to do the work.

So work done = KE of hammer

=> Fn = $\bf\huge\frac{1}{2}$ $\bf\huge mv^{2}$

=> F × 0.01 = $\bf\huge\frac{1}{2}$ × 1 × $\bf\huge 2^{2}$

=> 0.01 F = 2

=> F = $\bf\huge\frac{2}{0.01}$

= 200N

Force is 200N.

Force = Rate of change of momentum of hammer

=> 200 = $\bf\huge\frac{mv}{t}$

=> 200 = 1 × $\bf\huge\frac{2}{t}$

=> t = $\bf\huge\frac{2}{200}$

Time of impact = 0.01 sec

$\bf\huge\boxed{\boxed{\boxed{Radhe\:Radhe}}}$