Question

Hammer of mass 1kg strikes on head of an end with a velocity 2 metre per second it drives nail 0.01 m into a wooden block find the force applied by the hammer and the time of impact

Answer 1

Given -
Mass of Hammer (m) = 1 kg
Initial velocity (u) = 2 m/s
Distance till which the nail was driven (s) = 0.01 m
Since the hammer stops after hitting the nail, its final velocity (v) = 0

To find -
Time of impact (t)
Force exerted by the hammer (F)

Finding -

By third equation of motion, we know that,

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

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

Putting the values, we get,

$= > a = \frac{ {0}^{2} - {2}^{2} }{2 \times 0.01}$

$= > a = \frac{0 - 4}{0.02}$

$= > a = \frac{ - 4}{0.02}$

$= > a = - 200$

Therefore, acceleration of hammer = -200 m/s², i.e., the hammer is deacclerating or retarding.

Now, by First equation of motion,

$v = u + at$

$= > t = \frac{v - u}{a}$

Putting the values, we get,

$= > t = \frac{0 - 2}{ - 200}$

$= > t = \frac{ - 2}{ - 200}$

$= > t = 0.01$

Therefore, impact time of the hammer with the nail = 0.01 sec. (I)

Now, we know that,

$F = ma$

Putting the values, we get,

$F = 1 \times ( - 200)$

$F = - 200$

Therefore, the force exerted by hammer on nail is -200 N, i.e., 200 N in opposite direction. (II)

From equations (I) and (II), you get your answer.

Hope it'll help.. :-D
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