Question

A hammer of mass $500g$ moving at $50m{s^ - }^1$ strikes a nail. The nail stops the hammer in a very short time $0.01s$ . What is the force of the nail on the hammer?
(A) $2500N$
(B) $- 2500N$
(C) $1500N$
(D) $- 1500N$

Answer 1

The relation between a force and the momentum of a body on which the force is applied has to be known. From Newton’s second law of motion, we know that the applied force has a direct relation to the change in momentum. Also, we can know that the force is the product of the mass of a body and the acceleration during the motion of the body. Using these relations the problem can be solved.

Complete Step By Step Answer:
From the second law, the change in momentum of a body is directly proportional to the force applied, and this change in momentum takes place in the direction of the applied force.
$F = \dfrac{{dt}}{{dt}} = \dfrac{{d(mv)}}{{dt}}$
after simplification the equation becomes,
$F = ma$
where,
$F$ is applied force. $F = - 2500N$
$M$ is the mass of the body
$A$ is the acceleration of the body.
Here, the force of the nail on the hammer is,
$F = \dfrac{{{\text{change in the momentum of hammer}}}}{{{\text{Time}}}}$
This can be written as,
$F = \dfrac{{m(v - u)}}{t}$
Now substitute the given data in the above equation we get,
$F = \dfrac{{0.5(0 - 50)}}{{0.01}}$
After simplification, the force will be,
$F = - 2500N$
Here the negative sign indicates the nail's force on the hammer is in the opposite direction to the motion of the hammer.
Finally, the correct answer is option (B) the force of the nail on the hammer is $F = - 2500N$ .

Note:
Based on Newton’s second law the force on the body is equal to the change in momentum per change in time.
Acceleration is defined as the change of the moving state.
The process of slowing down is also called acceleration which is a negative acceleration. here we have to apply more force to accelerate the objects.