Question

A hammer of 1 kg moving with a speed 100m/s strikes at nail.the nail stops the hammer in a very short time. What is the force of the nail on the hammer?​

Answer 1

Answer

Force = 5000 N

Given

Mass of hammer = 1 kg

Initial Velocity = 100 m/s

Final velocity = 0 m/s

Since stops finally

Time = 0.02 s

To Find

Force of the nail on the hammer

Solution

Force is defined as product of mass and acceleration

$\bigstar\ \; \bf F=ma$

Acceleration is defined as rate of change in velocity

$\bf \bigstar\ \; a=\dfrac{v-u}{t}$

So , Final formula for force is ,

$\bigstar\ \; \bf F=m\left(\dfrac{v-u}{t}\right)$

$\to \rm F=(1) \left(\dfrac{0-100}{0.02}\right) \\\\\to \rm F=\dfrac{-100}{\frac{2}{100}}\\\\\to \rm F=\dfrac{-10000}{2}\\\\\to \rm F=-5000\ N\ \; \red{\bigstar}$

So , force of the nail on the hammer is - 5000 N

Note : - ve sign denotes force on hammer due to nail

Answer 2

Explanation:

Given that, a hammer of 1 kg moving with a speed 100m/s strikes at nail.the nail stops the hammer in a very short time.

We have to find the force of the nail on the hammer.

Force is defined as the product of mass and acceleration.

Force = mass × acceleration

Whereas, acceleration is defined as the change in velocity with respect to time.

Acceleration = (Final velocity - Initial velocity)/Time

Therefore,

F = m × (v - u)/t

Substitute the known values,

→ F = 1 × (0 - 100)/t

As the hammer comes to rest so the final velocity is 0 m/s. Also it comes to rest in very short period of time. But no time is given. Assume that it comes to rest in 1 sec.

So,

→ F = 1 × (1 - 100)/1

→ F = -99

Therefore, the force of the nail on the hhamme is -99N. Negative sign shows that the force on the hammer moving in the opposite direction to that of the hammer.

NOTE: It time is 0.1 sec then force is -990N and if time is 0.01 sec then force is -9900N.