Question

A bullet of mass 0.022 kg is shot perpendicularly towards a wall, arriving to it with a speed of 150 m/s. After hitting the wall, it makes a dent that is 0.07 m deep and comes to rest embedded in it. Use the work-energy theorem to estimate the force the wall did on the bullet to stop it, assuming it was constant.

Answer 1

According to the work-energy theorem, the work done on a body is equal to the difference in kinetic energies. That is if and are the initial and final kinetic energies, then the work done is given by

If m is the mass of the body and and are the initial and final velocities, the kinetic energies are given by

and

In the present problem,

Mass of the bullet

Initial velocity

Final velocity (since it is stopped by the wall)

Distance traveled within the wall

Therefore,

  

  

Thus the work done by the wall t stop the bullet is equal to . The negative sign shows that the force is opposite to the motion of the bullet. Then the force exerted on the bullet by the wall is given by

Thus the retarding force is .. The negative sign indicates the retarding nature of the force.