Question

A ball with mass m and speed ${v_0}$ hits a wall and rebounds back with the same speed. Calculate the change in the object's kinetic energy.
A. $m{{v}_{0}}^{2}$
B. $\dfrac{1}{2}m{{v}_{0}}^{2}$
C. Zero
D. $\dfrac{1}{2}m{{v}_{0}}^{2}$
E. $m{{v}_{0}}^{2}$

Answer 1

Hint:We will use the law of conservation of energy which states that energy cannot be destroyed nor can it be created, but only can be transferred from one form to another. Thus the total energy of the ball conserves and we find the initial and the final energy of the system which is only in the form of kinetic energy.

Complete step by step answer:
Energy of a body is the ability of the body to do work. Energy can exist in different types such as potential, kinetic, thermal, electrical, chemical and nuclear and many other various forms.The law of conservation of energy is written as follows; “In a closed system, that is, a system that is isolated from its surroundings, the total energy of the system is conserved.” In simple words, energy can neither be created nor destroyed; it can only be converted from one form to another.

When the ball is struck with a velocity ${v_0}$, and as it has a mass m, when it is struck to the wall, then it has a certain kinetic energy which depends upon the velocity. Now when the ball rebounds, the velocity of the ball remains the same. Thus the final kinetic energy is equal to the initial kinetic energy as there is no energy loss because the speed remains the same. Thus the change in the object's kinetic energy is zero.

Thus option C is the correct answer.

Note: This is an ideal case scenario where the velocity of the ball after bouncing back remains the same but in real life such cases seldom exist as some part of the energy does get transferred into potential energy or heat. Also as energy is a scalar quantity, it depends only on the speed of the ball and not the velocity; hence change in kinetic energy is zero.