The negative of the work done by the conservative internal force on a system equals the change in (a)total energy (b)potential energy (c)kinetic energy?Explain

Consider the following examples

• When an object is thrown upwards, it moves against the gravity in the upward direction
• Force of friction acting on a ball moving in a horizontal surface
• Work done by brakes on a moving vehicle
• Electrostatic force of repulsion when two positive charges move close towards each other

In all the above cases, work done by the body is negative as it opposes the motion.

Case 1 Now let us analyse the first example. When an object is thrown upward, it starts with very high Kinetic energy but no potential energy. As it progresses high, it gains potential energy and losses kinetic energy. At the highest part, it has only the potential energy and no kinetic energy. At any instant of time, the total energy is conserved, remains the same.

Case 2 In the next three cases, there is no potential energy as no vertical motion is present. Only kinetic energy is present because of the horizontal motion. Hence, kinetic energy is conserved in this case.