Suppose that there is significant air resistance in addition to the spring force

Question

Suppose that there is significant air resistance in addition to the spring force acting on the mass as it oscillates up and down. How will the elastic potential energy change? How will the mechanical energy change?

A. The amplitude of the oscillations will decrease thus the elastic potential energy will decrease. The speed of the mass will however increase (because it travels shorter distance) thus kinetic energy will increase and so the total mechanical energy will stay the same

B. The amplitude of the oscillations will decrease thus the elastic potential energy will decrease. The mass will also slow down and kinetic energy will decrease. Therefore the total mechanical energy as the sum of kinetic and potential will decrease.

C. The amplitude of the oscillations will remain the same but the speed of the mass will reduce. Therefore potential energy will stay the same, kinetic energy will decrease and total mechanical energy as the sum of kinetic and potential will decrease

Explanation / Answer

Correct answer is

B. The amplitude of the oscillations will decrease thus the elastic potential energy will decrease. The mass will also slow down and kinetic energy will decrease. Therefore the total mechanical energy as the sum of kinetic and potential will decrease.

The air friction will constantly oppose the motion hence keep on decreasing the velocity. As the velocity decreases its amplitude will also keep on decreasing, resulting in decrease in elastic potential energy too.

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