Question

a bucket of water is suspended from a fixed point by a rope. the bucket is set in motion and the system swings as a pendulum. however, the bucket leaks and the water slowly flows out of the bottom. how does the period of the swinging motion change as the water is lost? how does the amplitude change as the water is slowly lost?

Answer 1

As the water is lost, the period of the swinging motion increases. The amplitude also increases.

We have been told that the bucket of water that is suspended from the fixed point is set in motion and the system swings as a pendulum. The water inside it is leaking and flowing out from the bottom slowly.

Here, we observe that the mass of the bucket is decreasing but it has no effect on the period of the pendulum. As the water runs out the center of mass in the bucket moves to a lower position making the pendulum longer. So the period increases.

The period is what determines the amplitude as well. The amplitude varies directly with the period. When the period lengthens, the amplitude increases. Since the period here is increasing, the period of the pendulum will also increase.

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