A bucket of water is tied to an inextensible rope and swing in a vertical circul

Question

A bucket of water is tied to an inextensible rope and swing in a vertical circular motion. The distance from the centre of the bucket to the axis of rotation is 2.51 metres. Calculate the angular velocity, in rad s-1, of the swing, in order to prevent the water from falling out of the bucket. Give your answer to 3 decimal places. Hint: Consider the situation when the bucket is at the highest point in the vertical circular motion, with tension in the rope equals zero.

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Explanation / Answer

A bucket of water is tied to an inextensible rope and swing in a vertical circular motion. The distance from the centre of the bucket to the axis of rotation is 2.58 metres

. As the bucket moves around the circle, 2 forces are acting on it. The tension force is always directed toward the center of the circle, and the weight of the bucket is always directed toward the Earth. When the bucket is as the bottom of the circle, the tension force directed up toward the center of the circle, and the weight is directed down. When the bucket is at the top of the circle, both forces are directed down.

Since the tension of the rope = 0, when the bucket is at the top, the only force on the bucket is its weight. So the centripetal force = the weight.

Force centripetal = mass * velocity^2

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