Question

A popular physics demonstration is to swing a pail of water in a vertical circle fast enough so that the water doesn’t spill out. The slowest speed allowed at the top of the motion is determined by the acceleration being only that of gravity. If Mr. Ganim’s arm is 0.60 m long, what minimum speed does he need to not spill?

Answer 1

The minimum speed needed to prevent water spillage in a pail swung in a vertical circle is equal to the acceleration due to gravity (9.8 m/s²).

Step-by-step explanation:

To determine the minimum speed required to prevent water from spilling out of a pail swung in a vertical circle, we need to consider the forces acting on the water at the top of the motion.

At the top, the only force acting on the water is gravity. This force provides the necessary centripetal force to keep the water in the pail.

The centripetal force required is given by: Fc = m * a, where m is the mass of the water and a is the acceleration.

Since the acceleration is equal to gravity (9.8 m/s²), we can write: Fc = m * 9.8 m/s².

Now we can find the minimum speed required by equating the centripetal force to the weight of the water: m * 9.8 m/s² = m * g.

Canceling out the mass of the water, we find: 9.8 m/s² = g.

Therefore, the minimum speed required is equal to the acceleration due to gravity, which is 9.8 m/s².