physics circular motion

Question

A physics student is whirling a bucket of water in a vertical circle of radius 1.4 meters. What is the minimum speed the bucket must maintain at the top of its path so that none of the water spills out of the bucket?

Answer 1

This type of vertical circle problem can be analyzed with a free body diagrams. The minimum speed will be at the top of the path. At the minimum speed the tension in the bucket rope will be zero , so the only force is the force of gravity = mg. Newton's second law says this must equal m a. In this case the acceleration , a, is v^2/R . So g = v^2/ R. and then v^2 = R g = 1.4 x 9.8 = 13.72 and v = 3.7 m/s