Question

You hold a bucket in one hand. in the bucket is a 500 g rock. you swing the bucket so the rock moves in a vertical circle 2.6 m in diameter. part a what is the minimum speed the rock must have at the top of the circle if it is to always stay in contact with the bottom of the bucket?

Answer 1

As the rock is the top of the circle, the aspect of the gravity comes in. So the force is F = mg; But this force must always be less than mv^2/r for it fall. mg < mv^2/r => g < v^2/r => gr < v^2 Hence v > (gr)^1/2 => v > (9.8 * 1.3)^(1/2) v > 3.57 m/s So the minimum would be 3.57m/s