A light, rigid rod is 51.4 cm long. Its top end is pivoted on a frictionless horizontal axle. The rod hangs straight down at rest with a small, massive ball attached to its bottom end. You strike the ball, suddenly giving it a horizontal velocity so that it swings around in a full circle. What minimum speed at the bottom is required to make the ball go over the top of the circle?

4.489 m/s

Explanation:

We are given;

Length of rod;L = 51.4 cm = 0.514 m

When the ball is at the top end, it's velocity will be zero and it's kinetic energy will be transformed to potential energy.

Thus; ½mv² = mgh

m will cancel out to give;

v² = 2gh

Where:

g is acceleration due to gravity = 9.8 m/s²

h is the maximum height of the ball which is equal to twice the length of the rod.

Thus, h = 2(0.514) = 1.028 m

v² = 2 × 9.8 × 1.028

v = √20.1488

v = 4.489 m/s