Question

A ball is spinning in a vertical circle at the end of a string that is 3.0 m long . If the ball has a mass of 2.5 kg and moves at constant speed of 6.0m/s determine the tension in the string when the ball is at top of the loop. Determine the tension in the string when the ball is the bottom of the loop.

Answer 1

The tension in the string when the ball is at top of the loop

$mg+T=ma\to mg+T=m\cdot\frac{v^2}{r}\to T=m\cdot\frac{v^2}{r}-mg=$

$=2.5\cdot\frac{6^2}{3}-2.5\cdot9.8=5.5\ (N)$

The tension in the string when the ball is the bottom of the loop

$mg-T=-ma\to mg-T=-m\cdot\frac{v^2}{r}\to T=m\cdot\frac{v^2}{r}+mg=$

$=2.5\cdot\frac{6^2}{3}+2.5\cdot9.8=54.5\ (N)$