Question

1. A 200 g ball moves in a vertical circle on the end of a 50 cm long string, with no additional input of energy. If its speed at the bottom is 10 m s-1, calculate:

a. The velocity at the top of the circle

b. The tension at the top of the circle

Answer 1

(a) We can find the velocity at the top of the circle from the law of conservation of energy:

$$\dfrac{1}{2}mv_{top}^2+mg2r=\dfrac{1}{2}mv_{bottom}^2,$$ $$v_{top}=\sqrt{v_{bottom}^2-4gr},$$ $$v_{top}=\sqrt{(10\ \dfrac{m}{s})^2-4\times9.8\ \dfrac{m}{s^2}\times0.5\ m}=8.97\ \dfrac{m}{s}.$$

(b) We can find the tension at the top of the circle as follows:

$$T_{top}=\dfrac{mv_{top}^2}{r}-mg,$$ $$T_{top}=\dfrac{0.2\ kg\times(8.97\ \dfrac{m}{s})^2}{0.5\ m}-0.2\ kg\times9.8\ \dfrac{m}{s^2}=30.2\ N.$$