Answer to Question #182912 in Physics for Tummie

Question

A ball hangs on a thread. The mass of the ball is 200 g. The thread with the ball was deflected from the vertical by 45 degrees and released. Determine the tension force of the thread at the moment the ball passes the lower point of the trajectory.

Answer 1

Find the speed of the mass at the lower point using energy conservation principle:

$$v=\sqrt{2gh}=\sqrt{2gl(1-\cos\theta)}.$$

Find the centripetal force the motion of the ball cuases:

$$F_c=m\frac{v^2}{l}=2mg(1-\cos\theta).$$

Find the force of gravity:

$$F_g=mg.$$

The tension is

$$T=F_c+F_g=mg(3-2\cos\theta)=3.11\text{ N}.$$