Question: A simple pendulum has a string of length l and bob of mass m. When the bob is at its lowest position...

Question

A simple pendulum has a string of length l and bob of mass m. When the bob is at its lowest position, it is given the minimum horizontal speed necessary for it to move in a circular path about the point of suspension. The tension in the string at the lowest position of the bob is

Answer 1

Solution

Applying the principle of conservation of energy between A and B.

$\frac{1}{2}mv_{2}^{2} - \frac{1}{2}mv_{1}^{2} = mg'2l$

or $\frac{mv_{2}^{2}}{l} = \frac{mv_{1}^{2}}{l} + 4mg$

At B, $\frac{mv_{2}^{2}}{l}$ = T₂ - mg

or mg + 4 mg = T₂ – mg or T₂ = 6mg.