Answer to Question #329401 in Physics for Jane

Question

A pendulum is formed from a small rock with mass of 0.10 kg that is fastened to a massless string

with length 0.750 m. It is swinging so as to make a maximum angle of 45.0 with the vertical. Air

resistance is negligible. What is the tension in the string as it passes through the vertical?

Answer 1

The tension in the string as pendulum passes through the vertical

$$T=mg+\frac{mv^2}{l}$$

The speed of rock at this instant

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

Hence

$$T=mg+2mg(1-cos\theta)=mg(3-\cos\theta)\\ =0.10*9.8*(3-\cos 45^\circ)=2.25\:\rm N$$