Answer to Question #160996 in Classical Mechanics for ells

Question

A pendulum, of length 3m, supports a bob of mass 100g (0.1kg). The bob is pulled upwards until the pendulum string makes an angle of 20 degrees with the vertical. What velocity will the bob be moving at when the pendulum passes through the vertical position?

Answer 1

Let's write the law of conservation of energy:

$$PE_i+KE_i=KE_f+PE_f,$$ $$PE_i+0=KE_f+0,$$ $$mgh=\dfrac{1}{2}mv^2,$$ $$v=\sqrt{2gh}.$$

We can find $h$ from the geometry:

$$h=L-Lcos\theta=L(1-cos\theta).$$

Finally, we get:

$$v=\sqrt{2gL(1-cos\theta)},$$ $$v=\sqrt{2\cdot9.8\ \dfrac{m}{s^2}\cdot3\ m\cdot(1-cos20^{\circ})}=1.88\ \dfrac{m}{s}.$$