A pendulum bob of mass 0 1 kg is suspended by a string of 1m long The bob is displaced - Physics - Work Energy And Power

Question

A pendulum bob of mass 0 1 kg is suspended by a string of 1m
long The bob is displaced so that the string becomes horizontal and
released Find its kinetic energy when the string makes an angle of
(i) 0o, (ii) 30o with the vertical

Shikha Bhadoria · Accepted Answer

The pendulum of length 'l' is released from the horizontal Total Energy when the bob is horizontal is purely potential=mgl

1) When it makes an angle of 0 degrees, at that point its entire potential energy is converted into kinetic energy Thus, $\frac{1}{2} m v^{2} = m g l = 0 1 (9 8) (1) = 0 98 J$ 2) When it makes an angle of 30 degrees: At this point the bob possesses potential as well as kinetic energy However the mechanical energy remains conserved and is equal to mgl Thus, ME=KE+PE=mgl $\frac{1}{2} m v^{2} + m g h = m g l \frac{1}{2} m v^{2} = m g l - (m g h) P E = m g h = m g (l - l \cos 30^{\circ}) = m g l - m g l \cos 30^{\circ} = 0 98 (1 - \frac{\sqrt{3}}{2}) T h u s, K E = m g l - (m g l - m g l \cos 30^{\circ}) = m g l \cos 30^{\circ} = 0 98 (\frac{\sqrt{3}}{2}) J$

A pendulum bob of mass 0.1 kg is suspended by a string of 1m long.The bob is displaced so that the string becomes horizontal and released. Find its kinetic energy when the string makes an angle of (i) 0o, (ii) 30o with the vertical.

A pendulum bob of mass 0.1 kg is suspended by a string of 1m long.The bob is displaced so that the string becomes horizontal and released. Find its kinetic energy when the string makes an angle of (i) 0^o, (ii) 30^o with the vertical.