The figure below shows a simple pendulum of mass 200 g. It is displaced from the mean position A to the extreme position B. The potential energy at the position A is zero. At the position B the pendulum bob is raised by 5 m.

(i) What is the potential energy of the pendulum at the position B?
(ii) What is the total mechanical energy at point C?
(iii) What is the speed of the bob at the position A when released from B ?
(Take g = `10ms^(-2)` and there is no loss of energy.)

Explanation

(i) m = 200g = 0.2 kg, `g=10ms^(-2)`, h = 5 m
`therefore` Potential energy (U) = mgh
at position B = `0.2xx10xx5=10J`
(ii) 10 J `(becauseK+U="constant")`
(iii) At position A, kinetic energy (K) = 10 J
`1/2mv^(2)=10`
`rArr1/2xx0.2xxv^(2)=10`
`rArrv^(2)=(10xx2)/0.2=100`
`thereforev=sqrt100=10ms^(-1)`