A pendulum bob is released from some ini-
tial height such that the speed of the bob at
the bottom of the swing is 3.8 m/s.
The acceleration of gravity is 9.81 m/s2.
What is the initial height of the bob?
Answer in units of m.

A pendulum bob is released from some initial height such as the speed of the bob at

the bottom of the swing is 1.0 m/s. What is the initial height of the bob? Answer in

units of m

Solution:

We can use conservation on Energy equation:

Wtop = Wbottom

So for any increase in KE, there is an equal decrease in PE.

At the initial height all the energy is PE since the mass isn't moving (WKE = 0). At the

bottom of the swing, where v = 1

m

s

, the energy is all converted to KE (WPE = 0).

mgh =

mv

2

2

h =

v

2

2g =

(1

m

s

)

2

2 ∙ 9.8

m

s

2

= 51 × 10−3m

height of the bob is 51 × 10−3m.

Explanation: