A mass hangs on a string forming a pendulum. 

The length of the string is L = 1.5m 

The mass is pulled to one side until the string
makes an angle of 30° to the vertical, as shown. 

The mass is released from this position. 

Use the conservation of energy to calculate the
speed of the mass at the instant that it passes through the
equilibrium position (ie when the string is vertical). 

First we need to find how far the mass falls,
vertically. 








It should be clear from the diagram that 





this gives h = 0.232m 









As the mass falls, GPE is converted to KE. 

The principle of conservation of energy tells us
that the GPE lost is equal to the KE gained. 

Therefore we have 



We notice immediately that (not surprisingly) we
don't need to know the mass of the falling body. 

From this we have 



which gives v = 2.13ms^{1} 



Notice that the concept of energy and energy
conservation turns an apparently complicated question into a very
simple one. 



By the way, gravity is not the only force acting on
the mass. there is, of course, the force due to the string. 

Why does this force not have any effect on the speed
of the mass ? (answer below...) 























It always acts at 90° to the direction of motion of
the mass. 
