namely gL v , mgL m g L gL v B ∴ (iii) The ratio of the kinetic energies at B and C is : C C At point C, the string becomes slack and the velocity of the bob is horizontal and to the left. If the connecting string is cut at this instant, the bob will execute a projectile motion with horizontal projection akin to a rock kicked horizontally from the edge of a cliff. Otherwise the bob will continue on its circular path and complete the revolution. ⊳ .
THE POTENTIAL ENERGY OF A SPRING The spring force is an example of a variable force which is conservative. Fig. . shows a block attached to a spring and resting on a smooth horizontal surface.
The other end of the spring is attached to a rigid wall. The spring is light and may be treated as massless. In an ideal spring, the spring force F s is proportional to x where x is the displacement of the block from the equilibrium position. The displacement could be either positive [Fig.
. (b)] or negative [Fig. . (c)].
This force law for the spring is called Hooke’s law and is mathematically stated as F s = − kx The constant k is called the spring constant. Its unit is N m - . The spring is said to be stiff if k is large and soft if k is small. Suppose that we pull the block outwards as in Fig.
. (b). If the extension is x m , the work done by the spring force is F x s s x m