A Classical Approach of Newtonian Mechanics

5 CONSERVATION OF ENERGY 5.8 Power

Stable Equilibrium Unstable Equilibrium Neutral Equilibrium

x - >

Figure 44: Different types of equilibrium

in equilibrium (i.e., it will neither attempt to return to its initial state, nor will
it continue to move). A neutral equilibrium point corresponds to a fiat spot in a

U(x) curve. See Fig. 44.

5.8 Power

Suppose that an object moves in a general force-field f(r). We now know how to

calculate how much energy flows from the force-field to the object as it moves

along a given path between two points. Let us now consider the rate at which

this energy flows. If dW is the amount of work that the force-field performs on

the mass in a time interval dt then the rate of working is given by
dW
P =. (5.54)
dt
In other words, the rate of working—which is usually referred to as the power—is
simply the time derivative of the work performed. Incidentally, the mks unit of

power is called the watt (symbol W). In fact, 1 watt equals 1 kilogram meter-
squared per second-cubed, or 1 joule per second.

Suppose that the object displaces by dr in the time interval dt. By definition,
the amount of work done on the object during this time interval is given by

dW = f·dr. (5.55)

It follows from Eq. (5.54) that

P = f·v, (5.56)

U(x)