path i to f. . POWER Often it is interesting to know not only the work done on an object, but also the rate at which this work is done. We say a person is physically fit if he not only climbs four floors of a building but climbs them fast.
Power is defined as the time rate at which work is done or energy is transferred. The average power of a force is defined as the ratio of the work, W , to the total time t taken P t av = The instantaneous power is defined as the limiting value of the average power as time interval approaches zero, P t ( . ) The work dW done by a force F for a displacement d r is d W = F. d r .
The instantaneous power can also be expressed as P t = F. r = F.v ( . ) where v is the instantaneous velocity when the force is F . Power, like work and energy, is a scalar quantity.
Its dimensions are [ML T – ]. In the SI, its unit is called a watt (W). The watt is J s – . The unit of power is named after James Watt, one of the innovators of the steam engine in the eighteenth century.
There is another unit of power, namely the horse-power (hp) hp = W This unit is still used to describe the output of automobiles, motorbikes, etc. We encounter the unit watt when we buy electrical goods such as bulbs, heaters and refrigerators. A watt bulb which is on for hours uses kilowatt hour (kWh) of energy. (watt) × (hour) = watt hour = kilowatt hour (kWh) = (W) × (s) = .
× J . . Elastic and Inelastic Collisions In all collisions the total linear momentum is conserved; the initial momentum of the system is equal to the final momentum of the system. One can argue this as follows.
When two objects collide, the mutual impulsive forces