Power

Work Power And Energy of Class 11

Power is defined as the rate at which work is done. If an amount of work ΔW is done in a time interval Δt, then the average power is defined to be

Pav = ΔW/Δt (8.19)

The SI unit of power is J/s which is given the name watt (W) in the honour of James Watt.

Thus, 1 W = 1 J/s.

The instantaneous power is the limiting value of Pav as Δt → 0; that is

P = dW/dt (8.20)

The work done by force F on a object that has an infinitesimal displacement d is
dW = Since the velocity of the object is , the instantaneous power may be written as P = dW/dt =

or P =

Since the work and energy are closely related, a more general definition of power is the rate of energy transfer from one body to another, or the rate at which energy is transformed from one form to another.

P = dE/dt (8.21)

Example 8.16

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration ar is varying with time t as ar = k2rt2, where k is a constant, What is the power delivered to the particle by the forces acting on it.

Solution

Let v be the instantaneous speed of the particle, then centripetal acceleration is given by

ar = v²/r

Since ar = k₂rt₂ is given, therefore,

v²/r = k2rt₂

orv = krt

The tangential acceleration is given by

at = dv/dt = kr

The tangential force is Ft = mat = mkr

Work done by centripetal force is always zero.

Hence it doesn’t contribute to the power.

Hence, power delivered is