RATE OF DOING WORK

Published on: February 14, 2024

Rate of Doing Work

 

Objects that transfer energy at different times. For example,

  • A stronger person can do a task in relatively less time.

  • Powerful vehicles can complete a journey in a shorter time.

  • Powerful machines can perform much faster than less powerful ones.

The work done in unit time is otherwise named the rate of doing work or power.

 

Power = Work Time

 

Unit: Watt(W)

 

1 Watt is the power of an object that does 1 Joule of work in 1 second.

 

Power = Work Time

 

1 Watt = 1 Joule / second              = 1 Js-1

 

Larger rates of energy transfer are expressed in kiloWatts (kW).

1 kW = 1000 W = 1000 Js-1

Average Power = total energy consumed/ total time taken

 

Power is the rate of doing work or rate of transferring energy.

P = W/t. The unit of power is watt. Symbol of watt isW

 

Problem 1

A and B are two persons of weight 800 N each. Both start climbing a rope separately. Both reach a height of 8 meters.Time is different. Fill up the table below. Write down the inference.

 

Mass is the same. Height ℎ is also the same; it is 8m. Time is different.

Inference: Here, A is stronger than B. It is because A took only less time than B to do the same amount of work. In other words, A has more power than B.

 

Problem 2

A and B are the weight of two persons, 800N each. They are climbing up a rope to a height of 8 m. What is the power exerted by A and B?

 

Work done by A and B,  w = Fs = 800 × 8 = 6400 J

Power exerted by A = Wt  = 640015 = 426.67 W

 

Power exerted by B = Wt  = 640020=320 W

 

Problem 3

A boy of 50 kg is carrying a load of 30kg on his head. He climbs to the first floor at a height of 3 meters in 10 seconds. Calculate the power exerted. g=10ms-2.

 

Total mass, m = 50 + 30 = 80 kg

Work done, W = Fs = mgh = 80×10×3 = 2400 J

 Time Taken = 10 s

Power, P = Wt=240010=240 W

 

Frequently Asked Questions

 

Q1. Define power.

Ans: Power refers to the rate at which work is done or the rate at which energy is transferred or transformed. Mathematically, power (P) is defined as the amount of work (W) done or energy transferred per unit of time (t).

 

Q2. State the SI unit and mathematical equation of power.

Ans: The SI unit of power is the watt (W), which is equivalent to one joule per second. Mathematically,

Power = Worktime