Rate of doing Work CLASS 9TH

Consider two children, say A and B. Let us say they weigh the same. Both start climbing up a rope separately. Both reach a height of 8 m. Let us say A takes 15 s while B takes 20 s to accomplish the task.

            What is the work done by each? The work done is the same.

            However, A has taken less time than B to do the work.  So, A has done more work in a given time.  So his rate of doing work is more than that of B.  We say that A has more Power.

            A stronger person may do certain work in relatively less time. A more powerful vehicle would complete a journey in a shorter time than a less powerful one. We talk of the power of machines like motorbikes and motorcars. The speed with which these vehicles change energy or do work is a basis for their classification.

            Power measures the speed of work done, that is, how fast or slow work is done. Power is defined as the rate of doing work or the rate of transfer of energy.

            If an agent does a work W in time t, then power is given by:

Power = work/time or  P = W/t

Unit:  The unit of power is watt, W [in honour of James Watt (1736 – 1819)]  

1 watt is the power of an agent, which does work at the rate of 1 joule per second.

A body is claimed to possess power of one watt if it will work on the speed of 1 joule in 1 s.

We can also say that power is 1 W when the rate of consumption of energy is 1 Js^–1.

1 watt = 1 joule/second or 1 W = 1 Js^–1.

We express larger rates of energy transfer in kilowatts (kW).

1 kilowatt = 1000 watts

1 kW = 1000 W

1 kW = 1000 Js^–1.

            The power of an agent may vary with time. This means that the agent may be doing work at different rates at different intervals of time. Therefore the concept of average power is useful.

Average power = total energy consumed divided by total time taken.

Example 11.7 page 155: class 9 Science

Two girls, A & B, each of weight 400 N climb up a rope through a height of 8 m.  Girl A takes 20 s while B takes 50 s to accomplish this task. What is the power spent by each girl?

Solution: (i) Power spent by girl A:

Weight of the girl, mg = 400 N  [it is 40 Kg x 10 ms^-2]

Displacement (height), h = 8 m

Time taken, t = 20 s

As, Power, P = Work done/time taken = mgh / t = 400 N × 8 m / 20s = 160 W.

(ii) Power spent by girl B:

Weight of the girl, mg = 400 N

Displacement (height), h = 8 m

Time taken, t = 50 s

So, Power, P = mgh / t = 400 N × 8 m / 50s = 64 W.

Ans. Power spent by girl A is 160 W. Power spent by girl B is 64 W.

Example 11.8 Page 156: class 9 Science

A boy of mass 50 kg runs up a staircase of 45 steps in 9 s. If the height of each step is 15 cm, find his power. Take g = 10 ms^–2.

Solution:

Weight of the boy, mg = 50 kg × 10 ms^–2 = 500 N

Height of the staircase, h = 45 × 15/100 m = 6.75m [We divide 15 by 100 to convert cm into meter]

Time taken to climb, t = 9 s  

Power, P = Work done/time taken = mgh / t = 500 N × 6.75 m / 9s = 375 W

Ans.  Power is 375 W

In text question 3 page 156 class 9 Science

A lamp consumes 1000 J of electrical energy in 10 s. What is its power?

Solution:

Power = Work done /Time taken, P = W/T

Time = 10 s 

Work done = Energy consumed by the lamp = 1000 J

So, Power = 1000/10 = 100 Js^-1 =100 W

Ans. The Bulb is of 100 W

COMMERCIAL UNIT OF ENERGY

            The unit joule is too small and hence is inconvenient to express large quantities of energy. We use a bigger unit of energy called kilowatt hour (kW h).

What is 1 kW h? Let us say we have a machine that uses 1000 J of energy every second. If this machine is used continuously for one hour, it will consume 1 kW h of energy.

Thus, 1 kW h is the energy used in one hour at the rate of 1000 J s–1 (or 1 kW).

1 kWh = 1 kW ×1 h

            = 1000 W × 3600 s

            = 36,00,000 J

1 kW h = 3.6 × 10⁶ J = 1 Unit

            The energy used in households, industries and commercial establishments are usually expressed in kilowatt hour. For example, electrical energy used during a month is expressed in terms of ‘units’. Here, 1 ‘unit’ means 1 kilowatt hour.

Example 11.9 of Page 156 Class 9 Science

An electric bulb of 60 W is used for 6 h per day. Calculate the ‘units’ of energy consumed in one day by the bulb.

Solution:

Power of electric bulb = 60 W

                                    = 0.06 kW.

Time used, t = 6 h

Energy = power × time taken = 0.06 kW × 6 h = 0.36 kW h = 0.36 ‘units’.

Ans. The energy consumed by the bulb is 0.36 ‘units’.