# Chapter 11 WORK AND ENERGY

## A porter lifts a luggage of 15 kg from the ground and puts it on his head 1.5 m above the ground. Calculate the work done by him on the luggage.

Solution:Mass of luggage, m = 15 kg anddisplacement, s = 1.5 m. Work done, W = F × s = mg × s= 15 kg × 10 m s-2 × 1.5 m= 225 kg m s-2 m= 225 N m = 225 JWork done is 225 J.

## An object of mass 15 kg is moving with a uniform velocity of 4 m s–1. What is the kinetic energy possessed by the object?

Solution:Mass of the object, m = 15 kg, velocityof the object, v = 4 m s–1, E = 1/2 m v2 k . E = 1 / 2 × 15 kg × 4 m s–1 × 4 m s–1= 120 JThe kinetic energy of the object is 120 J.

## Find the energy possessed by an object of mass 10 kg when it is at a height of 6 m above the ground. Given, g = 9.8 m s–2 .

Solution:Mass of the object, m = 10 kg,displacement (height), h = 6 m, andacceleration due to gravity, g = 9.8 m s–2Potential energy = m g h= 10 kg × 9.8 m s–2 × 6 m= 588 J.The potential energy is 588 J.

## An object of mass 12 kg is at a certain height above the ground. If the potential energy of the object is 480 J, find the height at which the object is with respect to the ground. Given, g = 10 m s–2 .

Solution:Mass of the object, m = 12 kg,potential energy, Ep = 480 J.Ep = mgh480 J = 12 kg × 10 m s–2 × hh = 480 J / 120 kg m s –2 = 4 m.The object is at the height of 4 m.

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

Solution:(i) Power expended by girl A:Weight of the girl, mg = 400 NDisplacement (height), h = 8 m Time taken, t = 20 sPower, P = Work done / time taken Power = mgh / t P = 400 N × 8 m / 20 s= 160 W. (ii) Power expended by girl B:Weight of …

## 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 hEnergy = power × time taken= 0.06 kW × 6 h= 0.36 kW h= 0.36 ‘units’.The energy consumed by the bulb is 0.36 ‘units’.

## 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 m s–2 .

Solution:Weight of the boy,w = mg = 50 kg × 10 m s–2 = 500 NHeight of the staircase,h = 45 × 15/100 m = 6.75 mTime taken to climb, t = 9 s, power, P = Work done/time taken mgh / t Power (P) = (500 N × 6.75 m ) / 9s= 375 …

## COMMERCIAL UNIT OF ENERGY

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). kWh = (Watt x hour ) / 1000 What is 1 kW h? Let us say we have a machine that uses 1000 …

## Power

Definition “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 The S I unit of power is J s–1 = kg m2s-3 = watt (W) [in …