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2.11 Work

Work(W),Energy(E) and Power (P) and Efficiency

(a) The Definition and S.I. unit of Work

Work is defined as  the product of the applied force,F on the object and its displacement,s in the direction of the net force.


W = Fs      

 where W = Work,     F = force

and   s = displacement

The S.I.unit for Work is Joule(J)

I J  =  1 N m

Work is a scalar quantity.


Work done also can get from the graph



Example  1

A horse pulls a  carriage  with a total force 40 N  for 50m . Calculate the work done on the carriage by the horse.


Example 2

Figure shows an ice cube is pulled by a force 20N. At an angle of 60o to the surface of the smooth surface.


Calculate the done on the ice cube?



Example 3

Figure shows a graph force-displacement  of spring which is  compressed by a force increases from 0 N to 100 N for 0.15 m.


Calculate the work done on the spring.





(b) The Definition and S.I. unit of Energy(E)

Energy is the capacity or ability of a system  to do work. Without energy  the work cannot done.

When work is done , energy is transferred to the object or change into a different form.

Energy can exist in various form ; potential energy(Gravitational Potential Energy, Elastic Potential Energy, Electrical Potential Energy , Atomic Potential Energy ) kinetic energy,mechanical energy, heat energy,sound energy, electrical energy and nuclear energy.

The  S.I. of energy is Joule (J).Energy is scalar quantity.


Example 4

A student lifts  a brick of mass 0.8 kg from the floor to the table top of height 1.2 m.Determine

(a)           work done on the brick

(b)           energy  is used to lift the brick.


Kinetic Energy ( Ek )

Kinetic energy is  the energy possessed by a moving object.  

Ek = ½ mv2              m = mass ,

                                           v = velocity

Example 5

A bullet of mass 0.02 kg moves at a velocity 150 ms1 .

What is the kinetic energy  of the bullet ? 



Example  6

A moving lorry of mass 800 kg  has an energy of  160 k J. What is the velocity of the lorry.



Gravitational Potential  Energy ( Eg)

The  Gravitational potential energy of any object is the energy stored in the object because of its height above the earth’s surface

                                Eg = m g h

                                                 m = mass

                                                 g = acceleration due to gravity

                                                 h = height

Example 7


A ball of mass 0.2 kg is thrown to a height 15 m. How much gravitational potential energy does the ball gain?



Example 8

A boy of mass 50 kg  sitting on the top end of an inclined sliding board has an energy of 2 kJ. What is the height the inclined sliding board from the ground?  


Principle of Conservation of Energy

Energy cannot be created or destroyed.

Energy can be transformed from one kind to another,

but  the total energy in a system stays the same or is conserved .

Example  9


A stone is thrown with a velocity 20 ms-1.

What is the maximum height can be reached by the stone?



Example 10

Figure shows a ball of mass 0.5 kg slides from rest at  point A  through a  a frictionless rail height 0.8 m down . What is the velocity of the ball at the bottom of the rail?




Example  11

Figure shows a trolley  is released from a rest at point X  through a   frictionless  inclined plane.


What is the velocity of the trolley at point Y.



Example 12

Figure shows a ball moves on a frictionless curve track with a velocity 6 ms-1 at point A.



What is the velocity of the ball when it reaches at point B?




(c) The Definition and S.I. unit of Power (P)

Power is the rate at which work is done or

Power is the rate at which energy is changed or transferred.

@     P =  W      or   P = Fs     = F v

                 t                         t

@     P = E 



P = Power  , W = Work, E = Energy , t = time   v = velocity

The S.I. unit of power is   Watt(W)

1 W  =  1 Js-1

Example 13

A  monkey of mass 20 kg  climbs a coconut tree of height 15 m  in 2.5 s. What is the power of the monkey?




(d) The Definition of Efficiency

Efficiency = useful energy transferred   x  100%

                   total energy supplied

                =  useful energy output      x 100%

                      energy input


Example 14

A man pulls a box of mass 8 kg with a total force 100 N. After pulled for 5 m ,the box is moving at a speed of  6 ms-1. Calculate the efficiency with which the man is using his energy to pull the box.






Example 15

A crane lifts a load of 400 kg to a height of 100 m in 20 s. If the power input is 25 000 W, calculate

(a)           the useful energy output

(b)           the energy input

(c)           the efficiency of the crane



(e) Appreciating the importance of maximising the efficiency of devices.

Energy conservation demands that the total energy  output of a machine or device must equal its energy input.

However , when we measure the energy output as work done on the load by a machine or device, we find it is less than the energy input

It is because the machine or device also does work against frictional forces and sometimes does work in moving itself.

The work done against friction converts input energy into wasted heat energy and a little noise energy.

So the energy equation now looks like this:

Energy      =  useful energy    +    wasted energy

Input                   output                      output

Maximising the efficiency of machine or device makes the best use of the input energy and reduces wasted energy output.

     Maximising the efficiency of machine and device can helps

(a)     to conserve  resources since  fossil fuels such as coal, petroleum and natural gas are  non-renewable resources


(b)     to protect the enviroment  from deforestation,oil spills and radioactive wastes

(c)     to reduce the emission of air pollutants and greenhouse gases from power stations

(d)     to reduce the energy bill

The following are  several ways of increasing the efficiency of machines and devices


                Moving surfaces are made as smooth as Possible.

Lubricants such as oil and silicone are used to separate surfaces.

Rollers and ball bearings are used to separate rotating axles from their mountings.

Cushions of air  are used as elastic lubricant.

Machines which move through fluids are made streamlined in shape to reduce the frictional drag.


Heat engines:


Heat engine must be designed  with capability to do a greater  amount of mechanical work while discharging waste heat at a lower temperature.


                Electrical devices:

                (i) Lamp:

          A  fluorescent lamp is more efficiencient than a filament light bulb.

Use a lamp with a reflector so that the illumination can directed to  specific area.

     A lighting of a room should depend on the  size of the room.

 (ii) Water heater

      When having a shower during a hot weather, a lower temperature is needed

 (iii) Refrigerator

       The doors of the refrigerator must always be shut tight.

        Thermostat should be used in refrigerator to control the temperature

                  The power of refrigerator needed depend on the size of the family.

Another ways:

Recycling also conserves energy resources. Recycling  saves energy because we do not have to make new bottles, papers e.t.c.


3 Responses

  1. May i know the solution for checking?

    • Frau, i hope u can work out the example then email it to me, i will check and comment your work, TQ.

  2. totally simple n compact!!! thank you so much…

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