__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.

or

**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

force-displacement.

__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.

__Solution __

Example 2

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

Calculate the done on the ice cube?

__Solution __

__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.

__Solution __

__(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.

__ __

__Solution __

__Kinetic Energy ( E___{k}__ ) __

Kinetic energy is the energy possessed by a moving object.

**E _{k} = ½ mv^{2} m = mass , **

** v = velocity **

__Example 5 __

A bullet of mass 0.02 kg moves at a velocity 150 ms^{–}^{1} .

What is the kinetic energy of the bullet ?

__Solution __

__Example 6__

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

__Solution __

__Gravitational Potential Energy ( E _{g})__

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

**E _{g} = 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?

__Solution __

__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?

__Solution __

__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?

__Solution __

__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?

__Solution __

__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.

__Solution __

__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?

__Solution__

__(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 **

** t **

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?

__Solution __

__(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.

__Solution __

__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

__Solution __

__(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

*Machines: *

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.

Filed under: Fizik |

Frau, on 05/03/2017 at 1:58 pm said:May i know the solution for checking?

amimo, on 06/03/2017 at 10:08 am said:Frau, i hope u can work out the example then email it to me, i will check and comment your work, TQ.

bluRr, on 11/06/2011 at 1:40 pm said:totally simple n compact!!! thank you so much…