Work, Energy and Power

Work, Energy and Power

• Work:
Work is said to be done on an object when it moves under the influence of a force. The following statement gives the definition of work:
“Work done by a constant force is given by the product of the force and the distance moved in the direction of the force.”

In equation form,

W = F*S
Where, W = work done by a constant force
F = constant force
S = distance moved in the direction of the force.
The SI unit of work is Joule (J). From the equation W = F S, the relation between the units for work, force and displacement is given by,
1 Joule = 1 Newton 1 Meter

In symbol, 1 J = 1 Nm

One joule is defined as the work done by a force of one newton which moves an object through a distance of one metre in the direction of the force.








In the above figure the directions of the force and the displacement are not same. In this case work done depends on the angle between the force and the direction of displacement.
Here, Work done = Force displacement Cosine of the angle between force and displacement.


where, is the angle between force and displacement.

Exercise: 1: A person is pushing a trolley in a supermarket. If the force exerted by him on the trolley is 30 N and the trolley moves a distance of 5 m in the direction of the force, calculate the work done by the force on the trolley.


Exercise: 2: An object being lifted from the floor onto a table top which is 2 m above the ground. If the lifting force is 10 N, calculate the work done by this force on the object.

Exercise: 3: In fig – 2 if F = 13.9N and, S = 4m angle between F & S is = 300 then what will be the work done by the force F. Again if / = 450 and // = 600, calculate W.


• Energy:

Anything which is able to do work, is said to possess energy, and therefore,
“Energy is the capacity to perform work.”
The SI unit of energy is therefore joule (J).

• Some forms of energy :

1. Chemical energy Fuels such as oil, wood, coal, electric cells, food and explosives.
2. Nuclear energy Atomic bombs, nuclear reactors.
3. Radiant energy The electromagnetic (E.M) spectrum such as visible light, radio waves, infra-red radiation, ultraviolet radiation, X-rays and gamma rays.
4. Electrical energy The energy associated with the current in electric drills, power tools etc.
5. Internal energy The energy possessed by the atoms or molecules of matter in the form of kinetic energy and potential energy.
6. Mechanical energy:
a. Kinetic energy: all objects in motion.
b. Potential energy: a water fall, raised objects.
• Mechanical energy:
The two types of mechanical energy that a body may possess are kinetic energy and potential energy.
a. Kinetic energy:
Kinetic energy is the energy possessed by a body by virtue of its motion. In other words, any moving object has kinetic energy.
The defining equation for kinetic energy is
Ek = ½ mv2 where, Ek = kinetic energy (in J)
m = mass of the moving body (in Kg)
and v = speed of the body




(1) For two objects of the same mass moving at different speeds, the faster objects have greater kinetic energy.
(2) For two objects of different masses but moving at the constant speed, the object of greater mass has greater kinetic energy.
Exercise: 4: A bullet of mass 0.02 kg travels at a speed of 1200 m/s. Calculate its kinetic energy.
b. Potential energy:
Potential energy is the energy possessed by a body by virtue of its position or condition.
For example, an object raised above the ground has gravitational potential energy by virtue of its raised position while a stretched rubber band has elastic potential energy by virtue of its stretched condition.
An object of mass m being lifted vertically,
without acceleration, from the ground level to another
level of height h.

Work done by force, F is
W = F* h
But, F = mg
,
This is the gravitational energy of the object.

Exercise: 5: A 5 kg mass is lifted vertically through a distance 10 m. What is the gravitational potential energy gained by the object?
• Conservation of energy:
The principle of conservation of energy states that:
“Energy can neither be created nor be destroyed in any process. It can be converted from one form to another or transferred from one body to another, but the total amount remains constant.”
The following are some examples of the conservation and conversion of energy:
(1) A cyclist going up to the top of a hill.
(2) The burning of fuels such as oil, coal or wood.
(3) Connecting a battery to a filament lamp.
(4) Knocking a nail in to a wooden block with a hammer.
(5) A ball is released from a height.
• Interchange of energy between potential and kinetic energy

Let us look at the example of a pendulum (a bob suspended by a thin string) swinging back and forth. When the mass stops for an instant at the highest point of its swing, it has no kinetic energy. The energy is all potential. When the mass is at the lowest point of its swing, its velocity is greatest and its potential energy is lowest. The energy is all kinetic. The pendulum keeps swinging reaching a point where energy is again all potential. Thus during the course of the motion the energy has changed from potential to kinetic an back to potential, but the total amount of energy has not changed.
The pendulum can continue swinging for a long time, with the mass swinging back to the same height each time. The sum of the kinetic and potential energy is always same. This sum of pendulum’s potential and kinetic energy is called its mechanical energy.
Mechanical energy = potential energy + kinetic energy
E = PE + KE













• Efficiency:
The principle of conservation of energy suggests that the total energy output of a machine must be equal to its energy input. But it is found that the energy output is always less than the energy input i.e. some energy is wasted.

Energy input = useful energy output + wasted energy output.





Therefore, Efficiency of any machine is ,

%

• Power:
Power is defined as the rate of working or energy converted.


Where, P = power
W = work done
E = energy converted
t = time taken.
The SI unit of power is Watt (W)

1 Watt =

One watt is defined as the rate of working or energy conversion of one joule per second.
Exercise : 6: An electric heater is rated at 250 W. calculate the quantity of heat generated in 10 minutes.
Exercise : 7: An electric motor in a washing machine has a power output of 1.0 KW. Find the work done in half an hour.
Exercise : 8 An object of mass 50 kg is lifted to a height of 2m above the ground. What is the potential energy? If the body is allowed to fall find its kinetic energy (a) when it is half way down; (b) just before the impact with the ground.
What has become of the original energy when the body has finally come to rest?
Exercise : 9 A man whose mass is 60 kg walks up a flight of 12 steps each 20 cm high in 5 s . Find the power he develops.
Exercise : 10 A cable car is pulled up a slope by a constant force of 5000 N at a uniform speed of 6 meters per second. It takes the car 4 minutes to complete the journey
(a) How much work is done in getting the car to the top of the slope?
(b) How much work would be done if the speed were 12 metres per second ( the force remaining the same)
(c) How does the power developed compare in (a) and (b)?

Explain why “A 100 W lamp is more powerful than a 60 W lamp.”