Unit 5: Work, Energy and Power — Long Questions

Work Force and distance are two essential elements of work. When a constant force acting on a body moves it through some distance, we say that the force has done work.

Definition Work is defined as the product of magnitude of force and the distance covered in the direction of force.

Explanation Consider a block of wood lying on a table (Fig 5.1). If we exert a force F on the block to move it through a distance S in the direction of force, then the work W done by the force is:

Work = Magnitude of force × Distance

Or
W = F × S ........ (5.1)

Cases of Work

i. From above expression it is clear that if some force is acting on a body but there is no displacement, then no work is done. For example, a man is pushing hard a wall but the wall remains fixed in its place. In this case, the man is doing no work.

ii. Similarly, if a force acting on the body is zero and the body is moving with uniform velocity, work will be zero.

As F= 0 so W = 0 × S = 0

iii. If a force is acting on a body making an angle θ with the direction of motion. In this case, work is done due to the component of force which is acting along the direction of motion (Fig 5.3). Resolving the force F into its components, we have the component F cosθ that acts in the direction of motion. Therefore,

W = (F cosθ) S

Or W = FS cosθ ........ (5.2)

Special cases

i. If θ is zero, cos 0° = 1, then W = FS (1) = FS
This is the case when force and distance covered are in the same direction.

ii. If θ = 90°, then cos90° = 0 which means the force has zero component in the direction of motion. Thus, W =FS (0) = 0
This is the case when force is perpendicular to the displacement. Look at (Fig. 5.4). It suggests that if a person carries a bag to some distance, this work is zero, because the force applied to hold the load is upward which is perpendicular to the displacement.

Work done is a scalar quantity:
The work done to push an object is the same whether the object moves North to South or East to west, provided the magnitude of force and the distance moved are not changed. Work does not convey any directional information, so it is a scalar quantity.

Calculation of Work Done by Graph:
When a constant force F acts through a distance S, the event can be plotted on a force-distance graph as shown in fig. 5.5. If the force and distance covered are in the same direction, the work done is F×S. Clearly the shaded area in the figure is also F×S. Hence the area under a force distance curve can be taken to represent the work done by that force.

Units of Work The SI unit of work is joule (J).

One joule work is done when a force of one newton acting on a body moves it through a distance of one metre in its own direction.

From Eq. (5.1)
1 J = 1 N × 1 m

Or 1 J = Nm

Bigger units are also used like 1 kJ = 10³ J and 1MJ = 10⁶ J

Energy Our body cannot move unless we have energy from food. A car would not run without the energy it obtains from burning fuel. Machines in the factories cannot run without consuming energy supplied by electricity. Any change in motion requires energy. When we say that a certain body has energy, we mean that it has ability of doing work.

Definition Energy can be defined as the ability of a body to do work.

Explanation When someone does work, energy of the body has to be spent. In fact, energy is transferred from one system to another. For example, when you do work pushing a swing, chemical energy in your body is transferred to the swing and appears as energy of the motion of the swing.

Nature of quantity Like work, energy is scalar quantity. Its SI unit is joule (J).

When one joule work is done on a body, the amount of energy spent is one joule.

Forms of Energy There are many forms of energy. Electrical energy, chemical energy, nuclear energy, heat energy and light energy are some well-known forms which we shall study later on.

Basic form of Energy There are two basic forms of energy:

(i) Kinetic Energy
(ii) Potential Energy

The combination of these two types of energies is called mechanical energy.

Definition The kinetic energy of a body is the energy that a body possesses by virtue of its motion.

Explanation To find out how much kinetic energy a moving body possesses, an opposite force can be applied on the body to stop its motion. Then the work done by the force will be equal to the kinetic energy of the body i.e. Kinetic energy (Ek) = Work done (W)

Suppose a body of mass m is moving with velocity v. An opposing force F is acting on the body through a distance S brings it to rest. Then,

Ek = work done = F×S

As from Newton's Law F = ma and S = vav × time = (v+0)t = v ×t
2 2

Hence, Ek = ma × vt = 1 ma × vt
2 2

Using velocity-time graph, (Fig 5.7) the acceleration 'a' is given by its slope.

Hence, a = v , the slope is negative as the velocity and force are in opposite direction. (We take its magnitude positive.)
t

Thus Ek= 1 m(v )vt
2 t

Or Ek= 1 m v² ........ (5.3)

Potential Energy

Definition Potential energy is defined as the energy that a body possesses by virtue of its position or deformation.

Explanation In the previous section, we have seen that the work done on a body is used to increase its kinetic energy. Sometimes, the work done on a body does not increase its kinetic energy, rather it is stored in the body as potential energy.

Forms of Potential Energy There are many forms of potential energy. As mentioned above, the energy possessed by an object by virtue of its position relative to the Earth is known as gravitational potential energy.

The energy stored in a compressed or stretched spring is called elastic potential energy and the potential energy in the chemicals of a battery is called chemical potential energy, which is changed to electrical energy by chemical oil or gas through chemical reaction.

Nuclear energy is the hidden energy in the nuclei of atoms. When they are broken, energy is released in the form of heat and some other radiations. This is called nuclear fission.

Derivation of expression If the block shown in Fig. 5.8 is lifted to a height h above the ground, then the block would have potential energy in that raised position. Therefore, it has the ability to that work whenever it is allowed to fall. The potential energy is measured by work done on the block. Thus, potential energy Ep is given by

Ep = Work done to put the block in elevated position

The applied force necessary to lift the block with constant velocity is equal to weight w of the block and since w = mg, therefore, potential energy of the block at height h becomes,

Ep = wh

Or
Ep = mgh ........ (5.4)

Example The most obvious example of gravitational potential energy is a waterfall (Fig. 5.9), water at the top of the fall has potential energy. When the water falls to the bottom, it can be used to run turbines to produce electricity and thus can do work. (remains constant)

Conservation of energy

Statement Energy cannot be created or destroyed. It may be transformed from one form to another, but the total amount of energy never changes.

Explanation During energy transfer process, some energy seems to be lost and not accounted for in calculation. This loss of energy is due to work done against friction of the moving parts in the process. This energy appears as heat and is dissipated in the environment. This energy does not remain available for doing some useful work and may be called waste energy.

A process of energy conversion and conservation can be described with the given example.

Let a body of mass m be at rest at a point A above the height h from the ground (Fig 5.10). Its total energy is P.E is mgh,

Ep = mgh
and
Ek = 0

Then the body is allowed to drop to point B at a height 'x' from the ground. The body lose potential energy and gains kinetic energy as it gets speed while falling down. Assuming air resistance negligible.

Ep = mg(h - x)

The loss of potential energy will appear as the gain in kinetic energy, hence, at point B

Ek = mgx

Total energy at B Ek= mg(h - x) + mgx = mgh

Just before hitting the ground at point C, the whole of potential energy is changed into kinetic energy. Thus,

Ep = 0 and Ek = mgh

Thus, total energy remains the same as mgh. On hitting the ground, this energy is dissipated as heat and sound in the environment.

**Fossil Fuels**

Explanation The burning of these fuels gives out heat which is used to generate steam that runs the turbines to produce electricity. A block diagram of the process going on in electricity generation by fossil fuels is give in Fig. 5.11.

**Hydraulic Generation**

Hydraulic generation is the electricity generated from the power of falling water.

Explanation Water in a high lake or reservoir possesses gravitational potential energy stored in it. When water is allowed to fall from height, the potential energy is changed into kinetic energy (Fig. 5.12). Tunnels are made for water to flow from the reservoir to a lower place. Such a construction is known as dam.

The kinetic energy of running water rotates the turbine which in turn runs the electric generator.

**Solar Energy**

Sun is the biggest source of energy. The energy obtained from sunlight is referred to as solar energy.

Explanation Uses

Solar energy can be used in two ways either it can be used for heating system or can be converted to electricity.

(i) In one way, solar panels absorb heat of the Sun. They consist of large metal plates which are painted black (Fig. 5.13). Heat can be used for warming houses or running water heating system. If solar radiation is concentrated to a small surface area by using large reflectors or lenses, reasonably high temperature can be achieved.

At this high temperature, water can boil to produce steam that can run the turbine of an electric generator. In this way, electricity can be produced.

(ii) In the second method, sunlight is directly transformed to electricity through the use of solar cells. Solar cells are also known as photo voltaic cells. The voltage produced by a single voltaic cell is very low. In order to get sufficient high voltage for practical use, a large number of such cells are connected in series to form a solar cell panel as shown in Fig. 5.14 Solar calculators are also available which work by using the electrical energy provided by solar cells. Large solar panels are also used to power satellites.

**Nuclear Energy**

Nuclear energy is released in the form of heat when an atomic nucleus breaks. Nuclear power stations make use of nuclear fuels such as uranium and plutonium.

Explanation These materials release huge amount of energy as the nuclei of their atoms break during nuclear fission. The process is done in a nuclear reactor. Heat produced by the fuel is used to make steam that runs the turbines of electric generators. Pakistan also runs nuclear power stations at Karachi and Chashma.

**Geothermal Energy**

In some parts of the world, hot rocks are present in the semi molten form deep under the surface of the Earth. They are heated by energy released due to decay of radioactive elements. The temperature of these rocks is about 250°C. This energy is known as geothermal energy which can be extracted to run electric generators. A typical geothermal power plant is shown in Fig. 5.15.

Mechanism to extract energy

To make use of the heat of the rocks, two holes are drilled up to the rocks. Cold water is pumped down through one of the holes. It is heated up by the hot rocks and starts boiling. Steam is produced that comes out through the other hole. The steam runs the generator which produces electricity. Where there is water already present over the hot rocks, it comes out of the surface of the Earth in the form of hot springs and geysers. Such a geyser is shown in fig. 5.16.

**Wind Energy**

For thousands of year, people have been using windmills to draw water from the well or to grind grains into flour. The modern windmill used to run generators that produce electricity. Wind generator make electricity. Wind generators make electricity in the same way as steam generators in power stations. For large scale power generation, a 'wind farm' with a hundred or more windmills is needed. A windmills farm is shown in Fig. 5.17.

**Energy form Tides**

The gravitational force for the moon gives rise to tides in the seas. The tide raises the water level near the sea shore twice a day. The rise and fall of water can utilized to turn on turbine for electricity generation. The water at high tides can be trapped at a suitable location, a basin, by building a dam. The water is then released in a controlled way at low tide to drive the turbines for producing electricity. At next high tide, the dam is filled again and the incoming water also drives turbines.

**Energy from Waves in Sea**

The tides and winds blowing over the surface of the sea produce strong water waves. Their energy can be used to generate electricity. The method to harness wave energy is to use large floats which move up and down with the waves. One such device invented by Prof. Salter is known as Salter's duck (Fig.5.18). It consists of two parts.

(i) Duck Float

(ii) Balanced Float

The energy of the water waves causes duck float to move relative to the balance float. The relative motion of the duck float is used to drive the electricity generator.

**Biofuel Energy**

It is that energy which is obtained from the biomass. Biomass consists of organic materials such s plants, waste foods, animals dung, sewage, etc. Sewage is that dirt which is left over after staining dirty water. The material can itself be used as fuel or can be converted into other types of fuels.

Methods

(i) Direct combustion is a method in which biomass, commonly known as solid waste, is burnt to boil water and produce steam. The steam can be sued to generate electricity.

(ii) In another process, the rotting of biomass in a closed tank called a 'digester' produces methane rich biogas (Fig 5.19). In this process, micro-organisms break down biomass material in the absence of oxygen. Biogas produced in the tank is piped out and can be used for heating and cooking like natural gas. Biofuel such as ethanol (alcohol) can also obtained from the biomass. It is a replacement of petrol. In this case, bacteria convert it into ethanol.

Renewable Sources The resources of energy which are replaced by new ones after their use are called renewable energy sources. On the other hand, non-renewable sources are those which are depleted with the continuous use. Once they run out, they are not easily replaced by new ones. Sources such as hydroelectricity, solar energy, wind energy, tidal energy, wave energy and geothermal energy are renewable. These are replaced by new ones. For examples, snow fall and rain fall are continuous processes. Therefore, water supply to the reservoirs of dams for generation of hydroelectric power will never end up. Likewise, solar energy will remain available forever. Same is the case with wind and tidal energy. These are not going to run out in future.

Non-Renewable Sources Non-renewable sources include fossil fuels and nuclear energy. The remnants of plants and animals buried under the Earth took millions of years to change into fossil fuels. These fuels are in limited quantity. Once they are used up, it will take further millions of years to form new ones. Similarly, fuel for the nuclear energy are also limited.
As the need for energy is increasing day by day, there is need to develop other non-traditional renewable energy sources.

The Advantages and Disadvantages of methods of Energy production:

Advantages (i) The production of hydroelectric power is more economical and pollution free.
(ii) The solar power, wind, tidal and wave power need more initial cost but they do not produce pollution and are also economical as well.

Disadvantages (i) On the other hand, power generation by fossil fuels and nuclear fuel adds to the pollution of environment. Burning of fossil fuels produces smoke, carbon dioxide gas and heat (Fig. 5.20). They enhance direct pollution to atmosphere.
(ii) Wind-mills are very noisy. Some people think that wind turbines spoil the beauty of landscape.
(iii) Nuclear power generators are also run by steam produced by nuclear heat energy. Heat itself is a form of pollution. Moreover, there is always danger of leakage of the radioactive radiation which is harmful to living bodies. People living around the nuclear plants are always at risk. The disposal of nuclear waste is energy ends up as thermal energy that goes to the environment. Thus, thermal pollution is increasing day by day causing global warming.

Definition Power is defined as the time rate of doing work.

Mathematically,
Power = Work / Time

If W is the work done in time t, then
P = W / t .......(5.5)

Power of any agency can also be defined as energy transferred per unit time.

Units of Power Since both work and time are scalar quantities, so according to Eq. (5.5) power is also a scalar quantity. The SI unit of power is watt (W).

One watt is the work done at the rate of one joule per second.
1 W = 1J / 1s or 1Js^-1

Bigger Units of power are:
1 kW = 10³ W
1MW = 10⁶ W

In British engineering system, the unit of power used is horse-power (hp). The horse power is defined as
1 hp = 746 W

Explanation In many cases, the time to do work is as important as the amount of work done. Suppose you walk up to a height 'h' through upstairs (Fig. 5.21). You do work, because you are lifting your body up the stairs. If you run up, you can reach the same height in a shorter time interval.
The work done is the same in either case, because the net result is that you lifted up the same weight w to the same height h. But you know that if you run up the stairs, you would be more tired than you walked up slowly. In fact, there is a difference in the rate at which work is done. We say that you expend more energy when you go up the stairs rapidly than when you go slowly.
The concept of power can also be explained with another example of an electric motor or a water pump. A bigger motor draws more water during the same interval of time as compared to a smaller one. It is said that the power of bigger motor is greater than that of smaller one.

Definition The efficiency of a system is defined as:
The ratio of useful output energy and the total input energy is called the efficiency of a working system.

Or
Efficiency (n) = Useful output energy / Total input energy

%age efficiency:
Efficiency is often multiplied by 100 to give percentage efficiency. Thus,
Percentage Efficiency = (Useful output energy / Total input energy) × 100

It can also be given as:
Percentage Efficiency = (Useful power output / Total power input) × 100 ......(5.6)

Efficiency is less than 100% It is found that the energy output is always less than the energy input. During any conversion of energy, some energy is wasted in the form of heat. NO device has yet been invented that may convert all the input energy into required output. That is why a system cannot have an efficiency of 100 %. As the energy loses are inevitable in the working of a machine, hence, an ideal or perpetual machine cannot be constructed.

Efficiency • The efficiency of a working system tells us what part of the energy can be converted into the required useful form of energy and what part wasted out of the energy available.
• The available energy for conversion is usually called the input energy and the energy converted into the required form is known as the output energy

It is a hypothetical machine that can do work indefinitely, without any external source of energy. A perpetual machine would have to generate more energy than it consumes, effectively producing energy from nothing, which is impossible. In any real mechanical system, some energy is always lost as heat due to friction between moving parts and air resistance etc. Thus, making it impossible for a machine to keep moving without an external source of energy. Infact, it is a consequence of the principle of conservation of energy that I perpetual energy machine is not workable.