WORK, ENERGY AND POWER
ENERGY
The terms force and energy were not always clearly defined. Before the mid-nineteenth century, they were often used interchangeably. However, progress in mechanics and thermal physics helped clarify these ideas and the distinction between them. In 1807, the English scientist Thomas Young (1773 – 1829) introduced the word energy to denote the quantity of work that a system can do. Later, the Scottish engineer and thermal physicist W. M. J. Rankine coined the terms potential energy and conservation of energy. As is often the case in science, this classification of terms and definitions led to greater insights and understanding of natural laws and their consequences. Today the principle of conservation of energy is part of the framework of physical theory. Our faith in this principle is based on years of our experience.
Energy is a vital part of our daily lives. The food we eat gives our bodies energy for movement; electrical energy lights our homes and streets; oil and gas propel our cars and keep us warm. The use of energy is growing at an incredible rate. In the U.S. alone, energy demands have increased more than 250% since 1940. The increase maybe even more rapid in the years ahead. The energy demands are growing more rapidly than population itself. In other words, the use of energy per person is also rising.. The increase is largely a result of the improvement in the standard of living. The switch from human power to machine power has increased productivity and provided us with more goods and leisure time. Unfortunately, the use of labor-saving devices places serious demands on our available energy supplies.
The wise use of existing energy resources is one answer to this problem. By avoiding unnecessary use of energy for heating, lighting, air conditioning and transportation, serious energy shortages can be prevented.
Conservation of energy is only a partial answer, however; new energy sources must be found and developed in order to achieve and maintain a desirable living standard for the growing population of the world.
Actually, there is no shortage of energy at all. The sun floods the earth with enough radiant energy everyday to supply the whole world’s needs many times over. In fact, it has been calculated that present worldwide demands could be met if we could completely convert into electrical power the solar energy falling on a plot of ground near the equator at a mere 125 miles square ( 201.1 km square ). It has also been estimated that the Gulf Stream in the Atlantic Ocean transports enough warm water to generate the electric energy needs of the U. S. many times over.
The shortage lies in our knowledge and our means to convert the ample energy supplies in and around our planet into usable forms.
Many sources of energy on the earth come directly from energy radiated from the sun. Coal and oil, the fossil fuels, were formed from the sun millions of years ago. Hydroelectric power depends upon dammed-up rain water that was evaporated from the sea by solar energy. Winds and ocean currents, potential sources of additional energy, are caused by solar energy.
Some energy sources cannot be attributed to the sun. Nuclear energy comes from changing matter into energy. Geothermal energy ( heat from the earth ) uses heat locked in rocks since the Earth was formed as a molten mass. The Earth’s rotation and the gravitational attraction between the Earth and the moon moves large masses of water on the earth. These movements of water are called tides. In some places such as the Rance river in France, tides are usefully harnessed.
The amount of radiant energy we receive from the sun each day is limited. Also, the amount of fossil fuel is limited. Research efforts to supply more energy have aimed at increasing our supply of solar energy, using our solar resources more efficiently, and increasing energy production from non-solar sources.
ENERGY is the capacity or ability to do work.
POTENTIAL ENERGY is an energy due to its shape or position. A body is said to have potential energy if by virtue of its state or position is able to do work. Water at the top of a hydraulic dam has energy due to its position.. As the water runs downhill through a turbine, the potential energy of the water is converted to electrical energy.
ELASTIC POTENTIAL ENERGY is an energy possess by a compressed or stretched spring.
KINETIC ENERGY is an energy of motion. The kinetic energy possess by a moving body is defined as the energy possess by the body by virtue of its motion.
Sources of energy :
1. Sun
2. Water
3. Nuclear
4. Wind
5. Geothermal
6. Fossil fuels ( coal, oil natural gas)
Forms of energy :
1. Chemical energy
2. Nuclear energy
3. Electric energy
4. Light energy (solar/ Radiant energy)
5. Heat energy / Thermal (internal energy)
6. Atomic / molecular energy
7. Mechanical energy
[ Forms : a) kinetic and b) potential energies ]
WORK
The word work means many different things to us in our daily lives. We say that we work when we sweep the yard, buy groceries or drive a car. We also work if we drag or push an object across the floor. How much work we do depends on how hard we push and how far we move the object. In a layman’s point of view, work is the expenditure on one’s stored up bodily energy. In the physical sciences, work is more precise and restricted than in everyday usage. Work is defined as the product of force and the displacement through which the force acts as the object moves.
Factors to be considered in measuring work :
1. There must be an applied force.
2. The force must act through a displacement, S.
3. The force must have a component Fx parallel to the direction of the displacement.
If an applied force is not along the direction of motion, we can resolve it into components parallel to and perpendicular to the displacement. Only the component of the force that is parallel to the displacement contributes to the work.
UNITS OF WORK
1. Joule ( J ) – one joule is the work done by a force of one Newton in moving an object through a parallel distance of one meter. 1 J = 1 N m
2. Erg – one erg is the work done by a force of one dyne in moving an object through a distance of one centimeter. 1 erg = 1 dyne . cm
3. Foot–pound (ft-lb) – one foot pound is the work done by a force of one pound in moving an object through a parallel distance of one foot.
W =FS cos θ , if the force and the displacement are oblique with each other
W = FS , if the force and the displacement are in the same direction.
When a mass m is lifted to a height h, the force exerted is equal to the weight of the mass, the work done against gravity approaches the potential energy and S h.
Ep = mgh , potential energy [ Work done against gravity ]
If the mass is release from rest the speed of the mass is given by v = √ 2gh , v2 = 2gh and h = v2/ 2g.
The potential energy, Ep undergoes transformation to kinetic energy, Ek.
Ep = Ek = mg ( v2/ 2g ) = ½ mv2 , kinetic energy
Ep = ½ ky2, elastic potential energy ; k = spring constant, y = elongation or deformation
CONVERSION OF MASS TO ENERGY
In his special theory of relativity ( 1905 ) Einstein concluded that mass and energy are interchangeable. The quantitative mass-energy relationship is given in his equation,
E = mc2 , where m = mass and c = speed of light = 3 x 108 m/ s.
Mass is converted into energy in nuclear rectors and nuclear weapons. As well as in the sun and other stars. For nuclear reactors using U235 as fuel, about 1/1000 of the mass of each fissioning atom is converted into other forms of energy. Although the fraction of our energy needs supplied by nuclear reactors on earth is relatively small, it is increasing rapidly as energy from oil and natural gas becomes less plentiful and more expensive.
THERMAL ENERGY OR INTERNAL ENERGY is associated with the random kinetic energies of the atoms and molecules in the object.
FOODS AND OTHER FUELS
Many of the most common energy sources are chemical in nature such as food, gasoline and natural gas. The energy content in foods are given in units of kilocalories. ( 1 kcal = 4186 joule ). For foods and fuels the process by which stored chemical energy is released is by oxidation. In machines, the oxidation process produces thermal energy which is partially converted to work and other forms of energy. In animals, the oxidation process is complex which also results both in thermal energy and work being performed by the animal. If the animal consumes more food than it needs, it will convert the excess to fat, which is another form of chemical energy. The chemical energy stored in fats is used if and when there is a food deficit.
Dieting to lose weight would mean reducing of the food energy intake. Exercise aids dieting partially because more food energy is converted to work.
CALORIC CONTENT ( kcal/g ) OF COMMON FOODS AND FUELS
COMMON FOODS kcal/g Eggs 1.63 Sirloin,lean 1.66
Apples 0.58 Grapes 0.69 Sugar 4.00
Avocado 1.67 Ham, cooked 2.23 Tomato 0.22
Baby formula 0.67 Hamburger,lean 1.63 Tuna,in oil 1.97
Beans, kidney 1.18 Ice cream,chocolate 2.22 Wine 0.85
Beer 0.42 Lard ( fat ) 9.30 COMMON FUELS
Butter 7.20 Lobster, raw 0.91 Coal 8.00
Carrots 0.42 Milk, whole 0.64 Gasoline 11.4
Celery 0.14 Milk, low-fat 0.42 Furnace oil 10.5
Cheese, cheddar 4.00 Oranges 0.49 Methanol 5.20
Cheese,cottage 1.06 Peanuts, roasted 5.73 Natural gas 13.00
Chicken,roasted 1.60 Peas 0.71 Wood (average)4.00
Chocolate 5.28 Potato, baked 0.93
coffee, black 0.008 Raisins 2.90 Average carbohydrates 4.10
Cola,carbonated 0.36 Rice,white,cooked 1.09 Average protein 4.10
Corn flakes 3.93 Shrimps,snails,raw 0.91 Average fat 9.30
ENERGY CONSUMPTION RATE for VARIOUS ACTIVITIES
ACTIVITY RATE(kcal/min) Playing tennis 6.30
Sleeping 1.20 Swimming breaststroke 6.80
Sitting at rest 1.70 Ice skating(14.5 km/hr) 7.80
Standing, relaxed 1.80 Climbing stairs(116/min) 9.80
Sitting in class 3.00 Cycling (21 km/hr) 10.00
Walking slowly(4.8km/hr)0.80 Playing basketball 11.40
Cycling (13–18 km/hr) 5.70 Cycling,professional racer 26.50 ELECTRIC ENERGY
Capacitor is a device which stores pure electric energy. Many electronic instruments, such as the heart defibrillators use capacitors to store energy. Fibrillation is a potentially fatal malfunction of the beating of the heart. The electric energy stored in the large capacitor of the defibrillator is used to cause an electric current to pass through the patient’s heart to stop fibrillation – that is, to defibrillate the heart. Ironically, electric current through the heart can also cause fibrillation, depending on the amount of current, it may even cause electric shock. Currents as low as 20 mA may cause difficulty in breathing, and at 75 mA breathing may stop completely. Currents between 100 and 200 mA results in ventricular fibrillation of the heart, which means an uncoordinated and uncontrolled twitching of the heart muscles. The resulting loss in pumping action is fatal. The defibrillator used in medical emergencies apply a large momentary voltage to the body to stop the heart and facilitate the restoration of the normal heart rhythm.
LAW OF CONSERVATION OF ENERGY.
Energy can never be created or destroyed, it maybe transformed from one form to another, but the total amount of energy never changes ( remains constant ).
Total energy is the sum of all forms of energy in a system : kinetic, heat, potential chemical, etc. Experiments have shown that the total energy in a closed system is always conserved. Energy can be transferred from one system to another if one system does work on the other. The conservation of energy can be written in the form :
Ek + Ep + Eo = constant Eki + Epi + Eoi = Ekf + Epf + Eof
where the subscript i and f denote initial and final energies. Ek represents kinetic energy, Ep represents potential energy and Eo represents all other forms of energy. In the treatment of the equation if the Eo is constant, then Eoi = Eof and the equation can be reduced to Eki + Epi = Ekf + Epf. The law of conservation of energy principle is very useful in solving problems. It can be applied to any closed system, where only the initial and final conditions need to be considered.
POWER AND EFFICIENCY
Power is the time rate of doing work. It is the rate at which energy is used or expended, since work done results in energy being transferred from one system to another. The SI unit for power is the joule per second ( J/s ), which is called the watt in honor of James Watt ( 1736 – 1819 ). 1 J / s = 1 watt.
Watt is a very familiar unit. All light bulbs and other electric devices are rated in watts.
The horsepower was defined by Watt as a unit for power. He was interested in describing the rate at which his steam engine could do work and defined his unit in terms of the common source of power, the horse. He found out that on the average, the horse was doing about 550 ft-lbs of work per second. He called this unit one horsepower and measured the rate at which his steam engine could work and rated them in horsepower.
P = W / t
1 horsepower ( hp ) = 550 ft-lbs / sec = 33,000 ft-lbs / min = 746 watts = 0.746 kW
1. A 60 kg man climbs a flight of stairs 3.25 m high in 8 seconds. Determine the power generated in watts and horsepower. What is the power developed if the man is running up the stairs in 3 seconds ?
Note : It is no wonder that running upstairs is so stressful and causes the body to utilize its available energy
very quickly. People with heart problems are warned that climbing stairs is one of the most stressful
acts that they can perform.
EFFICIENCY is the ratio of the output work to the input work express in percentage.
Eff = Wout / Win = Pout / Pin = Eout / Ein
EFFICIENCY in humans
Body processes in humans requires energy not only in doing physical work but also in blood circulation, digestion sleeping, thinking. The body can be thought of as an energy converter, with the source of energy being stored chemical energy ( food ) that the body converts into mechanical work and thermal energy and back into stored chemical energy ( fat ).
Metabolic rate – is the rate of conversion of food energy to some other forms of energy.
Basal Metabolic Rate ( BMR ) – is the total energy conversion rate of a person at rest which is divided among various systems of the body : (a) the liver and the spleen, (b) brain, (c) skeletal muscles, (d) kidney, (e) heart and (e) other organs – smooth muscles, intestines, bone marrow, lymphatic systems.
The BMR of an individual is related to thyroid activity. An overactive thyroid results in a high BMR and hyperacidity while an underactive thyroid leads to a low BMR and lethargy.
Energy consumption is directly proportional to oxygen consumption, since the digestive process is basically one of oxidizing food. Roughly, 4.9 kcal of energy are produced for each liter of oxygen consumed, independent of the type of food. The digestive process is quiet effective in metabolizing food, only about 5 % of the caloric value of foods is excreted in the feces and urine without being used by the body. The body stores excess food energy by producing fatty tissue. During rest, most of the energy consumption of the body ends up as thermal energy. Work done by the heart on the blood is converted to thermal energy by friction in the circulatory system, and most skeletal muscles activity is in the form of small motions during rest.
Basal Metabolic rate and oxygen Consumption rate
Organ Power Consumed Oxygen Per Cent Kcal/min
at Rest Consumption of BMR
w mLO2/min
Liver and Spleen 0.33 23 67 27
Brain 0.23 16 47 19
Skeletal muscles 0.22 15 45 18
Kidney 0.13 9 26 10
Heart 0.08 6 17 7
Others 0.23 16 48 19
TOTALS 1.22 85 250 100