CITE BLACK HAWKS : NDMC SIDLAK 2012 CHEER DANCE CHAMPION

GO GO GO GO CITE BLACK HAWKS, the 2012 CHEER DANCE CHAMPION . . . .

Work, Energy and Power

    Pedal Bicycle Generator

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 position or elevation.  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  -- main source                                                 

         2. Wind                                      

         3. Water   

         4. Geothermal 

         5. Nuclear    

         6. Fossil fuels ( coal, oil natural gas) 

                                                 

    

 Forms of energy :

         1.  Chemical energy                          

         2.  Electric energy

         3.  Thermal / Heat energy (internal energy)

         4.  Mechanical energy

                          Forms :  a) kinetic and  b) potential energies 

         5.  Nuclear energy 

         6.  Light energy (solar/ Radiant  energy)  

         7.  Atomic / molecular energy 

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 F_x 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.  

            E_p = 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, E_p undergoes transformation to kinetic energy, E_k.  

       E_p =  E_k = mg ( v²/ 2g ) =  ½ mv² ,  kinetic energy

     E_p = 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 ( 4.8 km/hr)	3.80	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 :

        E_k + E_p + E_o = constant  ==> E_ki  +  E_pi  + E_oi  =  E_kf  +  E_pf  +  E_of

where the subscript i  and f  denote initial and final energies. E_k represents kinetic energy, E_p represents potential energy and  E_o represents all other forms of energy.  In the treatment of the equation if  the E_o is constant, then E_oi = E_of and the equation can be reduced to E_ki  +  E_pi =  E_kf  +  E_pf. 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 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 

Units of Power

     In the U.S. the watt and the kilowatt are used exclusively in connection with the electric power and horsepower is reserved for  mechanical power. This  practice  is purely  a  convention  and  by  no

means necessary. The unit watt is in honor of James watt.  1 J / s  = 1 watt.   
1 kilowatt = 1000 watts 

 1 horsepower (hp) = 550 ft-lbs / sec = 33,000 ft-lbs/min = 746 watts = 0.746 kw

     In the British Engineering system, power is expressed in ft– lb  per  second but more often is given in horsepower. The origin of the Hp started when James Watt was trying to sell steam engines for the British Coal Mines. He was asked how many horses would be replaced by his engine. Watt found out that on the average, horses were doing about 550 ft-l b/s work, then he called this unit one hp. He measured the rate at which his steam engines could work and rated them in horsepower.     

     1. A 75 kg man climbs a flight of stairs 5.25 m high in 15 seconds. Determine the power developed in watts and horsepower. What is the power developed if the man is running up the stairs in  5  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.

Power Billing

     The equation P = W/ t  can be solve for work:  W = P t . The kilowatt– hour  unit used by electric companies in billing is a unit for work, where power is in kilowatt and time is in hours.  The bill is for the amount of work that has been done to the consumer. The cost of the work done is obtained by multiplying the total energy consumption by the rate per kilowatt-hour. 

                        W = P t ,          C = W r 

             where : P = power in kilowatt,  t = time in hours ,  C = cost or amount of electric bill in P 

                           r = energy rate per kilowatt-hour 

   Ex. 1. Determine the total energy consumed in kilowatt-hour for loads of  a) one 1.5 hp air conditioning machine operating at 6 hours per day and 26 days per month, b) two 200 w computer operating 4 hours a day and 26 days per month, c) five 20 w lamps operating 4 hours a day and 30 days per month and d) one 150 w tv set operating 7 hours a day, 30 days per month. If energy rate is P 6.75  per kilowatt-hour, what is the bill for the month.   

 
         2.  A 1000 watts oven toaster operates for 6 hours per month. Determine the total energy consumed and the cost of energy for the month in kilowatt hour and in pesos if energy rate is P 6.75 per kilowatt-hour.

    INTERACTIVE SIMULATION ON PROJECTILE MOTION

Lesson 3 : Gravity and Falling Bodies

GRAVITY AND FALLING BODIES

Gravity is one of the most familiar forces in nature; its effect on motion has been a subject of discussion for centuries. If an object is dropped from a great height, it can be observed that it falls with ever increasing speed until air resistance balances the effect of gravity, at which time it is said to have reached its terminal velocity. The term free falling bodies is used for objects that are moving freely under the influence of gravity, whether they are moving upward or downward. Any object that has no forces other than gravity acting on it is said to be in free fall, whether it is moving upward, downward, or in any direction.

        It is found that if air resistance can be made negligible, then falling bodies will accelerate toward the center of the earth at the same rate, regardless of their mass. The value for the acceleration of gravity, given the symbol g, has been measured on earth as  g =  9.8 m/s².  Galileo was the first to demonstrate that all bodies fall at the same rate if air resistance is negligible. ( It is often said that he did this by dropping objects of various masses from the Leaning Tower of Pisa, although there is no historical evidence that he actually used the famed tower.) Galileo’s recorded experiments settled some very old controversies about falling bodies, proving less-popular ideas to be correct.

        Even more important than his discoveries about falling objects was his breaking away from old methods of determining truth. Galileo is often credited with being the Father of Modern Science because of his forceful demonstration of the value of observation and the discoveries he made through his ingenious experiments.

        The following is a data from one of Galileo’s earliest experiments of a ball rolling down an inclined plane. His data were recorded on his notes. Galileo held a ball at the top of an inclined, grooved board and marked its position. Releasing the ball, he marked its position at the end of equal intervals of time. This is much like dropping a ball from a height, except that the effect of gravity has been “reduced” by allowing the ball to roll slowly down the inclined board rather than falling straight down. The position as measured by Galileo are given in the following table :

Time t (equal intervals)	t2	Distance  S  (points)	S/ t2
1	1	33	33.0
2	4	130	32.5
3	9	298	33.1
4	16	526	32.9
5	25	824	33.0
6	36	1192	33.1
7	49	1620	33.1
8	64	2104	32.9

       The observations show what was already known quantitatively to Galileo and others of his time – that a rolling (or falling) object picks up speed as it continues to roll (or fall). However, the debt we owe to Galileo is for his careful measurements and his quantitative (mathematical) interpretation of the data. His object was to find a general rule describing how distances increase with increasing time of fall. After some trial and error, and with considerable insight, Galileo realized that the distance traveled was proportional to the square of the elapsed time.

                                                        S at²  ==>   S = h = ½ at²    

 Problems  

       1. A ball is thrown vertically up with an initial velocity of 15 m/s. How high does the ball rise from its projection point ? How long does it take for this ball to reach the highest point. How high does it go in 2 seconds ? in 3 seconds ?  What is the time required to travel a height of  9 m ?  5 m ?   

          Ans. ( 11.48 m ,  1.53 s , 10.4 m ,  0.9 m , 0.82 s ,  2.24 s ,  0.38 s ,  2.68 s )

       2. A rock is dropped from a bridge 55 m high relative to the water of a river below. How long will it take for the rock to reach the surface of the water ? Calculate the positions of  the rock  0.5s,  1.25 s, 2s after it was release relative to the water.  

       3. A metal sphere is dropped from a 50 m high tower. Determine the height traveled by the  sphere in the time interval from 0.25 s  to  1.25 s. 

     4. "Khalifa Tower", pronounced in English (/ˈbɜrdʒ kəˈliːfə/), known as Burj Dubai before its inauguration, is a skyscraper in Dubai, United Arab Emirates. It is the tallest man-made structure in the world, standing at 829.8 m (2,722 ft).  If an object falls from the top of this tower,  how many seconds does it reach the ground ?  What is the height travelled by the object in the interval  between  6 seconds and 10 seconds after falling?