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the head falls, and when it strikes the top of the pile it delivers the same amount of kinetic energy that it had of potential energy when it started. That is, its kinetic energy equals its potential energy. A simple way to compute kinetic energy is to find how far the velocity of the moving body would carry it vertically upward and use that distance for h in the expression for potential energy.

75. Work. Whenever a force acts upon a body in such a way as to move it, or to modify its motion, work is said to be done. However great the force used, no work is done unless the body is moved. A man going upstairs, a boy playing ball, and a steam engine unloading a ship (Fig. 49), are all doing work.

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76. Measurements of Work. - The amount of work done varies directly as the force employed and the distance through which it acts. Hence the formula may be written


Work (22) There are four fundamental units of work, as follows, depending on the units in which F and S are expressed:

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Absolute Units

I. The erg is the work done by a force of 1 dyne acting through a distance of 1 centimeter.

II. The foot poundal is the work done by a force of 1 poundal acting through a distance of 1 foot.

Gravity Units

III. The kilogrammeter is the work done in raising 1 kilogram 1 meter vertically against the force of gravity.

IV. The foot pound is the work done in raising 1 pound 1 foot vertically against the force of gravity.


FIG. 49. Steam Engine ("Donkey Engine") unloading a Ship

Other units of work may be used, depending upon the conditions. Since the erg is a very small unit, a larger unit, called the joule, is sometimes used; 1 joule 107 ergs, or 10,000,000 ergs. The foot pound and the kilogrammeter are the units generally used in engineering work.

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pound oz. nearly.

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1 gram = 980.2 dynes.

1 kilogrammeter = 98,020,000 ergs.
1 kilogrammeter 7.233 foot pounds.

Formula 22 shows that if a man lifts a stone weighing 100 lb. 2 ft. high, the work done is 100 × 21 = 250 foot pounds, and that if an engine raises 12 kg. 20 m. high, the work done is 12 X 20 = 240 kilogrammeters.

77. Time is not an Element in Work. Too great stress cannot be put upon the statement that the time employed in doing a certain amount of work has nothing whatever to do with the amount of work done. When 1 lb. is raised 1 ft., exactly 1 foot pound of work is done, no matter whether the time taken in the raising is 1 second or 1 hour or 40 hours. The dealer who pays a lump sum for the unloading of a boatload of coal, pays for that alone, and not for the time that may be consumed by the use of an imperfect hoisting machine.

78. Time; Rate of Work; Horse Power. The work done in a given time, divided by the time, gives the average rate of doing work, or power.

The C. G. S. unit of power is the erg per second. In practical work the joule per second is used; this is called the

watt in honor of James Watt, the inventor of the steam


1 watt 1 joule per second
1 kilowatt

1 horse power 1 foot

1 pound 1 gram

In the F. P. S. system the unit of power is the foot poundal per second. This is a small unit and is seldom used, the practical unit being the horse power, which means a rate of 33,000 foot pounds per minute, or 550 foot pounds per second; hence the expression for horse power is


No. foot pounds

No. H. P. =

33000 X No. minutes


(23) This unit was introduced by James Watt and its value was assigned by him. It is the work that would be done in one minute by a horse walking at the rate of three miles per hour and raising a weight of 125 pounds at the same rate by a rope passing over a pulley. One horse power is rated at 746 watts or 0.746 kilowatts. Hence the horse power is practically three fourths of a kilowatt and one kilowatt equals one and one third horse power.

The kilowatt is used to measure the power output of electric generators, while the steam power input, used in engines or turbines, is measured in horse power or myriawatts (1 myriawatt = 10 kilowatts).


1 The relation between the horse power and the watt is determined as follows:


= 107 ergs per second.


1000 watts



550 foot pounds per second.

30.48 centimeters.

453.6 grams.

981 dynes.


(The number varies with the value of g; this is about the value for the latitude of Paris.)

Hence 1 horse power 550 x 30.48 × 453.6 × 981 = 7,459,671,542 ergs per second. Hence 1 horse power

745.97 watts.

In New York, g = 980.2 dynes one horse power = 745.36 watts.



1. Define work; energy; horse power; kilowatt. Illustrate


2. State the difference between potential and kinetic energy. 3. What is meant by conservation of energy? Transformation of energy? Give examples of the latter.

4. Can force be used without doing work? Give examples. 5. What element enters into rate of work or power, that does not enter into work?

6. A boy tosses a 2-lb. weight vertically upward with such a velocity that it rises for two seconds. What is its greatest kinetic energy? What is its greatest potential energy?

7. A 4-lb. weight was allowed to drop freely for 4 seconds. From what height did it fall? What energy did it acquire?

8. What is the kinetic energy of a 5-lb. mass having a velocity of 96 ft. per second?

9. How much work is done if a kilogram force acts upon a body and moves it 1500 cm.?

10. A 2-lb. ball falls for 2 sec. and rebounds a distance of 40 ft. How much mechanical energy has the ball lost? What has become of the lost energy?

11. A boy holds a 2-lb. stone in his hand. Is he doing any work? Does he do any work when he throws the stone What kind of energy does he give to the stone?

12. A horse pulling a load uphill gives out when halfway up and is only able to keep the load from sliding back. Is he doing any work? Why?

13. If he were unable to keep the load from sliding back, would any work be done? If so, by what force?

14. What transformations of energy take place in the working of a locomotive?


1. A force of 98 dynes acts through a distance of 16 cm. How many ergs of work are done?

2. How much work is done in carrying a ton of coal (2240 lbs.) up two flights of stairs, the total height being 21 ft.?

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