=115. Conservation of Energy.=--In the study of matter we learned that it is indestructible. Energy is also believed to be indestructible. This principle stated concisely teaches that _despite the innumerable changes which energy undergoes the amount in the universe is unchangeable_, and while energy may leave the earth and be lost as far as we are concerned, that it exists somewhere in some form. The principle which teaches this is called the "Conservation of Energy." The form into which energy is finally transformed is believed to be heat.

Important Topics

1. Power defined. Units. Horse-power. Watt.

2. Transference and transformations of energy.

3. Forms of energy; heat, electrical, mechanical, radiant, chemical.

4. Effects of the several forms of energy.

5. Energy of the human body.

6. Conservation of energy.

Exercises

1. A boy weighing 110 lbs. ran up a stairs 10 ft. high, in 4 seconds.

How much work was done? What was his _rate_ of work (foot-pounds per second)? Express also in horse-power.

2. A locomotive drawing a train exerts a draw bar pull of 11,000 lbs.

How much work does it do in moving 3 miles? What is its _rate_ of work if it moves 3 miles in 5 minutes? Express in horse-power.[G]

[G] The following formula is of a.s.sistance in computing _horse-power_ in problems: H. p. = (lbs. ft.)/(550 sec.).

3. If 400 kg. are lifted 35 meters in 5 seconds what work is done? What is the rate of work? Express in horse-power, watts and kilowatts.

4. Trace the energy of a moving railway train back to its source in the sun.

5. Why does turning the propeller of a motor boat cause the boat to move?

6. Does it require more power to go up a flight of stairs in 5 seconds than in 10 seconds? Explain. Is more work done in one case than in the other? Why?

7. Can 1 man carrying bricks up to a certain elevation for 120 days do as much work as 120 men carrying up bricks for 1 day?

8. If the 1 man and 120 men of problem 7 do the same amount of work have they the same power? Explain.

9. If 160 cu. ft. of water flow each second over a dam 15ft. high what is the available power?

10. What power must an engine have to fill a tank 11 8 5 ft. with water 120 ft. above the supply, in 5 minutes?

11. A hod carrier weighing 150 lbs. carries a load of bricks weighing 100 lbs. up a ladder 30 ft. high. How much work does he do?

12. How much work can a 4-horse-power engine do in 5 minutes?

13. Find the horse-power of a windmill that pumps 6 tons of water from a well 90 ft. deep in 30 minutes.

14. How many horse-power are there in a waterfall 20 ft. high over which 500 cu. ft. of water pa.s.s in a minute?

15. The Chicago drainage ca.n.a.l has a flow of about 6000 cu. ft. a second. If at the controlling works there is an available fall of 34 ft.

how many horse-power can be developed?

16. How long will it take a 10-horse-power pump to fill a tank of 4000 gallons capacity, standing 300 ft. above the pump?

17. A boy weighing 162 lbs. climbs a stairway a vertical height of 14 ft. in 14.6 seconds. How much power does he exert?

18. The same boy does the same work a second time in 4.2 seconds. How much power does he exert this time? What causes the difference?

19. What is a horse-power-hour? a kilowatt-hour?

(3) SIMPLE MACHINES AND THE LEVER

=116. Machines and Their Uses.=--A man, while standing on the ground, can draw a flag to the top of a pole, by using a rope pa.s.sing over a pulley.

A boy can unscrew a tightly fitting nut that he cannot move with his fingers, by using a wrench.

A woman can sew a long seam by using a sewing machine in much less time than by hand.

A girl can b.u.t.ton her shoes much quicker and easier with a b.u.t.ton-hook than with her fingers.

These ill.u.s.trations show some of the reasons why machines are used. In fact it is almost impossible to do any kind of work efficiently without using one or more machines.

=117. Advantages of Machines.=--(a) Many machines make possible an _increased speed_ as in a sewing machine or a bicycle.

(b) Other machines exert an _increased force_. A rope and a set of pulleys may enable a man to lift a heavy object such as a safe or a piano. By the use of a bar a man can more easily move a large rock. (See Fig. 83.)

[Ill.u.s.tration: FIG. 83.--The rock is easily moved.]

(c) The _direction_ of a force may be changed thus enabling work to be done that could not be readily accomplished otherwise. As, e.g., the use of a pulley in raising a flag to the top of a flag pole, or in raising a bucket of ore from a mine by using a horse attached to a rope pa.s.sing over two or more pulleys. (See Fig. 84.)

(d) _Other agents_ than man or animals _can be used_ such as electricity, water power, the wind, steam, etc. Fig. 85 represents a windmill often used in pumping water.

_A machine is a device for transferring or transforming energy._ It is usually therefore an instrument for doing work. An electric motor is a machine since it _transforms_ the energy of the electric current into motion or mechanical energy, and _transfers_ the energy from the wire to the driving pulley.

[Ill.u.s.tration: FIG. 84.--The horse lifts the bucket of ore.]

=118. A Machine Cannot Create Energy.=--Whatever does work upon a machine (a man, moving water, wind, etc.) loses energy which is employed in doing the work of the machine. A pair of shears is a machine since it transfers energy from the hand to the edges that do the cutting. Our own bodies are often considered as machines since they both transfer and transform energy.

We must keep in mind that _a machine cannot create energy_. The principle of "Conservation of Energy" is just as explicit on one side as the other. Just as energy, cannot be destroyed, so energy cannot be created. A machine can give out no more energy than is given to it. It acts simply as an agent in transferring energy from one body to another. Many efforts have been made to construct machines that when once started will run themselves, giving out more energy than they receive. Such efforts, called seeking for _perpetual motion_, have never succeeded. This fact is strong evidence in favor of the principle of the conservation of energy.

[Ill.u.s.tration: FIG. 85.--A windmill.]

=119. Law of Machines.=--When a body receives energy, work is done upon it. Therefore work is done upon a machine when it receives energy and the machine does work upon the body to which it gives the energy. In the operation of a machine, therefore, two quant.i.ties of work are to be considered and by the principle of the conservation of energy, these two must be equal. _The work done by a machine equals the work done upon it, or the energy given out by a machine equals the energy received by it._ These two quant.i.ties of work must each be composed of a _force_ factor and a _s.p.a.ce_ factor. Therefore two forces and two s.p.a.ces are to be considered in the operation of a machine. The force factor of the work done on the machine is called the _force_ or _effort_. It is the force applied to the machine. The force factor of the work done by a machine is called the _weight or resistance_. It is the force exerted by the machine in overcoming the resistance and equals the resistance overcome.

If _f_ represents the force or effort, and _D_{f}_ the s.p.a.ce it acts through, and _w_ represents the weight or resistance, and _D_{w}_ the s.p.a.ce it acts through, then the law of machines may be expressed by an equation, _f D_{f} = w D_{w}_. That is, _the effort times the distance the effort acts equals the resistance times the distance the resistance is moved or overcome_. When the product of two numbers equals the product of two other numbers either pair may be made the means and the other the extremes of a proportion. The equation given above may therefore be expressed _w: f = D_{f}: D_{w}_. Or the resistance is to the effort as the effort distance is to the resistance distance. The law of machines may therefore be expressed in several ways. One should keep in mind, however, that the _same_ law of machines is expressed even though the form be different. What two ways of expressing the law are given?