CHAPTER VI

WORK AND ENERGY

_104. Work._--"Whenever a force moves a body upon which it acts, it is said to do work upon that body." For example, if a man pushes a wheelbarrow along a path, he is doing work on it as long as the wheelbarrow moves, but if the wheelbarrow strikes a stone and the man continues to push and no motion results, from a scientific point of view he is then doing no work on it.

"Work signifies the overcoming of resistance," and unless the resistance is overcome no work is done. Lifting a weight is doing work on it, supporting a weight is not, although the latter may be nearly as tiresome as the former. Work as used in science is a technical term. Do not attach to it meanings which it has in every-day speech.

=105. Measurement of Work.=--Work is measured by the product of the force by the displacement caused in the direction of the force, that is _W_ = _fs_. Therefore if a unit of force acts through a unit of s.p.a.ce, a unit of work will be done. There are naturally several units of work depending upon the units of force and s.p.a.ce employed.

_English Work Unit._--If the force of one _pound_ acts through the distance of one _foot_, a _foot-pound_ of work is done. A foot-pound is defined as the work done when 1 lb. is lifted 1 ft. against the force of gravity.

_Metric Work Unit._--If the force is one _kilogram_ and the distance one _meter_, _one kilogram-meter_ of work is done.

_Absolute Work Unit._--If the force of one _dyne_ acts through the distance of one _centimeter_ a _dyne-centimeter_ of work is done. This usually is called an i. Other work units are sometimes used depending upon the force and distance units employed. One, the i, is equal to 10,000,000 ergs or 107 ergs.

=Problem.=--If a load is drawn 2 miles by a team exerting 500 lbs.

force, how much work is done?

=Solution.=--Since the force employed is 500 lbs., and the distance is 2 5280 ft., the work done is 500 2 5280 or 5,280,000 ft.-lbs.

=106. Energy.=--In the various cases suggested in the paragraphs upon work, an agent, a man, an animal or a machine, was mentioned as putting forth an effort in order to do the work. It is also true that in order to perform work an agent must employ _energy, or the energy of a body is its capacity for doing work_. Where an agent does work upon a body, as in winding up a spring or in lifting a weight, the body upon which the work has been done may acquire energy by having work done upon it. That is, it may become able to do work itself upon some other body. For instance, a lifted weight in falling back to its first position may turn wheels, or drive a post into the ground against resistance; a coiled spring may run clock work, strike a blow, or close a door. Hence the energy, or the capacity for doing work, is often acquired by a body because work has first been done upon that body.

=107. Potential Energy.=--The wound up spring may do work because work has first been done upon it. The lifted weight may also do work because work has first been done in raising it to its elevated position since in falling it may grind an object to powder, lift another weight or do some other kind of work. _The energy that a body possesses on account of its position or shape and a stress to which it is subjected is called potential energy._ The potential energy of a body is measured by the work done in lifting it, changing its shape, or by bringing about the conditions by which it can do work. Thus if a block of iron weighing 2000 lbs. is lifted 20 ft., it possesses 40,000 ft.-lbs. of potential energy. It is therefore able to do 40,000 ft.-lbs. of work in falling back to its first position. If the block just mentioned should fall from its elevated position upon a post, it could drive the post into the ground because its motion at the instant of striking enables it to do work. To compute potential energy you compute the work done upon the body. That is, _P.E._ = _w_ _h_ or _f_ _s_.

=108. Kinetic Energy.=--_The energy due to the motion of a body is called kinetic energy_. The amount of kinetic energy in a body may be measured by the amount of work done to put it in motion. It is usually computed, however, by using its ma.s.s and velocity on striking. To ill.u.s.trate, a 100-lb. ball is lifted 16 ft. The work done upon it, and hence its potential energy, is 1600 ft.-lbs. On falling to the ground again, this will be changed into kinetic energy, or there will be 1600 ft.-lbs. of kinetic energy on striking. It will be noted that since energy is measured by the work it can do, work units are always used in measuring energy. To compute the kinetic energy of a falling body by simply using its ma.s.s and velocity one proceeds as follows, in solving the above problem:

First, find the velocity of the falling body which has fallen 16 ft. A body falls 16 ft. in _one_ second. In this time it gains a velocity of 32 ft. per second. Now using the formula for kinetic energy _K.E._ = _wv_/(2_g_), we have _K.E._ = 100 32 32/(2 32) = 1600 ft.-lbs. as before. The formula, _K.E._ = _wv_/(2_g_), may be derived in the following manner:

The kinetic energy of a falling body equals the work done in giving it its motion, that is, _K.E._ = _w_ _S_, in which, _w_ = the weight of the body and _S_ = the distance the body must fall freely in order to acquire its velocity. The distance fallen by a freely falling body, _S_, = 1/2_gt_ = _g__t_/(2_g_) (Art. 98, p. 111).

Now, _v_ = _gt_ and _v_ = _g__t_.

Subst.i.tuting for _g__t_, its equal _v_, we have _S_ = _v_/(2_g_). Subst.i.tuting this value of S in the equation _K.E._ = _w_ _S_, we have _K.E._ = _wv_/(2_g_).

Since the kinetic energy of a moving body depends upon its ma.s.s and velocity and not upon the _direction_ of motion, this formula may be used to find the kinetic energy of any moving body. Ma.s.s and weight in such problems may be considered numerically equal.

=Important Topics=

1. Work defined.

2. Work units, foot-pound, kilogram-meter, erg.

3. Energy defined.

4. Kinds of energy, potential and kinetic.

=Problems=

1. How much work will a 120-lb. boy do climbing a mountain 3000 ft.

high? Should the vertical or slant height be used? Why?

2. In a mine 4000 kg. of coal are lifted 223 meters: how much work is done upon the coal? What is the kind and amount of energy possessed by the coal?

3. A pile driver weighs 450 lbs. It is lifted 16 ft. How much work has been done upon it? What kind and amount of energy will it have after falling 16 ft. to the pile?

4. A train weighing 400 tons is moving 30 miles per hour. Compute its kinetic energy. (Change its weight to pounds and velocity to feet per second.)

5. What would be the kinetic energy of the train in problem 4 if it were going 60 miles per hour? If it were going 90 miles per hour?

How does doubling or trebling the speed of an object affect its kinetic energy? How does it affect its momentum?

6. What is the kinetic energy of a 1600-lb. cannon ball moving 2000 ft. per second?

7. Mention as many kinds of mechanical work as you can and show how each satisfies the definition of work.

8. A pile driver weighing 3000 lbs. is lifted 10 ft. How much work is done upon it?

9. If the pile driver in problem 8 is dropped upon the head of a pile which meets an average resistance of 30,000 lbs., how far will one blow drive it?

10. A 40 kg. stone is placed upon the top of a chimney 50 meters high. Compute the work done in kilogram-meters and foot-pounds.

(2) POWER AND ENERGY

=109. Horse-power.=--In computing work, no account is taken of the time required to accomplish it. But since the time needed to perform an undertaking is of much importance, the rate of work, or the _power or activity_ of an agent is an important factor. Thus if one machine can do a piece of work in one-fifth the time required by another machine, it is said to have five times the power of the other. Therefore the power of a machine is _the rate at which it can do work_. James Watt (1736-1819), the inventor of the steam-engine, in _expressing_ the power of his engine, used as a unit a _horse-power_. He considered that a horse could do 33,000 ft.-lbs. of work a minute. This is equal to 550 ft.-lbs. per second or 76.05 kg.-m. per second. This is too high a value but it has been used ever since his time. Steam engines usually have their power rated in horse-power. That is, locomotives produce from 500 to 1500 horse-power. Some stationary and marine engines develop as high as 25,000 horse-power. The power of an average horse is about 3/4 horse-power and of a man about 1/7 horse-power when working continuously for several hours.

=110. The Watt.=--In the metric system, the erg as a unit of work would give as a unit of power 1 erg per second. This amount is so small, however, that a larger unit is usually employed, the practical unit being 10,000,000 ergs a second, that is, one joule per second. (See Art.

105.) This practical unit is called a _Watt_ after James Watt. The power of dynamos is usually expressed in kilowatts, a kilowatt representing 1000 watts. Steam-engines in modern practice are often rated in kilowatts instead of horse-power. A horse-power is equivalent to 746 watts, or is nearly 3/4 of a kilowatt.

=111. Energy. Its Transference and Transformation.= We have considered energy as the capacity for doing work, and noted the two kinds, potential and kinetic, and the facility with which one may change into another. In fact, the transference of energy from one body to another, and its transformation from one form to another is one of the most common processes in nature. Take a pendulum in motion, at the _end_ of a swing, its energy being entirely due to its elevated position is all _potential_; at the _lowest_ point in its path its energy being entirely due to its motion is all _kinetic_. The change goes on automatically as long as the pendulum swings. A motor attached by a belt to a washing machine is started running. The energy of the motor is transferred by the belt to the washer where it is used in rubbing and moving the clothes.

The heat used in warming a house is usually obtained by burning coal or wood. Coal is believed to be formed from the remains of plants that grew in former geologic times. These plants grew through the help of the radiant energy of the sun. The following are transformations of energy that have occurred: The radiant energy of sunlight was transformed into the _chemical_ energy of the plants. This remained as chemical energy while the plants were being converted into coal, was mined, brought to the stove or furnace and burned. The burning transformed the chemical energy into heat energy in which form we use it for warming rooms. Take the energy used in running a street car whose electrical energy comes from a waterfall. The energy of the car itself is mechanical. Its motor, however, receives electrical energy and transforms it into mechanical. This electrical energy comes along a wire from a dynamo at the waterfall, where water-wheels and generators transform into electrical energy the mechanical energy of the falling water. The water obtained its energy of position by being evaporated by the heat of the radiant energy of the sun. The vapor rising into the air is condensed into clouds and rain, and falling on the mountain side, has, from its elevated position, potential energy. The order of transformation, therefore, is in this case, radiant, heat, mechanical, electrical, and mechanical. Can you trace the energy from the sun step by step to the energy you are using in reading this page?

=112. Forms of Energy.=--A steam-engine attached to a train of cars employs its energy in setting the cars in motion, _i.e._, in giving them kinetic energy and in overcoming resistance to motion. But what is the source of the energy of the engine? It is found in the coal which it carries in its tender. But of what kind? Surely not kinetic, as no motion is seen. It is therefore potential. What is the source of the energy of the coal? This question leads us back to the time of the formation of coal beds, when plants grew in the sunlight and stored up the energy of the sun's heat and light as _chemical_ energy. The sun's light brings to the earth the energy of the sun, that central storehouse of energy, which has supplied nearly all the available energy upon the earth. Five _forms_ of energy are known, viz., mechanical, heat, electrical, radiant, and chemical.

=113. Energy Recognized by its Effects.=--Like force, energy is invisible and we are aware of the forms only by the effects produced by it.

We recognize _heat_ by _warming_, by expansion, by pressure.

We recognize _light_ by _warming_, by its affecting vision.

We recognize _electrical_ energy by its heat, light, motion, or magnetic effect. We recognize _mechanical_ energy by the _motion_ that it produces. We recognize _chemical_ energy by knowing that the source of energy does not belong to any of the foregoing.

A boy or girl is able to do considerable work. They therefore possess energy. In what form does the energy of the body mainly occur? One can determine this for himself by applying questions to each form of energy in turn as in Art. 114.

_114. Source of the Energy of the Human Body._--Is the energy of the human body mostly heat? No, since we are not very warm. Is it light or electrical? Evidently not since we are neither luminous nor electrical.

Is it mechanical? No, since we have our energy even when at rest. Is it chemical? It must be since it is none of the others. Chemical energy is contained within the molecule.

It is a form of potential energy and it is believed to be due to the position of the atoms within the molecule. As a tightly coiled watch spring may have much energy within it, which is set free on allowing the spring to uncoil, so the chemical energy is released on starting the chemical _reaction_. Gunpowder and dynamite are examples of substances containing chemical energy. On exploding these, heat, light, and motion are produced. Gasoline, kerosene, and illuminating gas are purchased because of the potential energy they contain. This energy is set free by burning or exploding them.

The source of the energy of our bodies is of course the food we eat. The energy contained in the food is also chemical. Vegetables obtain their energy from the sunlight (radiant energy). This is why plants will not grow in the dark. The available energy is mostly contained in the form of starch, sugar and oil. Digestion is employed princ.i.p.ally to dissolve these substances so that the blood may absorb them and carry them to the tissues of the body where they are needed. The energy is set free by oxidation (burning), the oxygen needed for this being supplied by breathing. Breathing also removes the carbon dioxide, which results from the combustion. It is for its energy that our food is mostly required.