which seems to be lost in friction is not really lost or annihilated, but is transformed into heat as into another form of energy.

When, therefore, a pendulum comes to rest in consequence of friction (at its point of support, or between it and the air through which it swings) the original energy of the pendulum is not lost but transformed into heat.

77. Forms of Energy.-As a conclusion from innumerable experiments physicists have concluded that not only is heat a form of energy, but sound, light, and all electrical and magnetic actions are manifestations of energy, and require energy to be expended in causing them, just in proportion as they are capable of doing mechanical work or developing heat.

The different manifestations of energy may be summarized as follows:

When the energies involved in all these varied phenomena are studied it is found that one form of energy may be transformed into another, and that again into a third, but in every change the amount of the energy as measured by its power of doing work is unchanged.

78. Conservation of Energy.-The recognition of these varied forms of energy and careful measurements of the transformations from one form to another have led to the enunciation of a great principle or law known as the Conservation of Energy, which may be thus stated:

In any system of bodies which neither receives energy from without nor gives up any, the total amount of energy is unchanged whatever actions or changes may take place within that system, whether the energy manifests itself in mechanical forms, in sound,

heat, light, electric, or magnetic effects, or in chemical action or molecular or atomic changes.

In most cases the tracing of all the changes is a difficult matter. For example, a cannon ball receives energy from the work done by the powder gases as they expand forcing the ball from the gun. As it travels it is resisted by the air, losing kinetic energy exactly equivalent to the heat energy developed by friction in the air. On striking the target, sound waves carry off a small part of the energy, there may also be a flash of light which also takes away some energy, and the rest will be found in the form of heat developed in the target and in the ball itself and also in the form of kinetic energy in the fragments which may be thrown off. The principle of the conservation of energy asserts that if we add together all the energy that is derived from the motion of the ball the sum will be exactly equal to the amount of work which was required to give it its motion.

This law is the most important and extensive generalization of the science of physics and much of the progress of modern physics is due to its recognition. Every experiment in which the quantities of energy can be accurately determined is a test and confirmation of its truth, and no principle of physics is better established.

In consequence of this law, the determination of the energy involved in any action assumes new importance and is an essential part of the study of every physical phenomenon.

79. Availability of Energy. The presence of friction and analogous forms of resistance everywhere in nature causes a constant transformation of various forms of energy into heat, in which state it is conducted from one body to another and gradually becomes uniformly diffused so that although the energy still exists it is no longer available for the purpose of obtaining other forms of energy that may be desired. There is thus a constant degradation of energy going on throughout the universe, more available forms being constantly frittered away into heat.

FRICTION.

80. Friction. When one body slides over another the motion is resisted by a force which is called friction. It is always a

resistance, acting against the motion, and depends on the character of the surfaces in contact and on the force pressing them together.

It is a force of the greatest importance in daily life. If it were not for friction, nails and screws and knots would not hold, ropes could not be made, nor could we even walk across a floor. On the other hand, we would gladly be rid of friction in machines, for it is the cause of a large proportion of energy being lost in heat.

Friction appears to be due to the interlocking of minute roughnesses on the surfaces, together with the clinging together or adhesion of the points of closest contact. It is therefore diminished by polishing the surfaces, which diminishes the roughness and also makes the points of contact broader so that the film of air or oil is more effective in preventing adhesion.

After two surfaces have been resting in contact the friction on starting is greater than when the surfaces are in motion. It seems probable that this may be due to the closer contact due to the film of air or oil being squeezed out by the continued pressure.

Friction also resists the rolling of one body on another, though rolling friction in case of two given surfaces is much less than sliding friction. Rolling friction when surfaces are well polished appears to be due both to cohesion and to a slight de

P

FIG. 34.

formation of the surface and also of the roller at the point of contact; for the surface is compressed as it passes under the roller, and though it may spring back again it does not exert quite as much force in recovering as it opposed to the deformation.

81. Laws of Friction.-Let the block P be drawn along by the weight F, which is not sufficient to start it in motion, but will keep it moving with constant velocity when once started. The weight F is then equal to the force of friction, for it just balances it, neutralizing the resistance to the motion.

It is found in this way that the friction between two given surfaces is proportional to the force pressing them together. If the block P weighs 5 lbs. and if an additional weight of 5 lbs. is placed on the block, the force of friction is doubled.

It is also found that the force of friction, within wide limits, is independent of the area of the surface of contact. For instance, the friction of the block P is almost the same whether it slides on a narrow or a broad side, provided they are equally smooth.

The velocity with which one surface slides over the other makes little difference, the friction being appreciably the same for all moderate speeds; but the resistance to starting is greater than the friction after the motion is established.

It is evident, however, that these laws do not hold without limit. For if one surface is so small, as in case of a point resting on a plane surface, or if the pressure is so great that one body presses into the other, then one cannot move on the other without tearing or injuring the surface, and the law no longer holds.

82. Coefficient of Friction.-It follows from the first law of friction that the force of friction divided by the force pressing the surfaces together is a constant, this constant is called the coefficient of friction of the surfaces concerned; or, stated otherwise, the coefficient of friction between two surfaces is that fractional part of the force pressing the surfaces together which is required to overcome the friction.

Thus if the coefficient of friction in case of iron wheels on iron rails is 0.004, then, if the wheels weigh 1000 lbs., a force of four pounds will be required to overcome the friction.

When an engineer wishes to know how much force will be required in moving a house to cause it to slide on its ways, he has only to multiply the coefficient of friction for the soaped beams on which the house rests by the weight of the house itself.

Iron on bronze

thoroughly lubricated, may be as small as.... 0.06

Rolling Friction.

Cast iron wheels on rails

0.004

83. Limiting Angle of Repose.-The angle at which a surface may be inclined before a body resting on it begins to slip down is deter

W

mined by the coefficient of friction between the surfaces. Thus let a weight W rest on a surface inclined at an angle a. The earth attracts the weight with a force W which acts vertically downward. We may resolve this force into two components, one P which is perpendicular to the inclined surface and represents the pressure of the weight against the surface, and another F which is parallel to the surface and represents the force urging the weight down along the slope. If the angle a is such that the weight does not start to slide of itself, but if started

.a

W

FIG. 35.

slides down with constant speed, then the component F must exactly balance the friction, and so for that particular angle which may be

called the limiting angle of repose, we have k

cient of friction; but

=

F
P

where k is the coeffi

Or if h represents the height of the inclined plane and b its base

Hence by finding the limiting angle of repose in a given case the coefficient of friction is at once determined.

84. Means of Diminishing Friction. To make friction small the surfaces should be very hard and of fine even polish. Where there is much wear it is customary to make one of the bearing surfaces of a harder material than the other. Thus the crank pins on steam engines are made of polished steel and turn in brass boxes, the friction between the brass and steel being less than it would be between two parts of steel.

Rolling friction is very much less than sliding friction, therefore wheels are used on carriages, etc. It depends to some extent on the diameter of the wheels, being less when the diameter is greater. But even when wheels are used there is sliding friction in the hubs. The resistance to the motion of the vehicle due to this sliding friction is diminished by making the axles of small diameter, but the length of the axle in the hub of the wheel or the length of its bearing surface does not affect the frictional resistance.