Figure 20 - Kinetic energy equals the work to

produce the change of velocity = Mv²/2

 

Then the work done on the body in this distance is

Work = Fs = Mαs ergs or foot-poundals.

If the body starts from rest, its velocity in centimeters per second or feet per second at the end of t sec is

v = αt

where α is the acceleration in centimeters per second per second or in feet per second per second. The space passed over is equal to the average velocity times the time. Hence

O + v

s = –––––– t = ½ vt

2

and since v = αt and t = v/α, we have by substitution

 

 

1v²

s = ––––

2α ,

v² = 2 αs,

v²

αs = ––ЃE/i>

2

Substituting this value of αs in the expression for the work done on the body

 

Mv²

Work = Fs = ––––ЃEergs or foot-poundals.

2

 

This expression gives the work necessary to cause a mass M to acquire a velocity v. This work does not depend on the distance cov­ered or on the acceleration. It is determined solely by the mass of the body and its speed. If a retarding force is applied to this body so that it is brought to rest, the moving body will do work against this retarding force. When the body has come to rest, the amount of work that has been done will be just equal to the work done in start­ing the body. According to the law of conservation of energy, the energy spent in starting the body must be just equal to that derived from the body when it is stopped. Hence

 

Mv²,

Kinetic energy = ––––ЃEergs or foot-poundals.

2

If the body has an initial velocity u and an initial kinetic energy ½ Mu², the gain in kinetic energy is the work done on the body by the accelerating force.

Conservation of Energy. ЃEEnergy is defined as the ability to do work. It occurs in many forms. The work required to stretch a spring is stored up as energy in the spring. The work necessary to compress a gas may be stored up as heat in the gas. The study of the various forms in which energy may occur and of the transformation of one kind of energy into another has led to the statement of a very important principle known as the conservation of energy. This principle may be stated as follows: In any body, or system of bodies, which is not receiving or giving up energy, the total amount of energy is unchanged. This principle states that energy can never be created or destroyed. It can be transformed from one form into another, but the total amount in the end is unchanged. For example, a bullet leaves the muzzle of the gun with kinetic energy that it received because of the work done on it by the expanding gases. As it passes through the air, it loses some of this kinetic energy because of the heat devel­oped by the friction in the air. When it strikes the target, sound waves are sent out that carry away some of the energy. There may also be a flash of light, which uses up some energy. Heat will be developed in the target, and fragments of the bullet may carry away some of the energy. If all these energies are added together, they will be found to be just equal to the energy with which the bullet left the muzzle of the gun.

Prior to the modern views concerning matter and energy, it was customary to make a similar statement concerning the conservation of matter. Now matter is regarded as a form of energy. It can be trans­formed into energy and conversely energy can be transformed into matter. When the sun emits radiation, its mass decreases because of the decrease of energy due to radiation. The law of conservation of energy must therefore be extended to include transformations of both mass and energy. Experiments in nuclear physics have established the validity of this principle. Hence, the principle of the conservation of energy and the principle of the conservation of matter combine to form a single principle requiring the conservation of both matter and energy. The proportionality between mass and energy derived from the prin­ciple of relativity is given by the equation

E = c²m

where E is the energy in ergs; m is the change of mass in grams; c is the velocity of light in centimeters per second that equals 3x1010 cm per sec [2, С. 60 - 64].

2.7.6 Look through text 2.7.5 and find the English equivalents for the following Russian phrases and word-combinations:

ыM это ыD ь@язатеЃEыM таЃE ЃEсиЃE егЃEЃEЃEжеыGя; ЃEсиЃE егЃEдвиженЃE; ыGЃEим ь@разоЃE чть@ЃEЃEивести егЃEЃEдвижение; ЃEенебрегая ЃEЃEЃEбы то ыG быЃE ЃEтеЃEыLьH работоЃE чтЃEЃEсаетЃE ЃEыDтическьH эыDргии; есть ьCыM ь@стЃEтеЃEство (илЃEьCин ЃEЃEыQ), ЃEтороЃEследуеЃEъCЃEтить; ъь саЃEЃEдеЃE; до современыZЃEЃEедставЃEыGЃE всЃEдствие изЃEчеыGя.

 

Look through the text once again and summarize it. Can you remember any scientists interested in the phenomena of energy? Find supplementary information about them from Section I and prepare the presentation of your report on “EnergyЃE(use a projector in the multimedia class). You may use Internet to add some information.