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Read the texts about Work and Power, translate them and find one wrong statement in the list of the main statements below the texts.

Work

Work is done by a force when the point of application of the force moves so that the force has a component along the path of the point of application. This component we call the working component of the force and the length of the path of the point of application we call the distance through which the force acts. If the working component is constant, the amount of work done is equal to the product of the magnitude of the working component and the distance through which the force acts. When the working component acts in the direc­tion of the motion, the work of the force is positive; when the working component acts oppositely to the direction of motion, the work of the force is negative. Forces which do positive work are sometimes called efforts; those which do negative work, resistances.

We denote work by W.

Since it is the product of two scalar quantities, work is a scalar quantity. It can be expressed in any units of force and distance.

In the discussion above we have spoken of work as being done by a force but, since the force which does work must be exerted by some body on some other body, it is also correct to say that the work is done by one body on the other body. Thus a spring does the work of closing a door and the work is done on the door, etc. The amount of work done in any given case is usually determined by separately calculating the work done by each of the forces that act, and so we usually speak of the work done by a force rather than of the work done by a body.

Gravitational Units of Work. — Since work is measured by the prod­uct of the force times the distance through which it acts, in order to measure work it is necessary to measure two quantities — force and distance. In the English system, the force is measured in terms of a unit of force that is equal to the pull of gravity of a mass of 1 lb, and the distance is measured in feet. In this system the unit of work is called the foot-pound.

One foot-pound of work is defined as the work that is done when a force equal to the weight of 1 lb acts through a distance of 1 ft.

For example, 1 ft-lb of work is done when a mass of 1 lb is raised a distance of 1 ft at constant speed against the action of gravity.

In the metric system the unit of work may be chosen as the gram-centimeter or kilogram-meter.

One gram-centimeter of work is defined as the amount of work that is done when a force equal to the weight of 1 g acts through a distance of 1 cm, and the kilogram-meter is defined as the work which is done when a force equal to the weight of 1 kg acts through a distance of 1 m.

The gram-centimeter is the amount of work done when a mass of 1 g is lifted a vertical distance of 1 cm at constant speed against the action of gravity.

The Erg. — The gravitational units of work, like the gravitational units of force which enter into them, depend on the place on the sur­face of the earth at which they are used. For this reason an absolute unit of work, the erg, is frequently used. An erg of work is the work done when a force of 1 dyne acts through a distance of 1 cm. Since the weight of 1 g is equivalent to 980 dynes, a gram-centimeter of work is equivalent to 980 ergs; i. e., when a mass of 1 g is lifted a distance of 1 cm against the force of gravity, 980 ergs of work are done [2, С. 58 - 60].

Power

In defining work as the force multiplied by the distance through which it acts, it is to be observed that the element of time does not enter. The same work is done in lifting a mass of 300 lb a distance of 100 ft whether the work is done in a day or in a minute. The same work is done whether the mass is carried in a single load or in two or more loads. The amount of work done is measured by the end result, and it does not in any way depend upon the time to do the work. In the consideration of a machine it is necessary to know more than the total amount of work that the machine can do. It is desirable to know the rate at which the machine works. The time rate of doing work is called power. Hence

Power = work: time = force x distance: time = F x s: t = work, per unit of time

Since s: t = v

Power = force x velocity = Fv

Horsepower. — The English unit of power is called the horsepower. A horsepower denotes the ability of a machine to do 33,000 ft-lb of work in 1 min or 550 ft-lb in 1 sec [2, С. 60 - 61].

Main statements:

1. Working component is such a constituent of force and its direction determines whether the work of the force is positive or negative.

2. Work is a vector quantity and can be expressed in the units of force and distance.

3. In the English system they designate the unit of work as the foot-pound, while in the metric system it can be named as the gram-centimeter.

4. The erg is an absolute unit of work.

5. To find the machine amount of work we should know the rate of its doing work.

6. Horsepower is the English unit for the time rate of doing work.

2.7.4 Look through texts 2.7.1, 2.7.3 and find the English equivalents for the following Russian phrases and word-combinations:

закон формулируется следующим образом; обычно наблюдается; десятичная система мер; сила измеряется на основе (в единицах); гравитационная единица работы; конечный результат; действует в одном направлении с движением; желательно знать; абсолютная единица работы; произведение силы умноженной на расстояние.

Read the article about Energy, translate it and give the definitions to energy, potential energy and kinetic energy. Explain how to measure the kinetic energy and how to measure the potential energy. When should we use Newton’s second law of motion? State the law of the conservation of energy.

Energy

Definitions. — When the state or condition of a body is such that it can do work, the body is said to possess energy. It is customary to distinguish several kinds of energy. Thus a body may have kinetic energy by virtue of its motion, potential energy by virtue of its position in a field of force or by virtue of its state of internal stress, thermal energy by virtue of its temperature, chemical energy by virtue of its chemical composition. The amount of energy, of any given kind, that a body possesses at a given instant is the amount of positive work the body can do in changing from the condition it is in at that instant to some other condition taken as standard. Thus we may reckon the kinetic energy of a rotating flywheel to be the work the flywheel can do in coming to rest relative to the earth, and the poten­tial energy of a stretched spring to be the work the spring can do in contracting to its normal length.

Energy is measured in the same units as work and, like work, is a scalar quantity.

Potential energy is the energy a body possesses by virtue of its position or configuration relative to some standard position, or configuration, and is measured by the amount of work required to get it into its position, or configuration, or by the amount of work it can perform in returning to its original position, or configuration, with neglect or omission of any dissipated work.

Kinetic energy is the energy a body possesses by virtue of its velocity relative to a reference frame and is measured by the work done upon it to get it into its present motion, or numerically by the work that must be performed upon it to bring it to rest, or, finally, by the work it can do in being brought to rest, with neglect or omission of dissipated work.

In the definitions for potential and kinetic energy there is a catch that should be pointed out. Suppose a block rests upon an inclined plane. Its potential energy is usually expressed as Mgh, and if the block returns to the foot of the plane, it might be supposed that the block would perform an amount of work Mgh. But this need not be the case. Suppose that the block slides down the plane at an indefinitely slow speed under the action of its weight, the normal traction of the plane, and the tangential reaction of the plane. It is clear that the tangential reaction of the plane does work upon the block to the extent of - Mgh but the block does no work at all.

Similarly a compressed spring could be released to its natural length without its performing any work. It is for this reason that the definition reads with neglect of dissipated work. Thus it could be supposed that the block would slide frictionlessly down the plane and then compress a spring at the foot of the plane and, if the process were entirely frictionless, the work performed upon the spring would be equal to Mgh.

With regard to kinetic energy, consider the following. The ref­erence is a heavy vehicle, such as a truck, and the body is a light automobile. Suppose that the truck is at rest and that the automobile has a speed of 30 mi/hr down the road. The energy of the automo­bile is the work done upon it to get it under way, with neglect of dissipated work, and is of course 1/2 mv ². Its kinetic energy relative to the truck may be destroyed in two ways: (1) stop the automobile or (2) speed up the truck to 30 mi/hr. But the works (not including frictional work) required to do these are by no means equal, in fact they are 1/2 mv ² and 1/2 Mv ².

The definition, therefore, must speak specifically of the work per­formed by the body or upon the body.

How to Measure the Potential Energy. — The measure of the potential energy which a lifted body, such as a pile driver, has because of its position is equal to the work which has been spent in lifting the body. If the height in feet through which the body has been lifted is h and its weight in pounds is P, then the potential energy of the lifted body is

Potential energy = Ph ft.-lbs.

How to Measure the Kinetic Energy. — To find the kinetic energy which a body possesses by virtue of its motion, consider the work which must be done on it in order to give it a certain speed. When the body is stopped, it will give up an amount of energy that is equal to the work done in starting it. By definition, this latter is its kinetic energy.

From Newton's second law of motion, the force necessary to make a body move with an acceleration α is

F=Mα

where force is in dynes or poundals, mass in grams or pounds and acceleration in centimeters per second per second or feet per second per second.

Let s (Fig. 20) be the distance in centimeters or feet through which the body moves.

s=½αt²