2.7.2 Find the main sentences in the text and retell it. You may use Internet to get supplementary information.

2.7.3 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 сalled 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.

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.