Power and Efficiency

Power and Efficiency

Rate of doing work: power

 In practice, where work is done upon a body, both the amount of work and also the time during which that work is done are important. For example, if a motordriven soist has to raise its load quikly, a more powerful hoist and a larger driving motor are needer than if more time were allowed. Usually the size of machinery is determined, not by the total amount of work to be done, but by the rate ar which it to be done; that is, the amount of work required per unit of time, The time rate of doing work is caled power.

Since power is the time rate of doing work, the unit for power in any system of units is found by dividing the work unit in that system by the time unit. Thus, in the Sl system, power is expressed in watts, and in the British gravitational system it is expressed in foot-pounds (pound-force feet) per second.

In addition to the units of the standard systems, other practical units are in general use. The horsepower (hp) is the power prowided by an agent while doing work at the rate of 33 000 (ft x lb)/min. , or 550 (ft x lb)sec. The watt is a rate of doing work equal to l joule/sec. The kilowatt (kw) is a power unit used in rating electric machines.

Simple machines

It is a matter of common expirience that a stone firmly embedded in the ground can be dislodged with a crowbar, and that a heavy automobile can be raised by means of a jack. The crowbar or jack serves as an intermediate device upon which work can be done and which in turn does work upon some other object. A device that accomplishes this results is technicall called a machine. The complex machines used in industry are found upon analysis to be made up largely of certain elements that maybe considered simple machines in themselves. These simple machines comprise the lever, the wheel and axle, the pulley, the inclined plane, the screw, and the wedge.

Ushually a machine is epmployed order to lessen the force required in doing a certain piece of work. Thus, if a 500-lb weight is to be lifted, a machine can be used to exert this amount of upward force upon it while the person operating the machine exerts perhaps only 50 pounds. It is thus possible, and indeed usual, to obtain a larger force from a machine than that which is exerted upon it. Of course, this statement applies to force and not to energy; according to the law of conservation of energy, more work cannot be obtained from a machine than the energy supplied to it. Since work = force x distance, when the operator exerts a smaller force thandoes the machine, he exerts the smaller force through a correspondingly greater distance. 

The ratio of the force extred by a machine on a load to the force extred by an operator on the machine is called the mechanical advant of the machine.

Efficiency of a machine. Friction is present in all moving machinery, however well designed; consequently, the energy delivered by a machine is less than that supplied to it. More definitely, the principle of conservation of energy, of energy shows that 

energy input = energy output + energy wasted

if no energy is stored up in the machine, Since energy used per unit time is power, it can also be said that

power input = power output + power wasted.

The efficiency of machine is defined as the ratio of its output to its input, both input and output being expressed in the same units of energy or power. The ratio of output to input is always less than unity; in practice, it is usually multiplied by 100 and expressed in per cent. High efficiency in a machine implies that in a given time a largde part of the energy supplied to it is delivered by the machine to its loadand a small part wasted. The efficiency of a large electric generator may be as high as 98 per cent. In some of the simple machines - a screw jack, for exapmle - considerable friction is necessary to prevent the load from running down after it has been raised; because of the energy wasted in friction the efficiency of a terms of their output; thus, a 5-hp motor is one that can deliver 5 hp without exceeding its design limitaions; if its efficiency is 80 per cent, the power input to machine is 5 hp/0.80 - 6.25 hp.