POWER 43 the pendulum is inclined at an angle of 60° to the vertical. Compare its kinetic energy after describing an arc of 30° with its K.E. at its lowest point. Power. The power (or activity) of an agent is the rate at which it can do work, and is measured by the number of units of work done per unit of time. The unit of power commonly used by engineers in this country is the horse-power, which is defined as being the power of doing 33,000 foot-pounds of work per minute, or 550 foot-pounds of work per second. 128. Assuming that the pressure within the cylinder of a steam-engine remains constant throughout the whole of the stroke, find the horse-power developed in each cylinder of an engine, having given = A area of piston in square inches. P = pressure upon the piston in pounds per square inch. R = number of revolutions per minute. Here P denotes the intensity of the pressure on the piston in Thus the work done in each stroke is SAP foot-pounds. is H.P. = 2SRAP/33,000. 129. Water is supplied to a hydraulic motor at a pressure of 100 lbs. per square inch. Express the potential energy of the water in the reservoir in footpounds per gallon; and calculate the maximum H.P. which can be developed by the motor if the rate of --- in Co gallons per minute pounds weight per square foot = hp, where p = number pounds in a cubic foot of water = 62.5, ..hx 62.5/144 = pressure in pounds weight per square inch Thus the potential energy of one pound of water is 230.4 foo pounds, and the potential energy of one gallon (or 10 lbs is 2304 foot-pounds. (Notice that since the pressure is supposed constant in th question, we must also assume that the level of the water the reservoir is kept constant.) The work done by a supply of 50 gallons per minute is 2304 × 50 ft.-lbs. per min. 130. The nominal value of a horse-power is 33,00 foot-pounds per minute. Express this (1) in kilogramme metres per minute and (2) in ergs per second. 136. Determine the rate at which an engine is working when it drives a train of 150 tons at a rate of 30 miles an hour, the resistance to motion being equal to a weight of 16 lbs. for every ton. 137. The mass of a train is 200 tons, and the resistances to its motion amount to 20 lbs. per ton on a level line: find the horse-power of an engine which can just keep it going at the rate of 45 miles an hour. : 138. A steam-engine supplies 1000 houses with 100 gallons of water each, working 12 hours per day if the mean height to which the water has to be raised is 80 feet, at what rate does the engine work? 139. What alteration would be produced in the unit of work if the units of mass, length, and time were each increased ten-fold? If a horse-power be represented by 550 under the old system, what would be its numerical value in the new? EXAMINATION QUESTIONS.1 140. A particle whose mass is M pounds moves from rest under the action of a force of P units which is constant in magnitude and direction: how far will the particle move in n seconds, and what space will it describe in the nth second? If the force be the weight of the body, and the 1 The following abbreviations are used in marking the sources from which the examples at the end of each chapter are taken : London Examinations Camb. Schol. Camb. B.A. N. S. Tripos M. Tripos Balliol Coll. Vict. Int. Ind. C. S Brakenbury Natural Science Scholarship, Balliol College. =Intermediate B.A. and B.Sc. Exams., Victoria University. Indian Civil Service particle traverse 176.99 feet during the 6th second motion, find the value of "g." Matric. 1882. 141. Explain fully what is meant by the accelerati of gravity, and show how the value of "g" may determined by Atwood's machine. If the acceleration of gravity be represented by uni and one second be the unit of time, what must be t unit of length? Int. Sc. 1883. 142. The effect of force on matter being either stra or change of motion, show that either effect may be use Which is the more convenie Owens Coll. 1881. 143. Prove that when a foot and a minute are take as units of length and time, the same acceleration expressed by ten times the number required to expres it when the inch and 30 seconds are taken as th units. Owens Coll. 1880. 144. Enunciate Newton's second law of motion, and assuming that the force of gravity upon a pound is 32. poundals, find the force of gravity upon 5 grammes i dynes. cannon-shot rebounded with a velocity of 200 feet per second, what would be the measure of the impulse? Matric. 1883. 0148. Two weights, of 5 pounds and 7 pounds respectively, are fastened to the ends of a cord passing over a frictionless pulley supported by a hook. Show that when they are free to move the pull on the hook is equal to 11 pounds weight. Matric. 1886. 149. A jet of water is projected against a fixed wall so as to strike it at right angles. If the velocity of the jet be 80 feet per second, and 100 lbs. of water strike the wall in each second, what pressure will be exerted against the wall (1) when the water does not rebound; (2) when it rebounds with a velocity of 10 feet per second? Int. Sc. 1883. 150. What is the dynamical unit of force? that the unit of force when 10 feet, 100 seconds, and 1000 pounds are the fundamental units is equal to that when n feet, n seconds, and n pounds are the corresponding units. Camb. Schol. 1882. 151. Describe Atwood's machine. From the following data find the numerical value of g, the acceleration due to gravity, at a certain place: 152. Two scale-pans, each weighing 2 oz., are suspended by a weightless string over a smooth pulley. A mass of 10 oz. is placed in one and 4 oz. in the other: find the tension of the string and the pressure on each scale-pan. Matric. 1883. 153. In Atwood's machine one weight is double the other; the wheel is held at rest whilst the string is nailed the wheel the ton. if the weights he allowed to |