MEASUKEMENT AND UNITS 147 



the acceleration due to gravity, it follows that the practical unit 

 is g times the absolute unit. 



In practical British units, the unit force is the pound weight. 

 In absolute units, the corresponding unit is known as the poundal; 

 it is the force which will produce unit acceleration in a mass of 

 one pound. 



The practical unit of work, as we have said, is the work done in 

 raising a mass of one pound through one foot, i.e. in moving 

 through one foot the point of application of one pound weight. 

 There is also an absolute unit of work, namely the work done in 

 moving through one foot the point of application of one poundal. 

 This unit is called the foot poundal. Since one pound weight is 

 equal to g poundals, we obviously have the relation 



1 foot pound = g foot poundals. 



EXAMPLES 



1. At what speed can a horse of 1 horse power draw a cart weighing 1 ton, 

 friction being supposed to cause a horizontal force equal to one fortieth of the 

 weight of the cart ? 



2. A body resisted by a force of P poundals is moved against this resistance 

 with a velocity v. What horse power is required ? 



3. At what rate can a steam roller of 7 horse power and weight 1 ton roll a 

 path, the resistance due to friction being equal to the weight of the roller ? 



4. A snail weighing -j- ounce climbs a wall 6 feet in height in 4 hours. At 

 what horse power is he working ? 



5. A load of bricks weighing 5 tons has to be raised to the top of a house 

 50 feet in height by 10 laborers, each of whom works at an average rate of 

 ^ horse power. How long ought the job to take ? 



6. The piston of an engine has an area of a square feet and a stroke of 

 I feet, and the engine makes > re volutions per minute. If the pressure per unit 

 area acting on the piston is p pounds weight per square foot, prove that the 

 horse power at which the engine is working is 



plan 

 33,000 ' 



7. A locomotive has a circular piston of diameter 17 inches, and stroke 26 

 inches. It makes 250 revolutions per minute, the pressure being 225 pounds 

 weight per square inch. Find its horse power. 



