VIBTUAL WORK 155 



EXAMPLES 



1. A man who weighs 140 pounds walks up a mountain path at a slope of 

 30 degrees to the horizon at the rate of 1 mile per hour. Find his rate of work- 

 ing in raising his own weight in horse power. 



2. At what horse power is an engine working which hauls a train of 1000 

 tons up an incline of 1 in 200 at 12 miles an hour, the resistance due to friction 

 being ^ of the weight of the train ? 



3. An automobile weighing 1 ton can run up a hill of 1 in 60 at 8 miles an 

 hour. Taking the resistance due to friction as ^ of the weight of the car, 

 find at what rate it could run down the same hill, assuming the horse power 

 developed by the engine to remain the same. 



4. A cargo of stone weighing 18 tons is unloaded from a barge on to a quay 

 30 feet above the barge by cranes worked by an engine. If the unloading takes 

 three hours, find the average horse power at which the engine has been working. 



5. Assuming that a man in walking raises his center of gravity through a 

 vertical height of one inch at every step, find at what horse power a man 

 is working in walking at 4 miles an hour, his stride being 33 inches, and his 

 weight 168 pounds. 



6. A cyclist and his machine weigh 200 pounds, and he rides up an incline 

 of 1 in 80 at 16 miles an hour. His bicycle is geared to 72 inches, and the 

 length of his cranks is 7 inches. Find the average vertical pressure of his foot 

 on the pedal, assuming this pressure to exist only during the downward motion 

 of the pedal. 



7. A single-screw ship has engines of 5000 horse power, and, when working 

 at full power, the engines make 75 revolutions per minute. Find the couple 

 transmitted by the shaft. 



8. When one body rolls on another, there is found to be a couple opposing 

 the motion, equal to that produced by the normal reaction at the end of an 

 arm of length Z, where / is called the coefficient of rolling friction. 



If a railroad truck runs on wheel of radius a, show that the resistance to its 

 motion produced by rolling friction is I/a times its weight. 



THE PRINCIPLE OF VIRTUAL WORK 



122. By a small displacement is meant for the present a motion 

 in which each particle of a system is displaced from its original 

 position through a distance which is so small that it may be treated 

 as an infinitesimal quantity of which the square may be neglected. 

 If the system is under the action of forces, work will be done in 

 performing any small displacement. Since the displacement is 

 supposed to be a small quantity, the work performed will also be 

 a small quantity. 



