Transportation on Land 269 



plane enables him to do what would require two or more men 

 to do by lifting vertically. But how much less force is re- 

 quired with the incline than in direct lifting of a given weight ? 

 Common experience vaguely gives the ratio as less ; but it is 

 necessary in any important situation to know exactly how much 

 less. We can determine the ratio by a simple experiment. 



Exercise : Work and the inclined plane. Let a four pound weight, 

 a block or small box loaded with sand, represent the four hundred 

 pound box. Attach a spring balance to it by strings so that it can 

 be lifted vertically. Obviously it takes four pounds to lift it. If it 

 is lifted upwards a distance of one foot, the work done is four foot- 

 pounds, that is, the number of units force multiplied by the number of 

 units distance gives as a product the number of foot-pounds. If it is 

 lifted vertically a distance of four feet, it takes sixteen foot-pounds of 

 work. Whenever it is required to find the amount of work done the 

 terms are made to read " work is equivalent to force times distance." 



What now is the work done in lifting -the four pounds to a height 

 of four feet by means of an inclined plane? Suppose you have a 

 smooth plane sixteen feet long. Pull the box from bottom to top of 

 the plane by the spring balance. What is the average reading of the 

 balance? Suppose this takes just two pounds of force. Two (num- 

 ber of pounds force) times sixteen (distance in feet) equals thirty-two 

 foot-pounds. This shows that more work is done in lifting the load 

 by means of the inclined plane than by lifting it vertically. But less 

 force is required to do the work. 



The four hundred pound box may accordingly be lifted to the 

 wagon by means of the inclined plane with about one fourth of the 

 force required to lift it vertically. This of course implies that friction 

 is reduced to a minimum. 



The experiment may be carried out with wheels, which give 

 rolling instead of sliding friction. Assume that the load of 

 four pounds is lifted to the required height by means of the in- 

 cline and wheels, and minimum friction, with a force of 1.4 

 pounds. Making the necessary substitutions in the formula, 

 then 1.4 (number of pounds) times 16 (number of feet) equals 

 22.4, the number of foot-pounds, or the amount of work done. 

 Remember that the total amount of work necessary to lift the 



