106 



WELLS'S NATURAL PHILOSOPHY. 



How do we 

 derive a me- 

 clianical ad- 

 vantage from 

 an Inclined 

 plane ? 



How can we 

 eBtimate the 

 advantage gain- 

 ed by the use 

 of the inclined 

 plane ? 



directly, while to haul it up by pulleys would be very inconvenient, if not 

 impossible. We may, however, accomplish our object with comparative ease 

 by rolling the cask up an inclined plank, and exerting our force in a direction 

 parallel to the incUned surface of the plank. 



The plank, in this instance, forms an inclined plane, and we 

 gain a mechanical advantage, because it supports a part of 

 the weight. 



If we place a body upon a horizontal plane, or surface, it ia 

 evident that the surface will support its whole weight ; if we 

 incline the surface a little, it will support less of the weight, and as we elcvata 

 it more, it will continue to support less and less, until the surface becomes 

 perpendicular, in which case no support will bo afforded. 



2;;i. The advantage gained by the use of the inclined plane may be esti- 

 mated by the following rule : 



232. The power is to the weight as the per- 

 pendicular height of the plane is to its length. 



From this it will appear that the less the height of the in- 

 chned plane, and the greater its length, the greater will be 

 the mechanical advantage. Thus, in Fig. 88, if the plane, c 

 d, bo twice as long as the height, e d, FiG. 88. 



one pound at p, acting over the pulley, 

 would balance two pounds any where 

 between c and d. If the plane, c d, 

 were three times the length of d e, 

 then one pound at p would balance 

 three pounds any where on the plane, 

 c d, and so of all other quantities and 

 proportions. 



233. Roads which are not level may be considered as in- 

 clined planes, and the inclination of a road is estimated by 

 the height which corresponds to some proposed length. Thus, 

 we say a road rises one foot in twenty, or one in fifty, mean- 

 ing that if twenty or fifty feet of the road be taken, as the length of an in- 

 clined plane, the corresponding height of such a plane would be one foot, and 

 the difference of level between the two extremities of such a length of road 

 would be one foot. 



According to this method of estimating the inclination of 

 roads, the power required to sustain, or draw up a load, fric- 

 tion not considered, is always proportioned to the rate of ele- 

 vation. On a level road, the carriage moves when the horse exerts a strength 

 BufQcicnt to overcome the friction and resistance of the atmosphere ; but in 

 going up a hill, where the road rises one foot in twenty, the horse, beside 

 these impediments, is obliged to exert an extra force in the proportion of one 

 to twenty, or, in other words, he is obliged to lift one twentieth of the load. 

 It is, therefore, bad policy ever to construct a road directly over the summit 

 of a hill, when it can be avoided, because, in addition to the force necessary 



How do we es- 

 timate the in- 

 clination of 

 roads f 



IIow ought 

 roads to be 

 constructed ? 



