CHAPTER 4THE INCLINED PLANE AND THE WEDGECHAPTER LEARNING OBJECTIVESUpon completion of this chapter, you should be able to do the following:lSummarize the advantage of the barrel roll and the wedge.You have probably watched a driver load barrelson a truck. He backs the truck up to the curb. Thedriver then places a long double plank or ramp fromthe sidewalk to the tailgate, and then rolls the barrelup the ramp. A 32-gallon barrel may weigh close to300 pounds when full, and it would be a job to lift oneup into the truck. Actually, the driver is using a simplemachine called the inclined plane. You have seen theinclined plane used in many situations. Cattle ramps,a mountain highway and the gangplank are familiarexamples.The inclined plane permits you to overcome alarge resistance, by applying a small force through alonger distance when raising the load. Look at figure4-1. Here you see the driver easing the 300-poundbarrel up to the bed of the truck, 3 feet above thesidewalk. He is using a plank 9 feet long. If he didn’tuse the ramp at all, he’d have to apply 300-poundforce straight up through the 3-foot distance. With theramp, he can apply his effort over the entire 9 feet ofthe plank as he rolls the barrel to a height of 3 feet. Itlooks as if he could use a force only three-ninths of300, or 100 pounds, to do the job. And that is actuallythe situation.Here’s the formula. Remember it from chapter 1?LR—=—IEIn whichL = length of the ramp, measured along theslope,1 = height of the ramp,R = weight of the object to be raised, or lowered,E = force required to raise or lower the object.Now apply the formula this problem:In this case,L= 9ft,1= 3 ft, andR= 300 lb.By substituting these values in the formula, you get9E= 900E= 100 pounds.Since the ramp is three times as long as its height,the mechanical advantage is three. You find thetheoretical mechanical advantage by dividing the totaldistance of the effort you exert by the vertical distancethe load is raised or lowered.THE WEDGEThe wedge is a special application of the inclinedplane. You have probably used wedges. Abe Lincolnused a wedge to help him split logs into rails for fences.The blades of knives, axes, hatchets, and chisels act aswedges when they are forced into apiece of wood. Thewedge is two inclined planes set base-to-base. ByFigure 4-1.—An inclined plane.4-1