Chapter 4 The Inclined Plane and The Wedge

Summary - 14037_30

Applications Afloat and Ashore - 14037_32

Basic Machines - Intro to machines and motion theories
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CHAPTER 4 THE INCLINED PLANE AND THE WEDGE CHAPTER LEARNING OBJECTIVES Upon completion of this chapter, you should be able to do the following: l Summarize the advantage of the barrel roll and the wedge. You have probably watched a driver load barrels on a truck. He backs the truck up to the curb. The driver then places a long double plank or ramp from the sidewalk to the tailgate, and then rolls the barrel up the ramp. A 32-gallon barrel may weigh close to 300 pounds when full, and it would be a job to lift one up into the truck. Actually, the driver is using a simple machine called the inclined plane. You have seen the inclined plane used in many situations. Cattle ramps, a mountain highway and the gangplank are familiar examples. The inclined plane permits you to overcome a large resistance, by applying a small force through a longer distance when raising the load. Look at figure 4-1. Here you see the driver easing the 300-pound barrel up to the bed of the truck, 3 feet above the sidewalk. He is using a plank 9 feet long. If he didn’t use the ramp at all, he’d have to apply 300-pound force straight up through the 3-foot distance. With the ramp, he can apply his effort over the entire 9 feet of the plank as he rolls the barrel to a height of 3 feet. It looks as if he could use a force only three-ninths of 300, or 100 pounds, to do the job. And that is actually the situation. Here’s the formula. Remember it from chapter 1? L R —=— IE In which L = length of the ramp, measured along the slope, 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, and R = 300 lb. By substituting these values in the formula, you get 9E = 900 E = 100 pounds. Since the ramp is three times as long as its height, the mechanical advantage is three. You find the theoretical mechanical advantage by dividing the total distance of the effort you exert by the vertical distance the load is raised or lowered. THE WEDGE The wedge is a special application of the inclined plane. You have probably used wedges. Abe Lincoln used a wedge to help him split logs into rails for fences. The blades of knives, axes, hatchets, and chisels act as wedges when they are forced into apiece of wood. The wedge is two inclined planes set base-to-base. By Figure 4-1.—An inclined plane. 4-1

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