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
