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you climb a stairway, drive a road that
E R R E E R
switches back and forth when going up
a mountainside, or use a board to slide
a heavy box up to a loading dock. Each
use gives a large mechanical advan- First-class lever Second-class lever Third-class lever
tage by trading distance for force. For
example, sliding a heavy box up a 10 m BOX FIGURE 3.2 The three classes of levers are defined by the relative locations of the
ramp to a 2 m high loading dock raises fulcrum, effort, and resistance.
the box with less force through a greater
distance. The mechanical advantage of
this inclined plane is (Box Figure 3.2). A first-class lever has a circle. Examples are a screwdriver,
E _
d the fulcrum between the effort force door knob, steering wheel, and any
MA = and the resistance force. Examples are application of a turning crank. The

d
R
_ a seesaw, pliers, scissors, crowbars, and mechanical advantage is found from
10 m
= shovels. A second-class lever has the the radius of the wheel, where the
2 m
effort resistance between the fulcrum effort is applied, to the radius of the
= 5
and the effort force. Examples are axle, which is the distance over which
Ignoring friction, a mechanical nutcrackers and twist-type jar openers. the resistance moves. For example, a
advantage of 5 means that a force of A third-class lever has the effort force large screwdriver has a radius of 15 cm
only 20 newtons would be needed to between the resistance force and the in the handle (the wheel) and 0.5 cm
push a box weighing 100 newtons up fulcrum. Examples are fishing rods in the bit (the axle). The mechanical
the ramp. and tweezers. advantage of this screwdriver is
2. The wedge is an inclined plane that A claw hammer can be used as a d
E _

moves. An ax is two back-to-back first-class lever to remove nails from a MA =
d
inclined planes that move through the board. If the hammer handle is 30 cm R
3 cm
wood it is used to split. Wedges are and the distance from the nail slot to = _

found in knives, axes, hatchets, and nails. the fulcrum is 5 cm, the mechanical 0.5 cm
3. The screw is an inclined plane that advantage will be = 6
has been wrapped around a cylinder, d 6. A pulley is a movable lever that rotates
E _

with the threads playing the role of the MA = around a fulcrum. A single fixed
d
R
incline. A finely threaded screw has _ pulley can only change the direction

a higher mechanical advantage and = 30 cm of a force. To gain a mechanical
5 cm
requires less force to turn, but it also advantage, you need a fixed pulley and
= 6
requires a greater effort distance. a movable pulley such as those found
4. The lever is a bar or board that is free 5. A wheel and axle has two circles, in a block and tackle. The mechanical
to pivot about a fixed point called a with the smaller circle called the axle advantage of a block and tackle can be
fulcrum. There are three classes of and the larger circle called the wheel. found by comparing the length of rope
levers based on the location of the ful- The wheel and axle can be consid- or chain pulled to the distance the
crum, effort force, and resistance force ered to be a lever that can move in resistance has moved.
or the rate at which work is done is called power (Figure 3.4).
If the person had a time of 3 s on the same stairs, the power rat-
Power is measured as work per unit of time,
ing would be greater, 400 ft·lb/s. This is a greater rate of energy
_ use, or greater power.
work
power =
time When the steam engine was first invented, there was a need
W _ to describe the rate at which the engine could do work. Since

P =
t people at this time were familiar with using horses to do their
equation 3.2 work, the steam engines were compared to horses. James Watt,
who designed a workable steam engine, defined horsepower as
Considering just the work and time factors, the 120 lb person
a power rating of 550 ft·lb/s (Figure 3.5A). To convert a power
who ran up the 10 ft height of stairs in 4 seconds would have a
rating in the English units of ft·lb/s to horsepower, divide the
power rating of
power rating by 550 ft·lb/s/hp. For example, the 120 lb per-
(120 lb)(10 ft)
W _ __ _ son who had a power rating of 400 ft·lb/s had a horsepower of
ft·lb

P = =
= 300

t 4 s s 400 ft·lb/s ÷ 550 ft·lb/s/hp, or 0.7 hp.
3-5 CHAPTER 3 Energy 65