Page 116 - Making things move_ DIY mechanisms for inventors, hobbyists, and artists

Chapter 5 Mechanical and Electrical Power, Work, and Energy 97

Think of energy as the capacity for doing work. In this case, the mechanism dragging
the roller-coaster cars up the hill took the cars from zero potential energy to a lot of
potential energy.

Now suppose the roller-coaster cars weigh 1,000 lbs all together, and they’re dragged
to a height of 200 ft. By changing their elevation, the dragging mechanism did 1,000
lbs × 200 ft = 200,000 lbs-ft of work!

We can also define work as force multiplied by distance:

Work (W) = Force (F) × Distance (d) = Energy (E)

This should look familiar from Chapter 1, where we talked about simple machines.
Work is just the amount of energy transferred by a force through a distance. For our
roller coaster, the dragging mechanism carried the 1,000 lbs of coaster cars up 200 ft,
so the work equals 1,000 lbs × 200 ft = 200,000 lbs-ft, which is the same answer as
from the potential energy method. The potential energy method and the mechanical
work method are two ways of thinking about the same situation.
Mechanical power is the rate that work is performed (or that energy is used):

Power (P) = Work (W) / Time (t) = Energy (E) / Time (t)

In the United States, mechanical power is usually measured in horsepower (hp). This
curious unit is left over from the days when steam engines replaced horses, and
equals the power required to lift 550 lbs by 1 ft in 1 second—the estimated work
capacity of a horse. One horsepower also equals approximately 746 watts, or 33,000
ft-lb per minute. You will often see motors and engines rated in horsepower.

Up until now, we’ve talked about work and power only in straight lines, but what
about power for a rotating motor? You might remember from Chapter 1, when we
talked about bicycles, that the speed of something spinning is called rotational
velocity. You just saw that work has units of force × distance, and luckily, as you
learned in the previous chapter, so does torque! So in this case, you can think of
torque as work being performed in a circle. Here’s the equation form:
Power (P) = Torque (T) × Rotational Velocity (ω)