Buggé: Energy 7
Power Up!
7.1 ​Below is an excerpt from Marshall Brain’s “How Horsepower Works” on howstuffworks.com. You
can read the entire article at ​http://auto.howstuffworks.com/horsepower.htm
Chances are you've heard about horsepower. Just about every car ad on TV mentions it, people talking about their
cars bandy the word about and even most lawn mowers have a big sticker on them to tell you the horsepower
rating.
But what is horsepower, and what does the horsepower rating mean in terms of performance? In this article, you'll
learn exactly what horsepower is and how you can apply it to your everyday life.
The term ​horsepower​ was invented by the engineer James Watt. Watt lived from 1736 to 1819 and is most
famous for his work on improving the performance of steam engines. We are also reminded of him every day
when we talk about 60-watt light bulbs.
The story goes that Watt was working with ponies lifting coal at a coal mine, and he wanted a way to talk about
the power available from one of these animals. He found that, on average, a mine pony could do 22,000
foot-pounds of work in a minute. He then increased that number by 50 percent and pegged the measurement of
horsepower at 33,000 foot-pounds of work in one
minute. It is that arbitrary unit of measure that has
made its way down through the centuries and now
appears on your car, your lawn mower, your chain
saw and even in some cases your vacuum cleaner.
What horsepower means is this: In Watt's
judgment, one horse can do 33,000 foot-pounds of
work every minute. So, imagine a horse raising
coal out of a coal mine as shown above. A horse
exerting 1 horsepower can raise 330 pounds of
coal 100 feet in a minute, or 33 pounds of coal
1,000 feet in one minute, or 1,000 pounds 33 feet
in one minute. You can make up whatever
combination of feet and pounds you like. As long
as the product is 33,000 foot-pounds in one
minute, you have a horsepower.
a. What is horsepower?
b. What is power? Use the word “rate” in your definition.
c. What is 1 horsepower (hp) equivalent to in (J/s)?
Additional References:
● PTPA Section 6.9
● Wilson/Buffa Section 5.6
Buggé: Energy 7
7.2​ Hans, a weightlifter, can bench press 100 kg (220 lbs). Hans can lift the 100 kg, from a height of 0.8
m above the ground to a height of 1.3 m in 0.2 seconds. Hans wants to determine the rate at which work
is done on the barbell and weights. What would you tell Hans to do, to determine the rate at which he
does work on the barbell and weights?
7.3​ Caroline is doing what is called a dead lift. She lifts a 30-pound barbell (13.6 kg) from the floor to
the level of her waist (a vertical distance of 1.0 m) in 0.80 s. Determine the power during the lift.
7.4​ Caroline performs an overhead press—lifting the same barbell from her shoulders to above her head.
Determine the power involved in this process. The length of her arm is approximately 40 cm. It takes her
1.0 s to lift the bar.
7.5​ Mr. Sierzega (mass 60 kg) moves on rollerblades on a smooth linoleum floor a distance of 4.0 m in
5.0 s. Determine the power of this process.
7.6​ A crane lifts an I-beam up the side of a building. The crane’s power output is 1750W for 20 seconds.
After 20 seconds the I-beam was moving at 2 m/s and the mass has 200 kg. Use the work-energy process
to determine the change in height of the I-beam.
​
7.7​ A 1400-kg car is traveling on a level road at a constant speed of 27 m/s (60 mph). The drag force
exerted by the air on the car, and the rolling friction force exerted by the road on the car add to a net
force of 680 N pointing opposite the direction of motion of the car. (a) Determine the power due to the
work done by this opposing force during this process. (b) The car instead drives up a 4.0 degree incline
at the same speed. Determine the power due to the work of the opposing friction-like forces and the
force exerted on the car by Earth during this process. Express both results in watts and in horsepower (1
hp = 746 W).
7.8​ The quickest times for the Sears Tower stair climb (103 flights, or 2232 steps) is around 20 minutes.
(a) Estimate the mechanical power in watts for a top climber. Indicate any assumptions you made. (b) If
the body is 20 percent efficient at converting chemical energy into mechanical energy, approximately
how many joules and kilocalories of chemical energy does the body expend during the stair climb?
Note: 1 food calorie = 1 kilocalorie = 4186 J. ​Efficiency is a very ​complicated subject—especially
relative to mechanical work done by the human body. For example, it takes about 10 J of food energy
for the food we eat to produce the equivalent of 1 J of chemical energy in the body. If the body can
convert only 20 percent of this chemical energy to mechanical work, then we get 0.2 J of work for each
10 J invested in producing food.