Sub-Concept: Power Transmission
Agricultural Application: The agricultural industry relies on the efficient transmission of power in
mechanical systems.
Exercise: Measuring Rotary Horsepower
Applied Principle(s): Work and Power in Mechanical Systems
Goals:
Materials:
References: Refer to any high school physics textbook for information
2. Instruct the students to complete the activity as directed on their data sheets. You may wish to
monitor their progress as they work; however, it is suggested that the students be left to follow
the instructions and complete the activity on their own.
3. Once all groups have completed the exercise, discuss the answers to the discussion questions as
a class. Be sure to make note of the practical agricultural applications of the principles
demonstrated.
| Trial | Force
(lbs) |
Lever Arm
(ft) |
Torque
(lb-ft) |
Speed
(RPM) |
Horsepower
To x RPM 5252 |
| 1 | 0.5 | ||||
| 2 | 1.0 | ||||
| 3 | 1.5 | ||||
| 4 | 2.0 | ||||
| 5 | 2.5 | ||||
| 6 | 3.0 |
AGRISCIENCE EXERCISE
2. Fasten the output pulley to the end of the screwdriver.
3. Place the output pulley in the dynamometer load unit.
4. Secure the electric screwdriver in support blocks.
5. Set electric screwdriver rotation so that the lever arm pulls against the spring scale.
6. Adjust the load unit so that a force reading of one-half pound (1/2 lb) is obtained on the spring
scale as the output pulley rotates.
7. Count the number of rotations for a 15 second period. Transform revolutions/15 sec. to
revolutions/minute. Enter this value in the appropriate cell of the Data Table.
8. Repeat steps 5 through 7 with force readings for 1, 1.5, 2, 2.5, and 3 lbs. Record RPM data
for each trial in the appropriate cells of the Data Table.
9. Measure the length of the lever arm (horizontal distance from the center of the output pulley to
the center of the scale attachment point). Convert lever arm length to decimal parts of a foot, and
enter into the appropriate cells of the Data Table.
10. Calculate the torque (lb-ft) produced by the screwdriver during each trial. Enter values into
the appropriate cells of the Data Table.
11. Calculate the screwdriver's horsepower output for each trial. Enter values on the Data Table.
12. Develop a graph, based on your completed Data Table, that shows the relationship between
torque, speed, and horsepower for each trial.
13. Answer the following questions. Be prepared to share your answers with the class.
a. Assume that a given electric motor has a constant horsepower unit. What will be the
relationship between torque and speed for this motor? How can this be shown mathematically?
b. Why is a truck able to pull a heavier load when the transmission is in a lower gear (as opposed
to a higher gear)?
c. What conclusions about speed, torque and power can you make based on your completed Data
Table and graph?
TEACHER BACKGROUND SHEET
Equation 1: Horsepower = Force, lbs. X Distance, ft.
5252
Equation 1 is appropriate for calculating horsepower when the force moves in a linear (straight-line) fashion. (In fact, Equation 1 is sometimes called the "linear horsepower equation.")
However, since internal combustion engines and electric motors produce a rotary (rotating)
output force, Equation 2 (below) is used to calculate rotary horsepower.
Equation 2: Horsepower = Torque, lb-ft. X RPM
5252
Equation 2 is mathematically derived from the linear horsepower equation (Equation 1). This
derivation is shown below:
1. HP = F x D
T x 33,000
2. D = 2pr x RPM
3. HP = F x 2pr x RPM Note: Time has been eliminated from the 33,000 denominator because it is now included as
RPM (revolutions per minute) in the numerator.
4. F x 2pr x RPM / 2p Note: 2p = 2 x 3.1416 (or 6.2832)
33,000 / 2p
5. F x r x RPM
5252
6. To x RPM Note: Force x radius is the same as
5252 force x lever arm length. F x LA = Torque.
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