University of Arkansas - AgriScience Project

AGRISCIENCE EXERCISE

PHYSICAL SCIENCES IN AGRICULTURE


Key Concept: Energy & Power Systems

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:

  1. Calculate the horsepower output of an electric screwdriver based on data obtained using a prony brake dynamometer.
  2. Describe the relationship between torque, speed and power for an electric motor.
  3. Graph the torque, speed, power relationship for an electric motor.


Materials:



References: Refer to any high school physics textbook for information


Procedures for Conducting the Activity:

1. Divide the class into pairs of students, and provide each with a data sheet and the necessary materials for this exercise.

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.


DATA TABLE

Trial Force

(lbs)

Lever Arm

(ft)

Torque

(lb-ft)

Speed

(RPM)

Horsepower

To x RPM

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1 0.5
2 1.0
3 1.5
4 2.0
5 2.5
6 3.0



AGRISCIENCE EXERCISE

- Measuring Rotary Horsepower -

Student Data/Instruction Sheet


1. Gather the following materials:



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

- Measuring Rotary Horsepower -


In the United States, the horsepower unit is the commonly used measure of the power output of internal combustion engines and electric motors. By definition, one horsepower is the ability to do 33,000 foot-pounds (ft-lbs) of work in one minute (or 550 ft-lbs of work in one second). The basic horsepower formula is presented below as Equation 1:

Equation 1: Horsepower = Force, lbs. X Distance, ft.

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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

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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

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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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