Lesson B4–6



MECHANICAL POWER

TRANSMISSION

Student Learning Objectives. Instruction in this lesson should result in students achieving the following objectives:

1 Define force, torque, work, power, and energy and explain their relationship to

each other and mechanical power transmission.

2 Determine the relationship between diameter and number of teeth on a gear or

sprocket and the speed and torque of the gear or sprocket.

3 Apply the Law of Conservation of Energy to power, torque, and speed relationships for mechanical power transmission.

Anticipated Problem: What is the definition of force, torque, work, power, and energy and how do they relate to each other?

I. Force can be defined as a push or pull that tends to start, stop, or change the direction of motion of an object. Force will vary depending upon gravitational forces. That is the reason our weight can vary from the earth to the moon due to the lower amount of gravitational pull on the moon thus making us weigh less on the moon versus the earth.

A. However, mass (the amount of matter in an object) is the same no matter what location we are at on this planet or any planet. Gravity is a force that acts upon an object. The more mass an object has, the greater the force of gravity that acts upon the object.

1. Force causes acceleration. The more force you apply to an object, the greater the rate

of acceleration.

2. Newton’s Second Law summarizes that the acceleration of an object is directly proportional to the force applied to the object and inversely proportional to the object’s

mass. The more mass and object contained, the lower the rate of acceleration.

3. To honor Sir Isaac Newton, the newton was adopted as the SI unit of force. One

newton of force can accelerate one kilogram of mass at a rate of one meter per second

per second.

B. The force that tends to cause objects to rotate or turn is torque. When we use a wrench, we apply force to the handle. This force creates rotary motion or torque on the nut, which turns the nut to tighten or loosen.

1. When calculating torque, the force applied is multiplied by the distance from the

center (radius). English units of torque are inch-pounds or foot-pounds. The SI

units are expressed as newton-meters, in honor of Isaac Newton.

2. A torque wrench is used by a mechanic to tighten nuts and bolts to prevent them

from loosening during engine vibration. The torque wrench can be adjusted to

deliver the recommended amount of force to cylinder head bolts on a lawnmower

engine without over tightening.

3. If the wrench is one foot long and we apply 100 pounds of force on it when tightening,

we are generating 100 foot-pounds of torque.

C. Work is the application of force to an object that causes the object to move in the direction of the force being applied. Lifting an object from the ground and placing it on a

shelf is an example of work. The force being applied equals the weight of the object

being lifted and the distance equals the height from the ground to the shelf.

1. Work equals force multiplied by distance. The units most often used to express

work are foot-pounds or newton-meters. Work is energy that has been used.

2. Power is a measure of how quickly work can be done. Power equals work divided by

the time. The SI (International System) unit for power is the watt.

3. One watt is equal to one newton-meter of work completed per second (N×m/s). If

we pushed on an object with one newton of force, and moved it at a speed of one

meter per second, our power output would be one watt (1 N × m/s).

4. A horsepower is equal to 746 watts. One horsepower is equivalent to 550 footpounds

or work performed in one second or 33,000 foot-pounds of work done in

one minute.

D. Energy is the capacity to do work. Energy is a measure of how long you can sustain your power output.

1. Potential energy is waiting to be converted to power. Compressed springs, gasoline,

food in your stomach, a skier at the top of the slope, are all examples of potential

energy.

2. Kinetic energy is energy of motion. Any object that is in motion has kinetic energy.

The more an object weighs, and the faster the object is moving, the greater the

kinetic energy the object possesses.

Anticipated Problem: What is the relationship that exists between the diameter and number of teeth of a gear and the speed and torque of the gear?

II. A gear is a toothed wheel used to transmit power. Gears are used for four main reasons: 1) reverse the direction of rotation, 2) increase or decrease the speed of rotation, 3) move rotational motion to a different axis, and 4) keep the rotation of two axes synchronized.

A. The gear ratio is determined by the distances from the center of the gear to the point of contact. If one gear is three times the diameter of the other, the ratio would be 3:1. This means that for every one revolution of the larger gear, the smaller gear will rotate three times in order to cover the same distance as the larger gear.

1. The majority of gears contain teeth. The teeth have three advantages on gears: 1)

maintain synchronization and prevent slippage, 2) eliminate the concern about

slight imperfections in diameter and circumference, and 3) make it possible to calculate

exact gear ratios by counting the number of teeth and divide.

2. For example, if one gear has 50 teeth and the other gear has 25 teeth, the gear ratio

between the two gears is 2:1.

B. Gears have many uses in mechanized devices. One of their most important uses is to

provide gear reduction to help with power and torque requirements. A small motor is

usually spinning fast enough to provide speed and power but not enough torque.

1. Gear reduction can be implemented in a device to reduce the output speed and subsequently increase the torque of the machine. If the power is constant in a machine,

torque and speed are inversely related, meaning that a reduction in one will result in

an increase in the other.

2. The diameter and number of teeth on a gear or sprocket is also inversely related to

speed, meaning the larger gear with more teeth will spin at a slower speed.

3. Speed of gears is measured in revolutions per minute (RPM).

Anticipated Problem: What is the Law of Conservation of Energy and how does it affect power, torque, and speed relationships?

III. Energy cannot be created or destroyed. Whenever work is done, the work appears as potential energy, kinetic energy, and horsepower, or the combination of all three.

A. The energy input to a system must equal the energy output. The horsepower of most

power sources used for agricultural applications is finite.

B. Trade-offs must be made between torque and speed (RPM) when the power is transmitted.

MECHANICAL POWER TRANSMISSION

Part One: Matching

Instructions: Match the word with the correct definition.

a. Force e. Gear ratio

b. Mass f. Law of Conservation of Energy

c. Torque g. Acceleration

d. Power h. Work

_______1. Applied force that causes movement in an object.

_______2. Energy cannot be created or destroyed.

_______3. Work ÷ Time.

_______4. Amount of matter in an object.

_______5. Force that tends to rotate or turn things.

_______6. Push or pull that causes motion in an object.

_______7. The number of turns of one gear compared to another gear.

_______8. An increase in velocity of an object.

Part Two: Fill-in-the-Blank

Instructions: Complete the following statements.

1. Force × distance / time would be used to calculate __________.

2. As gear diameter decreases, the speed would then __________.

3. The diameter and number of teeth on sprockets is inversely related to _________.

4. If a small gear turns a larger gear, the larger gear will turn _________ than thesmaller gear.

5. Gear diameter and torque are __________ related.

6. If power is constant, the torque and speed are __________ related.

7. When a large gear with a diameter of 18 cm is meshed to a smaller gear of 6 cm, the gear ratio would be __________.

Illinois Physical Science Applications in Agriculture Lesson B4–6 • Page 8

Part Three: Multiple Choice

Instructions: Write the letter of the correct answer.

_______1. The _____ of the pulley, sprocket, or gear when connected in a power train is related to the speed (RPM).

a. width

b. arbor size

c. diameter

d. type of material

_______2. A driver pulley with a 2" radius traveling at 800 RPM would cause a driven pulley that has a 4" radius to turn at _____ RPM.

a. 800

b. 1600

c. 2400

d. 400

_______3. Machines increase our capacity to do:

a. energy

b. power

c. work

d. none of the above

_______4. Force through a distance would be known as:

a. RPM

b. work

c. ratio

d. energy

_______5. A rotating force on a shaft is called:

a. torque

b. ratio

c. work

d. rate of work

_______6. Torque is calculated by taking:

a. RPM × distance

b. mass × acceleration

c. force × the length of the radius of rotation

d. mass ÷ distance

_______7. If a small gear with 21 teeth is powered by a larger gear with 42 teeth, the small gear will turn:

a. half the rpm

b. twice the rpm

c. 21 times the rpm as the larger gear

d. the same number of rpm as the larger gear

_______8. If a gear with 56 teeth turns a smaller gear with 14 teeth, the larger gear will turn:

a. one fourth the speed

b. four times the speed

c. faster

d. the same speed

Illinois Physical Science Applications in Agriculture Lesson B4–6 • Page 9

Part Four: Short Answer

Instructions: Answer the following questions.

1. List four ways that mechanical power transmission can be accomplished.

2. What is the relationship between diameter and speed for pulleys, sprockets, and/or gears?

Illinois Physical Science Applications in Agriculture Lesson B4–6 • Page 10

Assessment

Illinois Physical Science Applications in Agriculture Lesson B4–6 • Page 21

TS–A

Technical Supplement

MECHANICAL POWER

TRANSMISSION

Mechanical power is the hallmark of modern agriculture. Ask students to identify agricultural applications utilizing mechanical power (identify applications beyond commercial production to emphasize applications and occupations emerging in contemporary agriculture; i.e., urban agriculture, aquaculture, food engineering, microirrigation, etc.). For each identified application, discuss the location of the power source and where the power is actually being applied. Example: a ten speed bicycle has the power source located at the pedals; the power is applied, however, at the rear axle. Also ask if the speed and direction of the applied power is the same as that of the source.

Virtually all agricultural applications of mechanical power require the transmission of

power to some location other than the source, usually at varying speeds and direction.

What are some of the methods used for mechanical power transmission? What physical

principles apply to mechanical power transmission? Certain requisite concepts must be

understood before we begin our investigation of mechanical power transmission.

1. What is force?

A force is a push or a pull: the action of one object on another tending to change its

relative motion, position, size, or shape. Every physical action in the universe is

caused by some combination of forces. A force has magnitude, direction, and a point

of application. Force = mass × acceleration. Force is usually measured in pounds.

Illinois Physical Science Applications in Agriculture Lesson B4–6 • Page 22

2. What is work?

Machines transform a given motion into a desired motion. They perform work.

Work is done when motion results from the application of a force. Work is the product

of a force times distance in the direction of the force. Work = force × distance

The forces against each work is done include: friction gravity, elasticity, pressure

and inertia. Work is measured in ft-lbs.

3. What is torque?

Torque is an action that tends to produce or modify rotation.

Torque = force × perpendicular distance

Torque is measured in ft-lbs

4. What is power?

The term power is often used when talking about engines and motors. Power refers

to the rate at which work is done.

Power = work (ft - lbs)/time (sec)

Power = force * distance / time

Distance/Time = velocity (speed)

Horsepower is a common measure of power.

1 HP =(330 lb.)(100 ft)/1 min. = (33,000 ft - lbs) / min

Illinois Physical Science Applications in Agriculture Lesson B4–6 • Page 23

5. What is energy?

The concept of energy is difficult to define. Energy and work are synonymous terms. Both are product of force and distance. Energy is defined as the capacity to do the work. It appears in many forms: electrical, chemical, nuclear, mechanical. Our interest is in mechanical energy. Mechanical energy is either energy of motion (kinetic) or energy of position (potential). KE is the energy created or possessed by a body in motion; work against inertia. PE is work done against forces causing a change in position; work against gravity, elasticity and pressure. The energy is recovered when allowed to return to original position. The sum of KE + PE = total mechanical energy Work against friction is converted to heat energy and is wasted.

6. What is the relationship of diameter and number of teeth of sprockets, pulleys

and gears to torque and speed (RPM)?

Chains and sprockets, belts and pulleys, and gears are devices used to transmit

power for a source to a location. Often torque and RPM must be changed.

7. What is the relationship between power, torque and speed (RPM)?

Most agricultural applications of power begin with rotating shafts of electric motors

or internal combustion engines. We can determine the HP generated by these shafts

by analyzing the work done per unit time. Power = force x distance / time.

Torque = (force)(length of lever)[a]

Force = torque / length of lever

Illinois Physical Science Applications in Agriculture Lesson B4–6 • Page 24

The total distance traveled per revolution equals the circumference traveled by the

rotation of the lever arm.

Distance / Revolution = 2 L / rev

The total distance traveled per unit time is:

Distance / Revolution × rev / time = distance / time

By substitution, this becomes:

2 L / rev_ n / min rev / min = 2 × Ln ft

Substituting [a] and [b] into the power equation and including the HP conversion

yields:

Power = force x distance / time = 1 HP / 33,000

HP = torque / L × 2 Ln ft / min × ft – lb / 33,000 min

Illinois Physical Science Applications in Agriculture Lesson B4–6 • Page 25

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