Materials Included In Kit

Additional Materials Required

Safety Precautions

This activity is considered safe. Please follow all laboratory safety guidelines.

Disposal

All materials can be stored for future use.

Teacher Tips

• Enough materials are provided in this kit for one group of students. The laboratory can be completed in one or two 50-minute class periods depending on the amount of data collected.
• It is important for the gears to be meshing properly when a heavy weight is added to the axle spool. Readings should be taken on the spring scale with an even pull when the gears are working smoothly, not the force needed to start the gear moving. Adjacent gears with a smaller ratio tend to mesh better than gears with larger ratios.
• It is important that the string is tied securely around the spool before wrapping the string on the spool. The string must be partially wrapped on the spool at all times when recording data.
• The “lock” nuts can be tightened with pliers or other tools if “finger-tight” is not sufficient.
• Alignment of the gears in the gear box is critical. Experiment with gear combinations and the various axle slots. Also, the nuts and arrangement on the axles can be adjusted for perfect alignment. Figures 5 and 6 may be helpful as you provide student assistance.
• A 50-g hanger for slotted weights may be used instead of a 100-g hanging mass.
  {13928_Tips_Figure_5_Top view of three-gear arrangement}
  {13928_Tips_Figure_6_Side view of three-gear arrangement}

Sample Data

Part I. Gear Specifications

Answers to Questions

Part I. Gear Specifications

1. What is the relationship between number of teeth and the radius of the gears?

   Since the teeth are evenly spaced, there is a direct correlation between the number of teeth and the diameter of the gears. When the radius doubles, the number of teeth also doubles.

Part II. Gearing Direction

1. Draw a sketch of a two-gear system with a driver and follower gear. Indicate the direction (CW/CCW) that each gear turns relative to the other gear.
   {13928_Answers_Figure_7}
2. Draw a sketch of a three-gear system with a driver, idler, and follower gear. Indicate the direction (CW/CCW) that each gear turns relative to the others.
   {13928_Answers_Figure_8}

Part III. Gearing Speed/Distance

1. Observe the larger driver gear as it drives the small follower gear.
   1. What happens to the speed of the follower gear compared to the driver gear?

      The follower gear turns faster than the driver gear.

   2. How many times does the follower gear rotate for each complete rotation of the driver gear?

      The smaller follower gear makes two revolutions for each revolution of the larger gear.

2. When the smaller gear is driving the larger gear, what happens to the speed of the follower compared to the driver?

   The follower gear is much slower (fewer revolutions per time) than the driver gear.

3. Examine the gear specifications in the data table on Part I of this worksheet. How does the number of teeth on the gears compare to the distance traveled and speed of the gears?

   With equal-sized meshing teeth, the distance each tooth moves is equal on all the gears. What changes is the number of revolutions or speed with various gear combinations. The ratio of the number of teeth of the driver and follower gears is inversely proportional to the ratio of the number of revolutions per unit of time.

Part IV. Gearing Up/Down
Weight of hanging mass ____1___ N

1. Record the amount of force required to lift the 100-g mass on the small gear with the medium gear. ___1.7___ N
2. Consider the two-gear arrangement described in Question 1.
   1. How does the ratio of the radii of the small to medium gears compare to the ratio of the weight lifted and the force required?

      The ratio of the radii is 1:1.5 and the ratio of the weight lifted and force is 1:1.7.

   2. Are the ratios the same? Why or why not?

      The ratio of the weight lifted and force is slightly greater than the ratio of the radii. Some force is needed to overcome friction between the gears and other moving parts.

   3. What is the mechanical advantage of the gear arrangement?

      MA = 1 N/1.7 N = 0.59

3. Record the amount of force required to lift a 100-g mass on the medium gear with the small gear. ___0.65__ N
4. What is the mechanical advantage of the gear arrangement described in question 3?

   MA = 1 N/0.65 N = 1.54

5. Consider the mechanical advantage of each gear arrangement from questions 2c and 4.
   1. When might a mechanical advantage greater than 1 be useful?

      A mechanical advantage greater than 1 is useful when an increase in force is needed or when a reduction in speed is desired.

   2. When might a mechanical advantage less than 1 be useful?

      A mechanical advantage less than 1 is useful when an increase in speed is desired.

Introduction

We are surrounded by gears. They are in our cars, clocks, dishwashers, wash machines, dryers, drills, saws and many other common mechanical devices. What do gears do? Why are they used? What are their advantages?

Concepts

• Work
• Mechanical advantage
• Simple machines
• Gears

Background

A simple machine is a piece of equipment that changes the size or direction of an applied force. Examples of simple machines include the pulley, screw, wheel and axle, gear, lever, inclined plane and wedge. These devices may appear simple, but by grouping various simple machines together, very complex machines can be created, such as engines or cranes.

Simple machines are useful because they reduce the amount of force needed to move or lift an object. Simple machines provide the means for a normal person to lift a two-thousand pound car in order to change a tire (using a car jack). The ratio of how much force is applied to how much force (weight) is moved is referred to as the mechanical advantage of the simple machine (abbreviated MA). For example, a simple machine that has a mechanical advantage of five will provide five times more lifting force compared to the applied force. That is, 100 N of applied force can lift a 500-N object. The mechanical advantage of a simple machine is determined by calculating the ratio of the force required to move the object without the assistance of a simple machine to the actual force applied to the simple machine (Equation 1).

A simple machine does not provide “extra force” for free without something in return. A simple machine with a mechanical advantage of five will provide five times more lifting force compared to the force that is applied. However, the smaller applied force must be used over a distance that is five times farther than the distance the heavier object moves. The ideal mechanical advantage of a simple machine is determined by comparing how far the applied force moves to how far the object moves. It is considered “ideal” because it is based only on distances. Actual mechanical advantage must account for the force needed to overcome friction, as well as other factors. Therefore, actual mechanical advantage will always be less than the ideal mechanical advantage.

A gear is a wheel with notches (called teeth) on its rim. Usually a gear is mounted on a shaft (axle). Two gears are often positioned so that their teeth mesh. When one gear turns, its teeth push on the teeth of the other gear. This causes the second gear to move.

When two gears mesh together in a gear box or other mechanical system, one gear drives the other by applying force to it. The gear that applies force is called the driver or input gear. The other gear is called the follower or output gear. The driver gear is turned by its shaft and the follower gear turns its shaft (see Figure 1).

Materials

Safety Precautions

This activity is considered safe. Please follow all laboratory safety guidelines.

Procedure

Part I. Gear Assembly

1. Before assembling the gears, make measurements of the three gears.
   1. Measure the diameter of each gear.
   2. Calculate the radius of each gear (d/2).
   3. Count the number of teeth on each gear.
   4. Fill in the data table for Part I of the Investigating Gears Worksheet. Answer the question for Part I on the worksheet.
2. Use Figure 2 to help assemble a small, medium and large gear on an axle.
   {13928_Procedure_Figure_2_Gear assembly}
3. The assembled gears can be set into the pre-cut slots in the gear box. When placed in the proper slots, the gears will mesh and can be turned smoothly by rotating the axle of the gear shaft.
4. Make adjustments to the gear positions on the shafts by turning the nuts in or out along the bolt axis. When best locations have been determined, pliers can be used to “lock” the axle in place by turning the two nuts in opposite directions (see Figure 3).
   {13928_Procedure_Figure_3_Top view of gear in gear box}

Part II. Gearing Direction

1. Place two gears in the gear box so that they are meshing smoothly and work easily with a twisting of their axles.
2. Make one gear a driver gear and one gear a follower by turning the axle of the one designated as the driver.
3. Turn the driver gear slowly and note whether it is turned clockwise (CW) or counterclockwise (CCW). Note: Always make CW/CCW observations from the same viewpoint to be consistent.
4. What direction does the follower gear turn? Draw a sketch of the two gears in Part II on the worksheet. Label the driver and follower gears and use labeled arrows to indicate the direction of rotation (CW or CCW).
5. Place three gears in the gear box so that they are meshing smoothly and work easily with a twisting of their axles. Make adjustments as necessary.
6. Designate one of the outer gears as the driver gear. The center gear is called an idler gear and the gear farthest from the driver is the follower gear.
7. Turn the driver gear slowly noting the direction it is turned (CW/CCW). Observe the idler gear and the follower gear and note their directions of rotation.
8. Draw a sketch of the three-gear setup in Part II of the worksheet. Label the driver, idler and follower gears and note their rotation directions with labeled arrows.

Part III. Gearing Speed/Distance

1. Place the small gear and large gear into the gear box so that they are meshing smoothly and work easily with a twisting of the axles.
2. Using the large gear as the driver, turn the axle and observe the effect of driving with the large gear. Record your observations in Part III of the worksheet, question 1a.
3. Place a mark with a marker or wax pencil on the gear tooth at the top of each gear. Rotate the driver gear one rotation. Count the number of times the follower gear rotates for each rotation of the driver gear.
4. Answer part b of Question 1 in Part III of the worksheet.
5. Now reverse the driver/follower arrangement. Use the small gear as the driver. Count the revolutions of the follower compared to the driver. Answer questions 2–3 for Part III of the worksheet.

Part IV. Gearing Up/Down

1. Tie a paper clip to the end of a 60-cm piece of string. Tie the other end tightly around the wooden spool on the gear axle of the smallest gear. Cut off any excess string at the spool. Transparent tape can be used to secure the string to the spool before winding the string around the spool.
2. Loosely wrap the string around the spool and place the gear in the gear box.
3. Tie a paper clip to the end of another 60-cm piece of string. Tie the other end tightly around the wooden spool on the gear axle of the medium gear.
4. Wrap the string loosely around the spool on the medium gear and place the gear in the gear box so that it meshes with the smallest gear.
5. The direction of the string wrapping is critical for the direction the gear rotates (as discovered in Part II). Experiment with the rotation of the gears until pulling down on the string wrapped on the large gear pulls the string up on the small gear.
6. Place the gear box between two tables or other flat objects so that the strings can hang below the gear box. (Alternately, use a C-clamp to clamp the gear box over the edge of the table.)
7. Zero the spring scale and then attach the hanging mass to the hook at the bottom of the spring scale.
8. Measure the weight of the 100-g hanging mass in newtons. Record the weight in Part IV of the worksheet.
9. While holding onto the string on the medium gear, hang a 100-g weight from the paper clip at the end of the string on the small gear. The string should be partially unwound and below the gear box (see Figure 4).
   {13928_Procedure_Figure_4_Experimental setup}
10. Hook a spring scale into the paper clip on the string on the medium gear. Without any tension on the spring, zero the spring scale in this position. Note: The spring scale must be zeroed in this position, which is different than in step 7.
11. Making sure that the gears are working smoothly, determine the minimum amount of force that is required to smoothly lift the weight attached to the smaller gear. Slowly and evenly pull down on the spring scale until the mass is lifted with a constant speed.
12. Record the required force in newtons in Part IV of the worksheet and answer Questions 2a–c of Part IV of the worksheet.
13. Repeat steps 9–12 but reverse the position of the weight and the spring scale on the two gears. Determine the amount of force required to lift the weight in the new configuration. Record the force in Part IV of the worksheet and answer Questions 4–5 on the worksheet.
14. Consult with your instructor about disassembly of parts.

Student Worksheet PDF

13928_Student1.pdf