Materials Included In Kit

Additional Materials Required

Prelab Preparation

Experiment 1. The Inclined Plane

1. At one end, measure approximately 12 cm from the end of the board and lightly mark this point with a pencil. The mark should be far enough from the end of the inclined plane so that all four wheels of the Hall’s carriage are on the inclined plane when the front of the carriage lines up with this mark.
2. Use a ruler to make a light pencil line through this 12-cm mark so the line is parallel to the end of the Board (see Figure 16). This line represents the “starting line.”
   {13280_Preparation_Figure_16}
3. At the opposite end, measure approximately 7 cm from the end of the board and lightly mark this point with a pencil.
4. Repeat step 3 to draw the “finish” line.

Experiment 4. Investigating Gears

1. Use the following drawing to help assemble a small, medium, and large gear on an axle.
   {13280_Preparation_Figure_17_Gear assembly}
2. 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.
3. 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.

Safety Precautions

The materials in this lab are considered safe. Please follow all normal laboratory safety guidelines.

Disposal

The materials from each lab should be saved and stored in their original containers for future use.

Lab Hints

Experiment 1. The Inclined Plane

• Enough materials are provided in this kit for one student group.
• The pulley, thin screws, washers and wing nut are supplied in this kit as an additional accessory. They are not required for this lab, but can be used if hanging masses are used to pull the carriage instead of a spring scale.
• In order to determine the necessary force needed to raise the Hall’s carriage, students must pull on the spring scale at a constant speed. When the carriage is being raised with a constant speed, the force registered on the spring scale will remain relatively constant (the pulling force and force due to gravity will be balanced). Students should record the force on the spring scale only when the carriage is moving at a constant speed.
• Textbooks can be placed under the support stand in order to raise it high enough to achieve the 45° or higher angles. If a tall support stand is used, textbooks may not be necessary.

Experiment 2. Investigating Levers

• Enough materials are provided in this kit for one student group. The laboratory activity and its discussion will likely require two or more 50-minute class periods.
• Advise students not to exceed the limit of the spring scale. If this should occur, students should reposition the mass, fulcrum or spring scale accordingly.
• By keeping the fulcrum at the center of mass of the meter stick, the mass of the meter stick will not contribute to the mass being held in position by the spring scale. If the fulcrum was not at the center of mass of the meter stick, the mass of the meter stick would need to be taken into account during the experiment. The meter stick with lever clamps weighs about 1.5–1.75 N.
• Students should twist the meter stick slightly so that it does not rub against the support stand rod.
• Spring scales are designed to be held vertically with the mass hanging down. When a spring scale is pulled down, inaccurate measurements will result (due to unaccounted-for mass in the spring scale). Therefore, for Lever Type I, a string and pulley system must be used to redirect the downward pulling force to a lifting force. Students should use their pencils and string to redirect the downward force (see Figure 7 in the student instructions).
• To reduce the frictional forces when redirecting the force for the Type I lever, a nail and a sewing bobbin can be used to make a simple pulley.
• The knife lever clamps will not fit meter sticks with metal ends. Use hardwood or plastic meter sticks with plain ends.

Experiment 3. Investigating Pulleys

• Enough materials are provided in this kit for three student groups. The laboratory can be reasonably completed in one 50-minute class period.
• The activity can be extended by testing different masses with the same pulley setups. How does the efficiency change as the mass is increased or decreased?
• The efficiency for parts of the experiment will not be high because the masses of the pulleys themselves contribute to the amount of mass lifted. For more accurate results, students should measure the mass of the bottom (moving) pulley and include this in the total load lifted.
• Setting up the pulley arrangement is the most time-consuming portion of this Simple Machines Kit. Three sets of pulleys are provided so that three groups can work on this experiment at one time.
• The last pulley arrangement is tricky to set up. Remind students to be patient with this pulley arrangement, and help students as needed. It helps to hang the mass on the lower pulley to create tension in the string, which keeps the string in the pulley sheave.

Experiment 4. Investigating Gears

• Enough materials are provided in this kit for two student groups. 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.
• 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.
• Other gear combinations can be tested and data collected—especially if the principles are not initially clear to students. Compound gearing (three or more gears) can also be tested by using all three gears in series.
• It is important that gears are placed in the gear box in the proper slots and facing in the right direction. The diagrams in the Prelab Preparation section might be helpful as you provide student assistance.

Teacher Tips

• Set up each lab station accordingly before class. Students should leave the stations as they find them before they move on to the next lab station.
• Before class, prepare copies of the student worksheets and Background information for each student.

Sample Data

Experiment 1. The Inclined Plane

Distance between starting line and finish line:     36.8 cm    
Mass of Hall’s carriage:    55.2 g     
Additional mass added to Hall’s carriage:    100 g    

Results Table
Weight of Hall’s carriage plus any additional mass:    1.52 N     Experiment 2. Investigating Levers Lever

Type I Worksheet

*Load is equal to the weight of the slotted masses. W = mg, where (0.1 kg)(9.8 m/s²) = 0.98 N≈1N.

Lever Type II Worksheet

*Load is equal to the weight of the slotted masses. W = mg, where (0.1 kg)(9.8 m/s²) = 0.98 N≈1N.

Lever Type III Worksheet

*Load is equal to the weight of the slotted masses. W = mg, where (0.1 kg)(9.8 m/s²) = 0.98 N≈1N.

Experiment 3. Investigating Pulleys

Answers to Questions

Experiment 1. The Inclined Plane

1. Multiply the mass of the Hall’s carriage plus additional mass (in kilograms) by the acceleration due to gravity constant to determine the weight (in Newtons) of the carriage. Record this in the results table.

   Sample calculation: 155.2 g x (1 kg/1000 g) x 9.81 m/s² = 1.52 N

2. Use Equation 2 to calculate the ideal mechanical advantage for each experimental angle of the inclined plane. Record this information in the results table.

   Sample calculation: 36.8 cm/(15.9 cm – 5.2 cm) = 3.44

3. Use Equation 1 to calculate the actual mechanical advantage for each experimental angle. Record this information in the results table.

   Sample calculation: 1.52 N/0.50 N = 3.04

4. Calculate the amount of energy that was needed to raise the carriage for each inclined plane angle. To do this, multiply the force needed to raise the carriage at a specific angle by how far the carriage traveled along the inclined plane (in meters). The resulting energy will have units called Joules (J). Record these calculations, including units, in the results table.

   Sample calculation: 0.50 N x 0.368 m = 0.184 J

5. Calculate the “ideal” energy required to raise the carriage from the starting line height to the finish line height by multiplying the weight of the Hall’s carriage by total height the carriage was raised. Record this in the results table.

   Sample calculation: 1.52 N x (15.9 cm – 5.2 cm) x (1 m/100 cm) = 0.163 J

6. What angle of the inclined plane made raising the Hall’s carriage the easiest?

   The smallest angle (17.0°) required the least amount of force to raise the Hall’s carriage.

7. How does the mechanical advantage compare to the ease of raising the Hall’s carriage?

   The larger the mechanical advantage, the easier it is to raise the Hall’s carriage. More force is required to lift the Hall’s carriage when the mechanical advantage is small.

8. What is an advantage of an inclined plane?

   An advantage of a simple machine is that it helps reduce the force needed to raise a heavier object.

9. What is a disadvantage of an inclined plane?

   The disadvantage of a simple machine is that, although a smaller force is required, the force must be applied over a longer distance compared to how far (or high) the object moves.

10. Explain why the energy required in each case is similar to the “ideal” energy even though the needed force was less than the weight of the carriage. If any “extra” energy was needed to raise the carriage up the inclined plane, compared to the ideal case, why was it needed?

    The energy required to raise the Hall’s carriage with an inclined plane was similar to the ideal case of simply lifting the carriage straight up because the force used to raise the carriage to a certain height was used for a longer distance along the inclined plane. The energy was a force multiplied by the distance. For each case, the actual energy required was slightly larger than the ideal case. It required more energy to raise the carriage using the inclined plane because “extra” energy was needed to overcome the forces of friction in the wheels of the carriage and in the spinning pulley.

11. Based on the results of this lab, what would be the best position of a ramp used to raise a 500-lb motorcycle into the back of a truck in the easiest possible way?

    In order to raise a motorcycle into the back of a truck with the least amount of force, a ramp must be used in such a way as to have the smallest angle with respect to the ground. The longer the ramp, the smaller the angle and the easier it will be to raise the motorcycle.

Experiment 2. Investigating Levers

Lever Type I Worksheet

1. In a Type I Lever, where is the fulcrum when the force and load are equal?

   The fulcrum is equidistant between the force and load.

2. In a Type I Lever, what happens to the force required to lift a load as the load gets closer to the fulcrum? What happens to the mechanical advantage?

   The force required to lift the load decreases and the mechanical advantage increases.

3. When the load is very close to the fulcrum and the force is far from the fulcrum, how does the distance the force moves compare to the distance the load moves?

   The load moves a very short distance compared to the lever at the point of the force.

4. True or False? Defend your answers.
   1. Lever Type I system would be good for moving a heavy object a small distance with less force required than the load.

      True. The mechanical advantage is large when the fulcrum is close to the load.

   2. Lever Type I system would be good for moving an object with great speed.

      False. The load moves very little distance compared to the force.

   3. A shovel is an example of a Lever Type I.

      If the arm positioned in the middle of the shovel is used as a fulcrum, it can be a Lever Type I. The arm positioned at the end of a shovel can be used as a fulcrum and then the shovel becomes a Lever Type III.

Lever Type II Worksheet

1. Where would you place a load with this lever system to spend the least force to lift the load?

   When the load is closest to the fulcrum, the least force is required to lift the load.

2. Would Lever Type II be a good system for lifting a heavy load with minimal force? Explain. How might the position of the lever be a problem with a Type II lever?

   Yes. The lever is very capable of having a high mechanical advantage. Getting the actual lever under the load can be a problem.

3. Would Lever Type II be a good system for moving a load a long distance? Explain.

   No. When the load is close to the fulcrum, the force moves a great distance while the load hardly moves any distance. The lever can have a good mechanical advantage, but has no speed or distance.

4. Think of at least one common item that illustrates a Lever Type II system and explain how it works. What are the advantages and disadvantages of using the item in doing work?

   A wheelbarrow is a Type II lever system. Its good mechanical advantage allows lifting a heavy load with little relative force. The load, however, is not lifted very high off the ground if this were desired.

Lever Type III Worksheet

1. What happens to the force required to lift the load as the force gets further from the load and closer to the fulcrum?

   The force required to lift the load increases.

2. What happens to the mechanical advantage as the force gets closer to the fulcrum?

   The mechanical advantage decreases as the force gets closer to the fulcrum.

3. When the force is close to the fulcrum and a load is lifted, how does the distance the force moves compare to the distance the load moves? When might such an arrangement be advantageous?

   The distance the load moves is much greater than the distance the force moves. Such an arrangement can use this distance travel to gain speed.

4. Why is the fulcrum maintained at the center of the meter stick for all the lever arrangements?

   To eliminate the mass of the meter stick during the measurements. The meter stick is maintained at its center of mass and therefore contributes to the mass equally on each side of the fulcrum.

Experiment 3. Investigating Pulleys

1. Examine the efficiency calculations for each pulley setup. What are some possible reasons that the efficiency is never 100%?

   The friction on the axle and the string riding on the wheel reduces efficiency as well as any stretch in the string. Also, the mass of the hanging pulley was not taken into account as part of the load.

2. What happens to the force (F) as the mechanical advantage gets larger? What happens to the distance the force moves as the mechanical advantage gets larger?

   The force required to lift the weight decreases as the mechanical advantage increases. The distance the force moves increases as the mechanical advantage increases. Force needed is traded for distance moved.

3. How does increasing the number of pulleys affect the mechanical advantage? How does the number of supporting strings relate to the mechanical advantage? How does the number of strings relate to the ideal mechanical advantage?

   The mechanical advantage value is very close to the number of supporting strings in a pulley system. As more pulleys are added to a system, the mechanical advantage tends to go up. The ideal mechanical advantage of the pulley system is equal to the number of supporting strings.

4. True or False: A machine reduces the amount of work you have to do. Explain your answer.

   False. The amount of Joules of work required to lift the weight with a pulley is actually greater than the work accomplished in lifting the weight. This is reflected in the efficiencies not exceeding or equaling 100%.

Experiment 4. Investigating Gears

Part I. Gear Specifications

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

   Since the teeth are perfectly spaced, there is a direct correlation between the number of teeth and the diameter of the gears.

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.
   {13280_Answers_Figure_24}
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.
   {13280_Answers_Figure_25}

Part III. Gearing Speed/Distance

1. When the larger driver gear is driving the small follower gear, what happens to the speed of the follower gear compared to the driver gear? (Compare revolutions per unit time.)

   The smaller follower gear makes two revolutions for every one of the larger gear. It is thus going more revolutions per unit time and its speed is faster.

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 (less revolutions per time) than the driver gear.

3. Examine the gear specification 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.

Part IV. Gearing Up/Down

1. Record the amount of force required to lift the 100 g (1 N) weight on the large gear with the small gear.

   0.75 N

2. How does the ratio of the number of teeth on the gears compare to the ratio of the weight lifted and the force required? How does the ratio of the diameters compare?

   Ideally, with no friction, etc., there should be a perfect direct correlation between the force required and the load in a ratio equal to the ratio of the number of teeth and diameters. (1 : 2)

3. What is the mechanical advantage of this gear setup? Where might such a gear setup be useful?

   The mechanical advantage would be

   {13280_Answers_Equation_9}

   when more force (torque) is required to lift a heavy load with minimum input.

4. Record the amount of force required to lift the 100 g weight on the large gear with the small gear.

   2.5+ N

5. What is the mechanical advantage of this gear arrangement? When might such a gear arrangement be used?

   The mechanical advantage would be

   {13280_Answers_Equation_10}

   when greater speed is desired from an output gear, such as in a drill.

Introduction

This all-in-one Simple Machines Kit provides the opportunity to experiment with four different simple machines. Gain an understanding of mechanical advantage, gear ratios and first-, second- and third-class levers as well as other benefits of simple machines. Four hands-on lab stations focus on experiments with each simple machine throughout the lab time.

Concepts

• Simple machines
• Mechanical advantage
• Inclined plane
• Force
• Load
• Fulcrum
• Lever types
• Wheel and axle
• Pulley
• Work
• Gear ratio
• Idler gear
• Driver gear
• Torque
• Follower gear

Background

Experiment 1. The Inclined Plane

A simple machine is a piece of equipment that changes the size or direction of an applied force. Examples of simple machines include pulleys, screws, gears, levers and wedges. These devices may appear “simple,” but by grouping various simple machines together, very “complex” machines can be created, such as engines or cranes. An inclined plane is another example of a simple machine. An inclined plane is more commonly referred to as a ramp.

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). Simple machines can also be used by a 200-lb man to move a two-ton boulder (using a lever). The comparison between how much force is applied to how much force (weight) is moved is referred to as the mechanical advantage of the simple machine. 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 lb of applied force can lift a 500-lb 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. For the inclined plane, the ideal mechanical advantage can be calculated using Equation 2. Experiment 2. Investigating Levers

Levers are rigid objects, usually in the shape of a bar, that can turn on one point or axis. This point is called the fulcrum in the lever system. A lever is used for the transfer and modification of force and motion. The movement of objects can be made faster/slower, longer/shorter or easier/harder and can occur in various patterns. In a lever system, the lever itself is always rigid—like a bar, rod, plank or other rigid object. The load is whatever is being moved—a rock, a load in a wheelbarrow or other heavy object. The force is anything capable of doing mechanical work; it may be a spring, a motor, a jet, a person, or any other item that can exert a force on the lever itself.

Lever systems in action are useful in gaining speed, distance, precision, or mechanical advantage. Mechanical advantage is defined as the ratio of force output to the force applied. Each lever system has its own unique properties and has tradeoffs between mechanical advantage and other properties. In general, there is a reverse relationship between mechanical advantage and both the amount and speed of movement, but there is no necessary relationship to precision.

The three basic lever types are diagramed in Figure 1. They are arbitrarily called Types I, II and III. Some texts call them A, B and C. Experiment 3. Investigating Pulleys

A pulley is a grooved wheel (sometimes referred to as a sheave) on an axle and has a string, rope, chain or other material in the groove which can be moved to turn the wheel. The use of pulleys dates back to ancient times. Records indicate that pulleys were used on Greek ships to hoist sails as far back as 600 B.C. Archimedes (c. 287–212 B.C.) is credited as being the inventor of multiple pulley systems. Archimedes reputedly used a pulley system to single-handedly drag a fully loaded ship onto dry land.

Pulleys can be used to change the direction of a force, to reduce the force needed to move a load through a distance or to increase the speed at which the load is moving. Pulleys do not change the amount of work done. However, if the required input force is reduced, the distance the load moves decreases in proportion to the distance the force moves.

A single pulley behaves like a Type I lever. The axle of the pulley acts as the fulcrum and both lever arms are equal in length (see Figure 2). The mechanical advantage of a simple machine is the ratio of the output force to the input force. Since the lever arms in a single pulley are of the same length (r) the input and output forces are equal (discounting any friction) and the ideal mechanical advantage is equal to 1. A single pulley only changes the direction of the force (pull down to move the load up).

When several pulleys are used (multiple lever systems) the analysis becomes more complex and the mechanical advantage can be increased. Since energy is conserved in any machine, the work done by the machine must be equal to the work put into the machine (work out = work in). The work done by a pulley equals the weight it lifts (W) times the height it lifts it (h). The work that is put into the lift is the force exerted on the pulley string (F) times the distance the string is pulled (d). For an ideal pulley: Of course, there is some friction present in a real pulley, so we would expect that some of the work that is put into the machine will be dissipated by friction and lost as output work. For a real pulley: so The actual efficiency of a pulley is the ratio of useful work done by the pulley (W•h) to the work put in (F•d) and is usually expressed as a percent: The mechanical advantage (MA) of a machine is the ratio of the output force compared to the input force or: Experiment 4. Investigating Gears

Think of the word machine and it conjures up images of big bulky cranes, bulldozers and trucks. However, in science and engineering, the word machine has a more specific meaning. A machine is any device that can apply mechanical energy at one point and deliver it in a more useful form at another point. A machine is thought of as any device that provides a mechanical advantage.

In mathematical terms the mechanical advantage (abbreviated MA) is the ratio of the load to the applied force (MA = Load/Applied Force). A mechanical advantage greater than one is considered good. The greater the mechanical advantage, the smaller the applied force needed to accomplish the task. Although a machine might use less force to accomplish a task, there is always a trade-off. Usually time, speed or distance are lost in the process.

There are different types of machines with varying capabilities and functions. Different machines may:

• Transform energy (change one type of energy to another type). Example—a generator changes mechanical energy into electrical energy.
• Transfer (deliver) energy. Example—an automobile’s drive train delivers energy to the front wheels.
• Increase or multiply force. Example—a pulley system can help lift more weight with less force.
• Increase or multiply speed. Example—bicycle wheels can move faster than the gears.
• Change direction of the force. Example—pull a flag pole rope down to make the flag go up.
• Reduce friction. Example—roll a heavy box on wheels up a ramp into a truck.

Some common, simple machines include: levers, inclined planes, wheels and axles, wedges, pulleys, screws, gears, springs and rotating wheels.

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” gear. The other gear is called the “follower” gear. The driver gear is turned by its shaft and the follower gear turns its shaft (see Figure 3). The lever is one of the most useful machines ever devised. The wheel is closely related to the lever (fulcrum in center) and the gear is closely related to the wheel. Force is the action which causes changes in linear motion. Newton’s second law states that the acceleration of a body is proportional to the net applied force, and inversely proportional to the mass (F = ma or a = F/m).

What is analogous in the gear example to the force used in linear motion? The new quantity introduced when a lever essentially pivots around a point is called torque. Torque is the rotational equivalent of force. Think of torque as a force twisting a lever around a point. Objects acted upon by a torque tend to rotate.
In Figure 4, the force applied by the driver gear A on the follower gear B is labeled F_A. The force results from one tooth pushing on another. The lever arm of gear B is equal to the radius of the gear. It is labeled L in Figure 4. Torque is the product of force (F_A) and the length of the lever arm (L). The torque that gear A exerts on gear B is therefore equal to the force applied by gear A times the length of the lever arm of gear B. The equation T = F_A x L shows that increasing or decreasing the length of the lever arm increases or decreases the torque produced. This means that the length of the lever arm also affects the work done by the gears and the rate at which the work is done.

Experiment Overview

Experiment 1. The Inclined Plane

The problem: A piano needs to be lifted onto a moving truck. The piano is too heavy to lift straight up. How is it possible to move the piano onto the truck without breaking it into many lighter pieces? In this experiment this question will be answered by studying one type of simple machine—the inclined plane.

Experiment 2. Investigating Levers

A wheelbarrow, a shovel, a hammer and nearly all tools are examples of lever systems in action. We utilize levers every day and have numerous examples in our own bodies. How do these simple machines work?

Experiment 3. Investigating Pulleys

A pulley is a simple machine consisting of a wheel turning on an axle. Pulleys can be arranged in various combinations to make work easier. In this activity, experiment with different pulley arrangements and study the mechanical advantage and efficiency of different arrangements.

Experiment 4. Investigating Gears

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

Materials

Safety Precautions

The materials in this lab are considered safe. Please follow all normal laboratory safety guidelines.

Procedure

Experiment 1. The Inclined Plane

1. Obtain a Hall’s carriage and thin string.
2. Measure the mass of the carriage to the nearest gram using the spring scale. Record the mass in the data table.
3. Measure and cut approximately 60 to 80 cm of string.
4. Tie one end of the string to the front of the carriage.
5. Tie a loop in the other end of the string (see Figure 5).
   {13280_Procedure_Figure_5}
6. Use a meter stick or ruler to measure the distance between the starting line and the finish line. Record this distance in the data table on the Inclined Plane Worksheet.
7. Set up the inclined plane as shown in Figure 6. The starting angle should be approximately 15º with respect to the tabletop.
   {13280_Procedure_Figure_6}
8. Measure the exact angle of the inclined plane with respect to the ground using a protractor. Record this angle in the data table.
9. Measure the height of the starting line from the tabletop. Record this height in the data table (see Figure 6).
10. Measure the height of the finish line from the tabletop. Record this height in the data table (see Figure 6).
11. Place the Hall’s carriage at the base of the inclined plane (see Figure 6). Add a 100-g mass to the Hall’s carriage. Record the amount of additional mass in the data table.
12. Start with the front of the Hall’s carriage at the starting line as shown in Figure 6.
13. Slowly pull on the spring scale until the carriage just begins to travel up the inclined plane. Observe the reading on the spring scale. When the spring scale maintains a constant value, record this value, in Newtons, in the data table.
14. Stop the carriage when the front of the carriage crosses the finish line.
15. Carefully lower the carriage to the base of the inclined plane.
16. Increase the angle of the inclined plane to approximately 30º.
17. Repeat steps 8–15. Use the same Hall’s carriage and any additional masses that were used for the first trial.
18. Increase the angle of the inclined plane to approximately 45º.
19. Repeat steps 8–15. Use the same Hall’s carriage and any additional masses that were used for the first trial.
20. Increase the angle of the inclined plane to approximately 60°.
21. Repeat steps 8–15. Use the same Hall’s carriage and any additional masses that were used for the first trial.

Experiment 2. Investigating Levers

Lever Type I: Fulcrum between the force and load

1. Use the lever materials to set up a Type I lever system like that shown in Figure 7.
   {13280_Procedure_Figure_7_Lever type I}
2. Cut a piece of string approximately 20 cm. Tie one end of the string to one of the lever clamps. Tie a looping knot at the other end (see Figure 8).
   {13280_Procedure_Figure_8}
3. Add the 100-g mass to one end of the lever. Be sure to hold the lever in place while adding the mass.
4. Use a spring scale to measure the force needed to hold the lever system in balance (level). Use a pencil to redirect the force to pull up on the spring scale as the lever arm moves down.
5. Change the position of the load and force in 10-cm increments. Measure the force required to hold the load at each position.
6. Record the distances D_f and D_l along with the force measurements for each load and force positions on the Lever Type I Worksheet.
7. Calculate the mechanical advantage for each position tested and record the calculations on the worksheet.
   {13280_Procedure_Equation_8}
8. Answer the questions on the Lever Type I Worksheet.

Lever Type II: Load between the fulcrum and force 

1. Use the lever materials to set up a Type II lever system like that shown in Figure 9.
   {13280_Procedure_Figure_9_Lever type II}
2. Add the 100-g mass between the fulcrum and the force. Be sure to hold the lever in place while adding the mass.
3. Use a spring scale to measure the force needed to hold the lever system in balance. Hold the spring scale vertically.
4. Without moving the position of the force or fulcrum, move the load to different positions along the lever. Measure the force required to hold the load level at each position.
5. Record the distances D_f and D_l along with the force measurements for each load position on the Lever Type II Worksheet.
6. Calculate the mechanical advantage for each position tested and record the calculations on the worksheet (Equation 8).
7. Answer the questions on the Lever Type II Worksheet.

Lever Type III: Force between the fulcrum and load

1. Use the lever materials to set up a Type III lever system like that shown in Figure 10.
   {13280_Procedure_Figure_10_Lever type III}
2. Add the 100-g mass on the end of the lever far away from the fulcrum with the force between the fulcrum and load. Be sure to hold the lever in place while adding the mass.
3. Use a spring scale to measure the force needed to hold the lever system in balance. (The top of the fulcrum will need to be held in place. See Figure 10.)
4. Without changing the position of the fulcrum or load, move the position of the force along the lever. Measure the force required to hold the load level at each position.
5. Record the distances and force measurements on the Lever Type III Worksheet.
6. Calculate the mechanical advantage for each position tested and record the calculations on the worksheet (Equation 8).
7. Answer the questions on the Lever Type III Worksheet.

Experiment 3. Investigating Pulleys

1. Obtain a support stand and support stand clamp. Set up the support structure as shown in Figure 11.
   {13280_Procedure_Figure_11}
2. Use the diagrams in Figure 12 to assist in the setup of various pulley arrangements.
   {13280_Procedure_Figure_12_Various pulley arrangements}
3. Use a 100-g hooked mass to test the pulley arrangements. Once the pulley system has been set up, carefully raise the mass by pulling horizontally on the spring scale (see Figure 12). It will be necessary to hold the top pulley with a free hand to prevent it from moving. When lifting the load with the spring scale, pull at a slow, steady rate using the minimum amount of force necessary to move the load steadily. For pulley arrangement 2, pull the spring scale vertically.
4. Record the weight (w), in Newtons, of the mass to be raised by multiplying its mass in kilograms (m) by the acceleration due to gravity (g). (Remember: W = m x g, where g = 9.8 m/sec² and 1 Newton = 1 kg/m/s².) Record the weight on the Pulleys Worksheet.
5. Carefully raise the mass by pulling on the string (no spring scale attachment). A second lab partner should measure the height that the mass is lifted and the distance the string moves, in centimeters, and record on the Pulleys Worksheet.
6. Attach the spring scale to the string. Carefully raise the mass by pulling horizontally on the spring scale while holding the top pulley with a free hand. Measure the force on the spring scale and record this as the Input Force in the Pulleys Worksheet.
7. Calculate the work output and the work input on the Pulleys Worksheet.
8. Complete the other columns on the Pulleys Worksheet for the pulley arrangement.
9. Repeat steps 1–7 for the other pulley arrangements shown in Figure 12.
10. Complete all sections on the Pulleys Worksheet and answer the questions on the worksheet.

Experiment 4. Investigating Gears

Part I. Gear Assembly

1. Measure the diameter of each gear and count the number of teeth on each gear. Record these specifications on Part I of the Investigating Gears Worksheet. Answer the question for Part I on the worksheet.
   {13280_Procedure_Figure_13_Gear assembly}
2. The assembled gears can be set into the precut 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.
   {13280_Procedure_Figure_14_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 on 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? On the Investigating Gears Worksheet draw a sketch of the two gears. 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 furthest 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 direction of rotation.
8. Draw a sketch of the three-gear setup on the Investigating Gears Worksheet, Part II. 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. How does the rotational speed of the follower compare to the rotational speed of the driver?
3. Place a pencil mark on the gear tooth on 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 Question 1 on Part III of the Investigating Gears 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 and 3 for Part III of the Investigating Gears Worksheet.

Part IV. Gearing Up/Down

1. Tie a paper clip to the end of a 24" 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 24" piece of string. Tie the other end tightly around the wooden spool on the gear axle of the largest gear.
4. Wrap the string loosely around the spool on the largest 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. (Alternatively, use a C-clamp to clamp the gear box over the edge of the table.)
7. While holding onto the string on the large 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 15.
   {13280_Procedure_Figure_15_Experimental setup}
8. 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.
9. Record the required force on Part IV of the Investigating Gears Worksheet and answer Questions 1–3 on Part IV of the worksheet.
10. Repeat steps 6–9 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 on Part IV of the worksheet and answer Question 5 on the worksheet.

Student Worksheet PDF

13280_Student1.pdf