Materials Included In Kit

Additional Materials Required

Prelab Preparation

Photocopy enough Create a Mobile: Fulcrum Placement Calculation Instructions handouts for each student. Distribute these instructions after Part A has been completed and before the students design their mobiles.

Safety Precautions

This laboratory activity is considered nonhazardous. Remind students to exercise caution when working with scissors, always cut away from yourself and others.

Lab Hints

• Enough materials are provided in this kit for 30 students working in groups of three, or for 10 groups of students. Both parts of this laboratory activity can reasonably be completed in two 50-minute class periods. The prelaboratory assignment may be completed before coming to lab, and the data compilation and calculations may be completed the day after the lab.
• Extra dowel rods are included so the instructor may make a sample mobile if desired.
• Pass out the Create a Mobile: Fulcrum Placement Calculation Sheet after Part A is completed but before Part B has begun.
• Provide a support stand with ring clamp for each group to hang their mobiles on during assembly. Completed mobiles in equilibrium may be hung from the ceiling for display.

Teacher Tips

• The concept about levers that students discover in Part A is known as torque. Torque (perpendicular force × length of lever arm) causes rotation. In order for each tier of the mobile to balance, the torque causing a clockwise rotation must equal the torque causing a counterclockwise rotation.
• Force is measured in newtons in the metric system, and the weight of the hanging objects is a force caused by acceleration due to gravity (9.8 m/s²). This activity calls for measuring in grams since the material for the objects is rather light-weight, and it may be difficult to weigh the individual objects with a spring scale. If desired, grams may be converted to newtons by multiplying grams by 0.0098, or 0.01 (1 N = 1 kg m/s²).

Answers to Prelab Questions

1. Read through Part A of the Procedure. Identify which materials serve as each component of the lever.
   1. Lever Arm: Ruler
   2. Fulcrum: Cork
   3. Load: Washers
2. Refer to the model of the mobile (Figure 3) if the Background section.
   1. What acts as the fulcrum for each tier?

      The string from which each rod is hanging is the fulcrum.

   2. Which object would you expect to have greater weight, the moon on tier 3 or the lightning bolt on tier 1?

      The moon on tier 3 would have greater weight than the lightning bolt on tier 1.

   3. Give evidence for your answer.

      Since the mobile is in equilibrium, the weight of the moon on tier 3 must be equal to the combined weight of all three objects and the rods on tiers 2 and 1.

3. Assume the fulcrum is in the center of the horizontal rod for each tier of the model mobile in Figure 3.
   1. If each shape were the same mass, which tiers would be in balance?

      Only tier 1 would be in balance with equal mass at each end of the rod.

   2. With all shapes the same mass, in what direction would the rods of each imbalanced tier tip?

      The right side of tiers 2 and 3 would tip downward, since the right side of each is heavier than the left side.

Sample Data

Part A

Part B Part B3
Tier 1 Calculation

3.6 g − X = 1.1 g (30 cm − X)
3.6 X = 33 cm − 1.1 X
4.7 X = 33 cm
X = 7.0 cm
Y = 23.0 cm

Tier 2 Calculation

7.5 g x X = 2.6 g (30 cm − X)
7.5 X = 78 cm − 2.6 X 10.1 X = 78 cm
X = 7.7 cm
Y = 22.3 cm

Tier 3 Calculation

12.7 g x X = 4.5 g (30 cm − X)
12.7 X = 135 cm − 4.5 X
17.2 X = 135 cm
X = 7.8 cm
Y = 22.2 cm

Answers to Questions

Part A 

1. Observe diagrams A2 and A3.
   1. What general observation can be made regarding the washers and their respective distances to the fulcrum when the lever is balanced?

      The stacks of two and three washers are closer to the fulcrum than the single washer.

   2. Underline the correct answer in the following sentence. “If the load on one side of a lever is greater than the load on the other side, then the distance from the heavier load to the fulcrum must be less than the distance from the fulcrum to the lighter load.”
2. Assume the washers all weigh the same.
   1. How does the weight of the two-washer load compare to the weight of one washer?

      The two-washer load weighs twice as much as one.

   2. How does the distance from the fulcrum to the two-washer load compare to the distance from the fulcrum to the single washer?

      The distance from the fulcrum to the two-washer load is about half the distance from the fulcrum to the single washer.

   3. How does the distance from the fulcrum to the three-washer load compare to the distance from the fulcrum to the single washer?

      The distance from the fulcrum to the three-washer load is about one-third the distance from the fulcrum to the single washer.

3. Let W₁ = the weight of the load on one side of a lever and X = the distance from the fulcrum to the load on that same side. Let W₂ = the weight of the load on the opposite side of a lever and Y = the distance from the fulcrum to W₂.

   Which of the following represents the relationship between the weight and distance to the fulcrum on one side of a lever to the weight and distance on the other side?

   1. W₁ + X = W₂ + Y The correct relationship is W₁ x X = W₂ x Y.
   2. W₁ x X = W₂ x Y
   3. W₁ / X = W₂ / Y

Part B 

4. Compare the calculated distances and the measured distances in Data Table B3.
   1. Do the calculated distances and the measured distances match?

      They do not match exactly; Tier 1 distances were off the most, followed by Tier 2. The Tier 3 distances were fairly close.

   2. Give some possible sources of error that might account for any differences.

      The objects were not hanging at the very ends of the dowel rods, so the actual length of each lever was less than 30 cm. Since each lever arm was not equal in length, the weight of each arm on either side of the fulcrum was not the same. This difference was not factored in the calculations. It was difficult to get the dowel rods exactly horizontal. Minor adjustments in the placement of the fulcrum caused the rod to rotate one way or the other.

5. Did the constructed mobile confirm the statement from Question 1b in Part A?

   Yes, the distance from the fulcrum to the heavier load on each tier is less than the distance to the lighter load.

Teacher Handouts

14063_Teacher1.pdf

References

Mahler, Marco. Mobiles. http://www.marcomahler.com/how-to-make-mobiles/ (accessed January 2016).

Introduction

Have you ever seen a large, brightly-colored geometric mobile in a museum? If you have, it most likely was the work of Alexander Calder, a famous American sculptor. Mobiles are moving sculptures possessing graceful balance and are very pleasing to the eye. Create your own mobile using science and mathematic principles.

Concepts

• Forces and equilibrium
• Levers
• Measurement
• Engineering design

Background

Levers are used for the transfer and modification of force and motion. They are beneficial because they allow greater loads to be lifted with less effort. In a lever system, the lever itself is always rigid, like a bar or plank and turns or pivots on one point called the fulcrum.

Levers are classified according to where the fulcrum is located in relation to the effort force and load. Hanging mobiles consist of first class levers where the fulcrum is located between two loads. A seesaw is an example of a first class lever. If the two arms on each side of the fulcrum are equal length, placing the fulcrum in the middle, the weight of the load on each side must be equal for the lever to balance (see Figure 1).

What if the two loads are not equal weight? If an adult is on one side of the seesaw and a child is on the other, the adult’s side with the greater weight will tip toward the ground (see Figure 2). The concept of levers is a key component in the design of mobiles. Alexander Calder (1898–1976) studied engineering in college, then decided to become an artist. He is known as the originator of mobiles. A mobile is a kinetic (moving) sculpture composed of balanced shapes that move in response to environmental changes such as air currents or physical touch. They consist of several rods from which loads (objects or other rods) can hang using wire or string. When a mobile is balanced, all of the forces acting on the system are in equilibrium. The main difference between the mobile in Figure 3 and the seesaw in Figure 2 is that the mobile hangs in balance from a central point and the seesaw is balanced on top of a central point. The mobile in Figure 3 consists of three tiers, all hanging in equilibrium. Air currents may cause the mobile to sway or turn, but each tier remains balanced.

Experiment Overview

In Part A of this experiment, levers are studied to determine the relationship between load weight and distance from the fulcrum. The principles learned in Part A will be used in Part B to design a three-tiered mobile that balances.

Materials

Prelab Questions

1. Read through Part A of the Procedure, Investigating a Simple Lever. Identify which materials serve as each component of the lever.
   1. Lever Arm:
   2. Fulcrum:
   3. Load:
2. Refer to the model of the mobile (Figure 3) in the Background section.
   1. What acts as the fulcrum for each tier?
   2. Which object would you expect to have greater weight, the moon on tier 3 or the lightning bolt on tier 1? 
   3. Give evidence for your answer.
3. Assume the fulcrum is in the center of the horizontal rod for each tier of the model mobile in Figure 3.
   1. If each shape were the same mass, which tiers would be in balance?
   2. With all shapes the same weight, in what direction would the rods of each imbalanced tier tip?

Safety Precautions

Exercise caution when working with sharp objects such as scissors. Always cut away from yourself and others. Wash hands thoroughly with soap and water before leaving the laboratory. Please follow all laboratory safety guidelines.

Procedure

Part A. Introductory Activity—Investigating a Simple Lever

1. Obtain a ruler, cork and four washers.
2. Place the cork, which acts as a fulcrum, on the lab bench with the narrow end facing upward.
3. Balance the ruler, which acts as the lever, on the fulcrum.
4. Place one washer (load) on each end of the lever.
5. Draw a diagram of the lever system under A1 Diagram in the Observations section of the Create a Mobile worksheet.
6. Measure the distance in cm from the center of the fulcrum to the center of each load, respectively. Label each distance on the worksheet.
7. Place an additional washer on top of one washer so that one side of the lever has one washer and the other side has a stack of two. The lever will be imbalanced.
8. Leave the single washer in place and adjust the location of the stack of two washers so that the lever is once again in balance. Note: Since the fulcrum is fairly wide, the lever may appear balanced with the stack of two washers over a range of distances. Observe the lever at eye level to make sure it is horizontal and place the washers in the center of the observed range of distances.
9. Once the lever is balanced, draw a diagram on the worksheet under A2 Diagram.
10. Measure the distance between the fulcrum and each load and record the values on the A2 Diagram on the worksheet.
11. Place another washer on top of the stack of two to make a stack of three. The lever will once again be imbalanced.
12. Repeat step 8.
13. Once the lever is balanced, draw a diagram on the worksheet under A3 Diagram.
14. Measure the distance between the fulcrum and each load and record the values on the diagram on the worksheet.
15. Complete Part A of the Post-Lab Questions.

Part B. Design Challenge
Form a working group with other students to design and construct a balanced mobile that meets the following criteria and constraints.

• The mobile must have three tiers.
• It must include four objects, each a different weight. The difference in weight from one object to another must be at least 0.5 g.
• The mobile must be made from the materials provided. Glue may be used to create objects of more than one color.
• Decide on a theme for your group’s mobile. Be creative! Example: A space theme mobile has the following objects—sun, moon, planet Earth and a spaceship.

B1. Creating the Hanging Objects

1. Obtain foam pieces, scissors and glue and construct the four objects.
2. Check the mass of each object and adjust if needed to meet the criteria.
3. Unbend a paperclip part way to form a hook and poke a tiny hole through one of the objects near the top.
4. Push the straight portion of the paper clip through the hole so the object hangs from the bottom of the paper clip.
5. Bend the paperclip back into its original shape.
6. Repeat steps 3–5 with the other three objects.
7. Once all four objects are finished, use a balance to find the mass of each object with the paper clip and record in Data Table B1on the worksheet.

B2. Constructing the Tiers

1. Determine which two objects will be attached to Tier 1 (bottom), which will be on Tier 2, and which object will be on Tier 3.
2. Place one rubber band on one of the dowel rods and wrap it around until secure on the rod.
3. Move the rubber band to near the middle of the rod.
4. Unbend a paper clip to form an “S” shape.
5. Insert one end of the bent paper clip through a few of the layers of the rubber band. The rubber band and paper clip will serve as the fulcrum for the tier.
6. Obtain approximately 120 cm of string. Using scissors, cut into six 20-cm pieces.
7. Use the string to attach one Tier 1 object to each end of the dowel rod.
8. Use a balance to determine the mass of the entire Tier 1, rod, strings, and objects. Record the mass in Data Table B2 on the worksheet.
9. Repeat steps 7–8 with the Tier 2 dowel rod and object.
10. Use a balance to determine the mass of Tier 1 and Tier 2 together. Record the total mass in the data table.
11. Repeat steps 7–8 with the Tier 3 dowel rod and object.

B3. Designing and Constructing the Mobile

1. Obtain the Create a Mobile—Fulcrum Placement Calculation Instructions from the instructor and read through it thoroughly.
2. Using the mass data from the worksheet and Equation 3 on the Fulcrum Placement handout, calculate where the fulcrum should be on each dowel rod. Begin with Tier 1. Show your work and record the predicted distances of X and Y for each tier in Data Table B3 on the worksheet.
3. Begin construction of the mobile.
4. Move the center rubber band to the location determined by calculation in B3 step 2.
5. Hang Tier 1 by the paper clip attached to the rubber band-fulcrum and allow the objects to hang freely. If the dowel rod is not horizontal, move the fulcrum until Tier 1 is balanced.
6. Measure and record the actual distances from each object to the fulcrum in Data Table B3.
7. Attach Tier 1 to Tier 2 and repeat steps 4–6.
8. Attach Tiers 1 and 2 to Tier 3 and repeat steps 4–6.

Student Worksheet PDF

14063_Student1.pdf