Chapter 14 Work, Power, and Machines Investigation 14A Comparing the Mechanical Advantage of Levers Background Information A lever consists of a rigid bar that is free to rotate around a fixed point. The fixed point on the bar rotates around the fulcrum. Like all machines, a lever changes the size of a force that is applied to it, the direction of a force applied to it, or both. The force exerted on a lever is the input force. The distance between the fulcrum and the point where the input force acts is the input arm. The force that the lever exerts on the load is the output force. The distance between the fulcrum and the output force is the output arm. Note that the output force may be larger or smaller than the input force, depending on the type of lever. There are three types of levers, called first-class, second-class, and third-class levers. The three classes differ in the relative positions of the fulcrum and the input and output forces. A first-class lever, such as a seesaw, has its fulcrum between the input and output forces. In a second-class lever, such as a wheelbarrow, the output force, is between the input force and the fulcrum. A third-class lever, such as a broom, has its input force between the fulcrum and the output force. The mechanical advantage of any machine is the number of times that the machine multiplies the input force. The actual mechanical advantage (AMA) of a lever is equal to the output force divided by the input force. Output force AMA = Input force In this investigation, you will determine and compare the actual mechanical advantage of first-class and second-class levers. Then, you will design and carry out an investigation to determine the mechanical advantage of a third-class lever. Problem How do the mechanical advantages of first-class, second-class, and third-class levers differ? Pre-Lab Discussion Read the entire investigation. Then, work with a partner to answer the following questions. 1. Designing Experiments Why are you told in Step 1 to record the weight of the 500-g mass as the output force for every first-class and second-class lever that you will use in this investigation? Physical Science Lab Manual Investigation 14A 145
2. Calculating How will you calculate the actual mechanical advantage (AMA) of the levers in this investigation? 3. Predicting What factors do you predict will affect the actual mechanical advantage of the levers in this investigation? 4. Controlling Variables Identify the manipulated, responding, and controlled variables in this investigation. a. Manipulated variables b. Responding variables c. Controlled variable 5. Predicting Which class of levers do you expect to have the greatest actual mechanical advantage? Explain your answer. 6. Formulating Hypotheses State a hypothesis that you could test in Part C of this investigation. Materials (per group) 500-g mass with hook spring scale wedge-shaped block of wood, about 10 cm high meter stick string scissors loop of wire 146 Physical Science Lab Manual Investigation 14A
Safety Put on safety goggles. To prevent injury from falling objects, do not wear sandals or open-toed shoes. Wear only closed-toed shoes in the laboratory. Note all safety alert symbols next to the steps in the Procedure and review the meaning of each symbol by referring to the Safety Symbols on page xiii. Procedure Part A: Determining the AMA of First-Class Levers 1. Work with a classmate. Hang the 500-g mass from the spring scale. Read the weight of the mass on the spring scale. Record this weight as the output force in each row of Data Table 1. 2. To make a first-class lever, place the wedge-shaped block of wood on the table to serve as a fulcrum. Place the 50-cm mark of the meter stick on the fulcrum so that the 100-cm end of the meter stick extends beyond the edge of the table, as shown in Figure 1. Use string to tie the Block of wood Meter stick 500-g mass to the meter stick at the Wire loop 10-cm mark. This mass serves as the load that the lever will lift. 3. Place the wire loop around the meter stick at the 90-cm mark, 40 cm away from the fulcrum. Hang the spring scale from the wire loop. Spring scale 4. In the first row of Data Table 1, record the distance from the fulcrum to the spring scale as the input arm. Record the distance from the fulcrum to the mass as the output arm. 5. Pull the spring scale down slowly and steadily to lift the mass. When the meter stick is horizontal, read the input force on the spring scale. Record this value in Data Table 1. 6. Leaving the mass and the spring scale at the same positions, move the fulcrum to the 30-cm mark. Record the lengths of the new input and output arms in Data Table 1. 7. Repeat Step 5. 8. Repeat Steps 6 and 7, but this time, move the fulcrum to the 20-cm mark. 9. Calculate the mechanical advantage of the first-class lever in all the positions you tested. Record these values in Data Table 1. 500-g mass Figure 1 Physical Science Lab Manual Investigation 14A 147
Part B: Determining the AMA of Second-Class Levers 10. To make a second-class lever, place the 10-cm mark of the meter stick on the fulcrum as shown in Figure 2. Tie the mass to the meter stick at the 50-cm mark. Figure 2 11. Place the wire loop around the meter stick at the 90-cm mark, 80 cm away from the fulcrum. Attach the spring scale to the wire loop. 12. In Data Table 1, record the distance from the fulcrum to the spring scale as the input arm. Record the distance from the fulcrum to the mass as the output arm. 13. Have your partner hold the meter stick down on the fulcrum so that the meter stick does not slide or rise up off of the fulcrum. Pull the spring scale up slowly and steadily to lift the mass. When the meter stick is horizontal, read the input force on the spring scale. Record this value in Data Table 1. 14. Leaving the fulcrum and the spring scale at the same positions, move the mass to the 30-cm mark. Record the lengths of the new input and output arms in Data Table 1. 15. Repeat Step 13. 16. Repeat Steps 14 and 15, but this time, move the mass to the 20-cm mark. 17. Calculate the actual mechanical advantage of the second-class lever in all the positions you tested. Record these values in Data Table 1. Part C: Design Your Own Investigation 18. Design an investigation to determine the actual mechanical advantage of a third-class lever. Record the hypothesis that you will test. Hypothesis 148 Physical Science Lab Manual Investigation 14A
19. In the lines below, write a detailed plan of how you will carry out your investigation. You may choose to base your investigation on the method of determining the actual mechanical advantage of a lever that you used in Parts A and B. Construct Data Table 2 in which to record your observations in the space provided on page 150. 20. What are the manipulated, responding, and controlled variables in your investigation? a. Manipulated variable b. Responding variable c. Controlled variables 21. What safety precautions will you need to take in your investigation? Physical Science Lab Manual Investigation 14A 149
22. List the possible results of your investigation. State whether each possible result would support or contradict your hypothesis. 23. Show your plan to your teacher. When your teacher approves your plan, carry out your investigation and record your observations in your data table. Observations DATA TABLE 1: Parts A and B Actual Fulcrum Output Input Output Input Mechanical Position (cm) Arm (cm) Arm (cm) Force (N) Force (N) Advantage 50 30 20 First-Class Lever 10 10 10 Second-Class Lever DATA TABLE 2: Part C If you need more space, attach additional sheets of paper. 150 Physical Science Lab Manual Investigation 14A
Analysis and Conclusions 1. Analyzing Data How did moving the fulcrum of the first-class lever closer to the output force affect the actual mechanical advantage? 2. Comparing and Contrasting Did changing the lengths of the input and output arms affect the actual mechanical advantage of all three classes of levers in the same way? Explain your answer. 3. Evaluating and Revising In Part C of this investigation, did your data support or contradict your hypothesis? Explain your answer. 4. Drawing Conclusions Based on the mechanical advantages that you calculated for each class of lever, how do third-class levers differ from the other two types? How could a third-class lever be useful? 5. Drawing Conclusions What could you do to any lever to increase its actual mechanical advantage? Go Further Suppose you need to use a nutcracker to crack an especially tough nut. You have the choice of two similar nutcrackers that each have two handles connected at one end. One nutcracker has longer handles than the other one. Which class of lever are the nutcrackers? How can you tell? Which nutcracker would you use? Where would you place the nut relative to the arms? Explain your answer in terms of actual mechanical advantage. Physical Science Lab Manual Investigation 14A 151