Activity 3: Pulleys Background Pulleys are simple machines that consist of a grooved wheel that turns around a fixed point, similar to the fulcrum of a lever. A rope, cord, or chain runs along the groove on the wheel which, when force is applied, can change the direction and/or multiply the applied force. Pulley systems can be arranged in many combinations and configurations. There are fixed pulleys, where the pulley is fixed at one position and the resistance and effort forces are applied to either end of the rope. There are movable pulleys, where the pulley moves along the rope as it is pulled on at one end by an effort force; the other end of the rope is fixed in position. There are also block-and-tackle pulley systems that consist of both fixed and movable pulleys working together to multiply and change the direction of an applied force (Figure 5). (a) fixed pulley (b) moveable pulley (c) block-and-tackle pulley Figure 5. Types of pulleys: (a) fixed pulley, (b) moveable pulley, and (c) block-and-tackle pulley. In this investigation, you will experiment with different types and configurations of pulley systems. As you work with the different systems, you will observe the direct correlation between the number of cord segments supporting the resistance force and the mechanical advantage of the pulley system. 2 0 0 5 C a r o l i n a B i o l o g i c a l S u p p l y C o m p a n y S-10
Materials base stand rod T connector extension rod pulley cord 2 single pulleys 2 double pulleys spring scale mass hanger 10 mass pieces (10 g each) calculator meter stick or meter measuring tape permanent marker scissors electronic balance, accurate to 0.01 g Focus Where have you seen pulleys used? List several examples of pulleys and describe for what purpose they are used. Procedure Assembly 1. To set up the pulley system, first place the stand rod in the base. Then, using a permanent marker and a meter stick, place a mark every centimeter from the bottom of the stand rod to the top. Label every 5-cm mark. This will help you to measure the distance of the resistance force and effort force. 2. Place the T connector on the stand rod. Insert one end of the extension rod into the side opening of the T connector. 3. Cut a piece of pulley cord about 10 cm long and tie it in a loop. Slide this loop on to the extension rod. This loop will allow you to hang pulleys from the extension rod. Investigation 1. Using a balance, determine the mass of the mass hanger. Place nine 10-g masses on the mass hanger. Calculate the total mass of the hanger plus the mass pieces and record this value in the Activity 3: Pulleys Data Table. 2. Calculate the total force being placed on the pulley by the mass hanger using the formula for force, Force = mass acceleration due to gravity. Remember to convert mass in g to mass in kg before doing this calculation. Record this information in the Activity 3: Pulleys Data Table. 3. Hang one of the single pulleys on the loop of the extension rod. This will create a single fixed pulley system. 4. Cut a piece of pulley cord about 2.5 m long. (Having a cord of this length will allow you to use the same piece of cord for all of the pulley combinations in this investigation. If the cord seems too long to manage, cut a piece of cord about 1 m long for the single fixed pulley system.) 2 0 0 5 C a r o l i n a B i o l o g i c a l S u p p l y C o m p a n y S-11
5. Thread the pulley cord over the groove of the hanging single pulley. 6. Tie a loop at one end of the pulley cord. Place the loop around the hook of the hanging mass. Place the hanging mass on the base of the pulley stand (Figure 6). 7. Tie another loop in the cord hanging on the opposite side of the pulley from the side that has the hanging mass. Place the hook of the spring scale in this loop. 8. Using the spring scale, the pulley cord, and the pulley, raise the hanging mass to a height 25 cm above the base of the pulley stand. As you pull, note the force measurement of the spring scale. Also, measure the distance that you pull the spring scale in order to raise the hanging mass to this height. 9. Lower the hanging mass to the base of the pulley stand. Repeat the pulling exercise at least two more times to gain a consistent measure of effort force and effort distance. 10. Record the measurement for effort force and effort distance on the data table. 11. Count the number of cords that support the resistance force. Record this number in the data table. 12. Change the pulley system to a single moveable pulley system (Figure 7): a. Place the loop of the long piece of pulley cord (that was around the hook of the hanging mass) onto the extension rod. b.hook the mass hanger to one of the hooks on the pulley. c. Thread the free end of the pulley cord through the groove on the pulley. d.tie a loop on the free side of the pulley cord and attach the hook of the spring scale. e. You should now have a complete moveable pulley system. 13. Pull upward on the spring scale to raise the hanging mass 25 cm from the base of the pulley stand. As you pull upward, notice the force measurement of the spring scale. Also, measure the distance that you pulled the spring scale to raise the hanging mass. 14. Repeat this exercise at least two more times in order to gain a consistent measure of effort force and effort distance. 15. In the data table, record the effort force, effort distance, and number of cords supporting the resistance force. Figure 6. Single fixed pulley system. Figure 7. Single moveable pulley system. 2 0 0 5 C a r o l i n a B i o l o g i c a l S u p p l y C o m p a n y S-12
16. Change the pulley system to a block-and-tackle system with a single fixed pulley and a single moveable pulley (Figure 8): a. Hang one pulley on the extension rod using a small loop of cord, as with the fixed pulley system. b.attach one pulley to the hanging mass hook, as with the moveable pulley system. c. Place the loop at the end of the long piece of pulley cord onto the hook at the bottom of the pulley that is hanging from the extension rod. d.thread the free end of the pulley cord underneath the groove in the pulley that is attached to the hanging mass. e. Thread the free end of the pulley cord over the groove of the pulley that is hanging from the extension rod. f. Tie a loop on the free side of the pulley cord and attach the hook of the spring scale. 17. Pull downward on the spring scale to raise the hanging mass 25 cm. Note the measurement of force on the spring scale. Also, measure the distance that you pull the spring scale in order to raise the hanging mass. 18. Repeat this process at least two times in order to gain a consistent measure of effort force and effort distance. 19. In the data table, record the effort force, effort distance, and number of cords supporting the resistance force. 20. Change the pulley system to a block-and-tackle system with a double fixed pulley and a single moveable pulley (Figure 9): a. Hang a double pulley from the extension rod. b.attach a single pulley to the hook of the hanging mass. c. Attach the loop tied in the end of the long pulley cord to the hook at the top of the single pulley. d.thread the free end of the pulley cord over the groove of one of the wheels of the double pulley, then down underneath the groove of the single pulley, and finally back up over the other wheel of the double pulley. e. Tie a loop in the free end of the pulley cord and attach the spring scale. 21. Pull on the spring scale to raise the hanging mass to a height of 25 cm. (You may have to arrange the setup so that the hanging mass hangs down lower than the tabletop to have enough room to raise the bottom of the hanging mass 25 cm.) 22. As you pull on the spring scale, note the measurement of force and the distance that the spring scale moves. Figure 8. Block-and-tackle system with two single pulleys. Figure 9. Block-and-tackle system with a double fixed pulley and a single moveable pulley. 2 0 0 5 C a r o l i n a B i o l o g i c a l S u p p l y C o m p a n y S-13
23. Repeat this process at least two times to gain consistent measurement readings. 24. In the data table, record the effort force, effort distance, and number of cords supporting the resistance force. 25. Change the pulley system to a block-and-tackle system with double fixed pulleys and double moveable pulleys (Figure 10). 26. Pull on the spring scale to raise the hanging mass 25 cm. 27. Repeat this process at least two times to gain consistent measurement readings. 28. In the data table, record the effort force, effort distance, and number of cords supporting the resistance force. Reflection 1. Complete the data table by calculating the following information for each trial: a. Work output (Wo): amount of work needed to move the hanging mass; Wo = (Fr)(dr) b.work input (Wi): amount of work exerted to move the hanging mass; Wi = (Fe)(de) Figure 10. Block-and-tackle system with two double pulleys. Activity 3: Pulleys Data Table Pulley System No. of cords effort force acts on Mass unit = g Resistance Force (Fr) unit = N Resistance Distance (dr) unit = m Work Output (Wo) unit = J Effort Force (Fe) unit = N Effort Distance (de) unit = m Work Input (Wi) unit = J Mechanical Advantage (MA) Ideal Mechanical Advantage (IMA) Efficiency (eff) % Single fixed 0.250 m Single moveable 0.250 m Single fixed; single moveable 0.250 m Double fixed; single moveable 0.250 m Double fixed; double moveable 0.250 m 2 0 0 5 C a r o l i n a B i o l o g i c a l S u p p l y C o m p a n y S-14
c. Ideal mechanical advantage (IMA): ratio of distance the spring scale moves, effort distance (de), to distance the hanging mass moves, resistance distance (dr); IMA = de/dr d.mechanical advantage (MA): mechanical advantage, ratio of force of the hanging mass, resistance force (Fr), to force used to move the hanging mass, effort force (Fe); MA = Fr/Fe e.efficiency (eff): ratio of mechanical advantage (MA) to ideal mechanical advantage (IMA); eff = MA/IMA 100% 2. Why does a single moveable pulley require less effort force than a single fixed pulley? 3. Compare the data for resistance force and effort force for each trial. Develop a statement that explains the relationship between the effort force and each of the pulley combinations. 4. What happens to the effort distance as the number of pulleys used in combination increases? 5. Develop a statement that explains the relationship between the ideal mechanical advantage and the number of cords supporting the resistance force. 6. Examine the data table and compare the effort forces, effort distances, work inputs, and efficiencies of each pulley combination. State which combination of pulleys seems most beneficial and explain your answer. Support your reasoning with data from your data table. 2 0 0 5 C a r o l i n a B i o l o g i c a l S u p p l y C o m p a n y S-15