Name:_________________________ EXPLORATION GUIDE: TORQUE “Give me a place to stand and a lever long enough and I will move the world.” In his famous quote, Archimedes failed to mention one important detail. Even with a gigantic lever and a fulcrum, Archimedes would have needed a very long time to move the Earth. In this activity, you will balance a see‐saw by positioning various masses on a bar. 1. In the Gizmo™, check that the Mass of bar = 0.0, and the Number of objects is 2. (To quickly set a slider to a number, type the number to the right of the slider and hit Enter.) Then, turn on the Show ruler checkbox. Note the positions of the objects on the see‐saw and the position of the fulcrum (the brown triangle). To move any object, just click on it and drag to the left or right. After you move the objects, click Release and observe what happens. a. Click Reset. Drag object A to the left and position it at ‐2.0 meters. Click and drag object B to 1.5 meters. b. Based on the mass and position of each object, which side of the see‐saw do you think will fall down? Click Release and observe. c. Click Reset. Experiment with placing the two objects in different locations on the bar and releasing it until you find a location where the see‐saw remains balanced when the supports are released. d. Using the following table, record the location and mass of both objects in the first two columns labelled A and B. (Remember to include the negative sign in the location.) Leave the last row blank. Balanced Experiment A B A B A B Mass of Object (kg) Location of Object (m) What is the relationship between the location of object A and the location of object B? e. Click Reset. Without changing the mass of object A or B (and keeping the same fulcrum position), try to find a different balanced situation. When balance is achieved, record the masses and locations of the two objects in the next two columns of your data table. f. Examine the data shown in your table. What pattern do you see? When object B is twice as massive as object A, what do you notice about their locations in a balanced situation? g. Click Reset. With the fulcrum at 0.0 m, set the Mass of object B to 3 kg and moveobject A to −1.5 m. What location of object B will balance object A? Make a hypothesis and test it using the Gizmo. When you have achieved balance, record the results in your data table for the last two columns. h. Summarize your observations so far with a general rule. Given a mass of object A and a different mass of object B, how can the objects be positioned so that they balance? Discuss your ideas with your classmates if possible. 2. Objects that rotate around an axis, such as a fulcrum, obey a set of laws that are analogous to Newton's laws of motion. For these equations, torque is equivalent to force. The equation for torque is T = Fd, where F is the force that causes rotation and d is the distance between that force and the axis of rotation, or fulcrum. In this Gizmo, the force of gravity on each object causes the rotation. The force on a particular object can be calculated using the equation F = mg, where g is the gravitational acceleration on Earth (g = 9.81 m/s2). a. Label the fourth row of your data table Torque (Nm). Calculate the torque caused by object A and record it in the first cell of the Torque (Nm) row. Record the torque of object B in the next cell. For example, the gravitational force on a 1‐kg object is 9.81 m/s2 • 1 kg = 9.81 N. If the object is positioned at −2 meters, the torque is −2 m • 9.81 N = −19.62 Nm. b. Notice that the torque from object A will rotate the bar in a counter‐clockwise motion, and the torque from object B will rotate the bar in a clockwise motion. Clockwise torques are generally considered positive, and counter=clockwise torques negative. c. What is the sum of the object A and object B torques from the first balanced experiment? If the see‐saw is unmoving, the torques on it must be balanced, and the net torque on the system must be zero. d. Calculate the torque for the remaining rows of your data table. What is the sum of the torques for the other experiments that you did? e. Click Reset. Change the Number of objects to 3. Place object A (1 kg) at −0.5 m and object C (3 kg) at +1.5 m. f. Calculate the torques for these two objects, and find the sum of their torques. What torque must object B (2 kg) exert to balance the see‐saw? Where should it be placed to produce this torque? g. Place object B in the location you calculated and turn on the Show initial torque checkbox. Click Release. Notice that the initial torque is displayed after the supports are released. What is the initial net torque on the system? Does it balance? If not, recalculate the torque and location needed for object B and try again.
Once you have reached this point, complete the multiple choice assessment questions underneath the Gizmo!