Atwood’s machine

A classic experiment in physics is the Atwood’s machine: two masses on either side of a pulley connected by a light string. When released, the heavier mass accelerates downward while the lighter one accelerates upward at the same rate. The acceleration depends on the difference in the two masses, as well as the total mass.

In this lab, you will investigate the factors that influence the acceleration of an Atwood’s machine using a Photogate to record the machine’s motion.

For this experiment you will keep the total mass used constant, but move weights from one side to the other. The difference in masses changes.

1. Set up the Atwood’s machine apparatus as shown in Figures 1 and 2.

Note: The masses must be able to move at least 40 cm before striking the ground.

2. Connect the Photogate with Ultra Pulley to a digital (DIG) port of the interface.

3. Open the file “10 Atwoods Machine” in

PRELIMINARY QUESTIONS

1. If two objects of equal mass are suspended from either end of a string passing over a light pulley, as in Figure 1, what kind of motion do you expect to occur? Why?

2. Draw a diagram of Figure 1. Include all forces acting on each mass.

3. Do the two masses have the same acceleration? Why?

4. How would you expect the acceleration of an Atwood’s machine to change if you Increase the mass on one side and decrease the mass on the other, keeping the total mass constant? Gradually increase the mass of both sides, keeping the difference in mass constant?

PROCEDURE the Physics with Vernier folder.

4. Arrange a collection of masses totalling 200 g on m2 and a 200 g mass on m1. What is the acceleration of this combination? Record your values for mass and acceleration in the data table.

5. Move 50 g from m2 to m1. Record the new masses in the data table.

6. To measure the acceleration of this system, start with the masses even positioned with each other. Steady the masses so they are not swinging. Click

to start data collection. After a moment, release the smaller mass, catching the falling mass before it strikes the floor or the other mass strikes the pulley.

7. Click Examine, , and select the region of the graph where the velocity was increasing at a steady rate. Click Linear Fit, , to fit the line y = mt + b to the data. Record the slope, which is the acceleration, in the data table. 8. Continue to move masses from m2 to m1 in 50 g increments, changing the difference between the masses, but keeping the total constant. Repeat Steps 6–7 for each mass combination. Repeat this step until you get at least five different combinations.

DATA TABLE

Part I Constant Total Mass

ANALYSIS

1. Using your diagram of the system, apply Newton’s second law to each mass. Assume that the tension is the same on each mass and that they have the same acceleration. Show that Fnet = m1g - m2g

2. Why is Fnet also equal to mTa

3. Complete the table

4. For each of the experimental runs you made, calculate the expected acceleration using the expression you found with Newton’s second law of motion and the specific masses used. Compare these figures with your experimental results. Are the experimental acceleration values low or high? Why?

5. In this experiment we varied the mass difference but kept the total mass constant. What would happen if we varied the total mass but kept the difference constant. Back up your argument with analysis.