Mass and Hanger Set
Universal Table Clamp
60-cm Long Threaded Rod
Braided Physics String
Required (Not included):
850 Universal Interface
Balance or Scale
Calipers (suggested: Digital Calipers)
The purpose of this activity is to study the relationship between net force, mass, and acceleration as stated by Newton’s 2nd Law, using an Atwood’s Machine apparatus, built with a PASCO Super Pulley. The Super Pulley has very low friction and small mass.
The Photogate Head, when attached to a Super Pulley, is used to measure the velocity of both masses as one moves up and the other moves down. The slope of the graph of velocity vs. time is the acceleration of the system. Careful measurement when there is no net force allows the student to compensate for friction.
The effect of the motion of the pulley on the measured experimental acceleration will also be examined. This will provide a way to roughly compensate for the (small) effect of the pulley.
The acceleration of a system is directly proportional to the net applied force and inversely proportional to the system’s mass, as stated by Newton’s 2nd Law of Motion: a = Fnet/Msystem .
Atwood's Machine consists of two unequal masses connected by a single string that passes over an ideally massless and frictionless pulley as in Figure 1. When released, the heavier object accelerates downward while the lighter object accelerates upward.
The free-body diagrams below show the forces acting on each of the masses. T is the tension in the string, assumed to be the same for both masses. This is a good assumption as long as it is a single strand of string and a relatively light pulley system. With m1 > m2, m1 is descending mass and m2 is the ascending mass. The magnitude of the acceleration, a, is the same for each mass, but the masses accelerate in opposite directions. We adopt the convention that down is positive. Then the equation of motion of the descending mass, m1, is m1g – T = m1a .
The equation of motion for the ascending mass, m2, is m2g –T = m2(-a) .
Eliminating T between the two equations yields: (m1 – m2)g= (m1 + m2)a
Which may be solved for the acceleration a = (m1 – m2)g /(m1 + m2) = Fnet/Msystem Eq. (1)
Figure 1: Atwood’s Machine Figure 2: Free Body Diagram for Atwood’s Machine
1. Attach the PASCO Super Pulley to the Photogate using the 15 cm treaded black rod as shown in Figure 3. Attach one end of the photogate wire to the telephone jack on the photogate and the other end to Digital Input 1 on the 850 Universal Interface.
2. Attach the Multi Clamp to a table and arrange the rods as shown in Figure 4.
3. Cut 1.5 m piece of the braided string and tie loops on each end to hold a mass hanger. Determine the mass of the string in grams and enter it in column 1 (String Mass) of the Acceleration Data table under the Analysis tab. Enter the value in each of the first four rows.
4. Add a single 50 g mass to one mass hanger (5 g) for a total mass of 55 g. We will call this mass hanger m1. To a second mass hanger (call it m2) add one 20 g, one 10 g, two 5 g, two 2 g, and one 1g mass for a total of 50 g (including the 5 g hanger).
5. Adjust the height of the pulley so that when mass hanger m1 is touching the floor, mass hanger m2 is a few centimeters below the pulley. The Photogate should be horizontal so the string does not pull sideways on the pulley.
Friction & String Mass Compensation:
1. Add an additional 5 g to m2. The two masses should now balance. If there were no friction and the string were massless, then if we gave m1 a push downward, it would continue at constant speed.
2. Move m1 to its highest point. Click RECORD. Give m1 a gentle push downward and release it.
3. When m1 stops