PASCO scientific Physics Lab Manual: P13-1 Experiment P13: Atwood's Machine (Smart Pulley) Concept Time SW Interface Macintosh file Windows file Newton's Laws 45 m 500 or 700 P13 Atwood's Machine P13_ATWD.SWS EQUIPMENT NEEDED Interface table clamp, universal Smart Pulley thread mass set & hanger (two) PURPOSE The purpose of this laboratory activity is to study the relationship between force, mass, and acceleration using an Atwood's Machine apparatus. THEORY The acceleration of an object depends on the net applied force, and the mass. In an Atwood's Machine, the difference in weight between two hanging masses determines the net force acting on the system of both masses. This net force accelerates both of the hanging masses; the heavier mass is accelerated downward, and the lighter mass is accelerated upward. In the free body diagram of the Atwood s machine, T is the tension in the string, M1 is the lighter mass, M2 is the heavier mass, and g is the acceleration due to gravity. Assuming that the pulley has no mass, the string has no mass and doesn t stretch, and that there is no friction, the net force on M1 is the difference between the tension and M1g (T>M1g). The net force on M2 is the difference between the tension and M2g (T<M2g). Mass 1 Pulley Mass 2 T M1g M1 T M2g M2 T M 1 g = F net = M 1 a M 2 g T = F net = M 2 a Solve for a, the acceleration of the system of both masses. The theoretical acceleration is g times the difference in mass divided by the total mass. PROCEDURE a = g M M 2 1 M 1 + M 2 For this activity, the Smart Pulley measures the motion of both masses as one moves up and the other moves down. The program calculates the changing speed of the masses as they move. A graph of speed and time reveals the acceleration of the system. dg 1996, PASCO scientific P13-1
P13-2: Physics Lab Manual PASCO scientific PART I: Computer Setup 1. Connect the interface to the computer, turn on the interface, and turn on the computer. 2. Connect the stereo phone plug of the Smart Pulley to Digital Channel 1 on the interface. 3. Open the document titled as shown: Macintosh P13 Atwood's Machine Windows P13_ATWD.SWS The document opens with a Graph display of Velocity (m/sec) versus Time. Note: For quick reference, see the Experiment Notes window. To bring a display to the top, click on its window or select the name of the display from the list at the end of the Display menu. Change the Experiment Setup window by clicking on the Zoom box or the Restore or Maximize button in the upper right hand corner of that window. P13-2 1996, PASCO scientific dg
PASCO scientific Physics Lab Manual: P13-3 The Sampling Options are: Periodic Samples = Fast at 10 Hz, Digital Timing = 10000 Hz, and Start Condition = Ch. 1, Low ( Photogate Blocked ). PART II: Sensor Calibration and Equipment Setup You do not need to calibrate the Smart Pulley. 1. Mount a clamp to the edge of a table. Place the Smart Pulley in the clamp so that the Smart Pulley s rod is horizontal. 2. Use a piece of thread about 10 cm longer than the distance from the top of the pulley to the floor. Place the thread in the groove of the pulley. 3. Fasten mass hangers to each end of the thread. You can fasten the mass hangers to the thread by wrapping the thread four or five turns around the notched area of the mass hanger. 4. Place about 100 grams of mass on one mass hanger and record the total mass as M 1. Be sure to include the 5 grams from the mass hanger in the total mass. Place slightly more than 100 grams on the other hanger. Record this total mass as M 2. Smart Pulley Clamp 5. Move the heavier of the two masses upward until the lighter mass almost touches the floor. Hold the heavier mass to keep it from falling. Turn the pulley so that the photogate beam of the Smart Pulley is unblocked (the red light-emitting diode (LED) on the photogate does not light). Mass 1 Mass 2 dg 1996, PASCO scientific P13-3
P13-4: Physics Lab Manual PASCO scientific PART IIIA: Data Recording Constant Total Mass 1. Click the REC button ( ). Let the heavier mass fall. Data recording will begin when the photogate beam of the Smart Pulley is blocked. 2. Click the STOP button ( ) to end data recording just before the heavier mass reaches the floor. Don t let the upward moving mass hit the Smart Pulley! Run #1 will appear in the Data list in the Experiment Setup window. 3. Change the relationship between M 1 and M 2 by removing mass from one hanger and adding it to the other. This allows you to change the net force without changing the total mass. 4. Repeat the data recording procedure using different combinations of M 1 and M 2. Record the mass of M1 and M2 for each combination. Change the net force each time, but keep the total mass constant. PART IIIB: Data Recording Constant Net Force 1. Arrange the masses as they were for the beginning of Part IIIA. Now, change the total mass but keep the net force the same as for the first run in Part IIIA. To do this, add exactly the same amount of additional mass to both mass hangers. Make sure that the difference in mass is the same as it was for the beginning of Part IIIA. 2. Record your new values for M1 and M2. 3. Record data as in Part IIIA. 4. Repeat the process several times. Change the total mass each time but keep the net force constant. P13-4 1996, PASCO scientific dg
PASCO scientific Physics Lab Manual: P13-5 ANALYZING THE DATA Data Table #1: Constant Total Mass Trial M1 (Kg) M2 (Kg) aexp Fnet (N) M1+ M2 (Kg) atheory % Diff. Run #1 Run #2 Run #3 Run #4 Run #5 Data Table #2: Constant Net Force Trial M1 (Kg) M2 (Kg) aexp Fnet (N) M1+ M2 (Kg) atheory % Diff. Run #1 Run #2 Run #3 Run #4 Run #5 Use MKS units (Meters, Kilograms, Seconds). 1. Calculate the net force for each trial. The net force is the difference between the two masses times the acceleration of gravity, or g(m 2 - M 1 ) 2. Calculate the total mass for each trial, (M 1 + M 2 ). Use the net force and total mass to calculate the theoretical acceleration using Newton's Second Law: QUESTION 1. Compare the experimental acceleration with the theoretical acceleration by determining the percentage difference. What are some reasons that would account for the percentage differences? dg 1996, PASCO scientific P13-5