Second Law. In this experiment you will verify the relationship between acceleration and force predicted by Newton s second law.

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1 Second Law Objective In this experiment you will verify the relationship between acceleration and force predicted by Newton s second law. Apparatus Table clamp, Vertical rod, Right-angle clamp, Horizontal rod, Pulley, Thread, Scissors, Slotted mass set, Photo gate, Foam pad, Pasco interface, Computer, Meter stick. Theory The second law a = F m (1) states that if the mass m of an object is constant, then its acceleration a is proportional to the force F it experiences (the net force). The figure below shows the experimental setup. This Atwood s machine consists of two unequal masses connected by a string over a pulley. Interestingly, it was originally designed to obtain an experimental value of g since the acceleration of the masses is much less than that of an object in free fall. a m 2 m 2 g m 1 m 1 g Since the masses are connected they move together and have the same acceleration. It is therefore easier if we analyze the motion of this system of masses m 1 + m 2 ; the net force on the system is just the difference in the weights of the masses. F net = m 1 g m 2 g (2) 1

2 Theoretically the second law then yeilds a = m 1g m 2 g m 1 + m 2 = ( m1 m 2 m 1 + m 2 ) g (3) Experimentally, in order to test the relationship above you would need to vary the force on the system and measure the corresponding acceleration (while keeping the mass constant). You will do this by letting m 1 and m 2 be hangers onto which you can place slotted masses. If you vary these masses such that the their difference changes but sum remains constant then you will be varying the force on the system while keeping the mass constant. All that remains is the measurement of acceleration. The rotation of the pulley is monitored by a photo gate and its linear velocity plotted as a function of time. The slope of this line is the acceleration. Procedure 1. If not already, turn on the computer and interface. Open Capstone and the experiment entitled Second Law. 2. Cut off a piece of thread about 1m long. Attach one end to a hanger, thread the other end over the pulley and attach a second hanger. 3. Place the foam pad on the table under the pulley so the hangers will strike it rather than the table top. Adjust the height of the pulley so that the upper hanger is just below the pulley when the lower hanger touches the pad. 4. To ensure good data, make sure that the plane of the pulley is vertical; you should check this periodically as you are collecting data. 5. Use the slotted masses to make m 1 = 155g (remember the hanger itself is 5g); m 2 should be 145g. Calculate the net force and theoretical acceleration. 6. Hold m 2 on the pad and stop any swinging motion of m 1. Click the Record button and then release m 2 (data collection does not begin until there is motion). Click the Stop button before m 1 hits the pad. 7. The slope of the Velocity vs. Time graph is the experimental acceleration of the system. Using the Curve-Fit tool in the graph window, fit the data to a Linear function. 8. Repeat for a total of three trials and calculate the average acceleration. 9. Repeat the procedure with m 1 = 160g and m 2 = 140g. 10. Repeat the procedure with m 1 = 165g and m 2 = 135g. 11. Plot a graph of the average acceleration vs. force. 12. Using the slope of the line on your graph, determine the mass of the system. 2

3 Analysis 1. What is the relationship between acceleration and force you tested? Does your graph confirm the relationship? Why or why not? If not, offer an explanation as to why this might be the case. 2. How close (%) was your calculated mass of the system (from the slope) to the actual mass used in the experiment? 3

4 Data Sheet g (m/s 2 ) m 1 m 2 Net Theoretical Force Acceleration (g) (g) (N) (m/s 2 ) Net Acceleration Average Force Acceleration (N) (m/s 2 ) (m/s 2 ) System mass (kg) 4

5 Pre-Lab: Second Law Name Section Answer the questions at the bottom of this sheet, below the line (only) - continue on the back if you need more room. Any calculations should be shown in full. 1. What is Newton s Second Law of Motion? Write it in equation form and express it in words. 2. What is the relationship between acceleration and force? 3. What is the relationship between acceleration and mass? 4. What is the system being accelerated in this experiment? 5. What is the force on the system in this experiment? 5