Newton s Second Law. Newton s Second Law of Motion describes the results of a net (non-zero) force F acting on a body of mass m.

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1 Newton s Second Law Newton s Second Law of Motion describes the results of a net (non-zero) force F acting on a body of mass m. F net = ma (1) It should come as no surprise that this force produces an acceleration a. This acceleration varies as a function both of the force and the mass. This suggests two separate relationships - one between a and F (m constant), and the other between a and m (F constant). Figure 1 shows the experimental setup - a cart of mass M connected to a hanger of mass m by a string that runs parallel to the track and over a pulley. It is this system M + m that is accelerated by the applied force. An ultrasonic motion sensor monitors the motion of the cart. This system is ideal for two reasons: Figure 1: The System The force on the system is easily quantified, as it is just the weight of the hanger and anything on it. Any masses in the cart or on the hanger become part of the system. By judicious placement of these masses, it is easy to maintain either constant mass or constant force. Apparatus Dynamics track, Low-friction cart, String, Pulley, Mass hanger, Slotted masses, Load masses, Motion sensor, Pasco interface, Computer, Capstone software. 1

2 Procedure Preliminaries 1. If not already, turn on the computer and 750 interface. Open Capstone and the activity entitled Second Law. 2. Cut off a piece of string about as long as the track. Attach one end to the cart and the other to the mass hanger. 3. Make sure that the motion sensor is set to narrow beam (switch on top) and that the front of the sensor is vertical; i.e., perpendicular the the track. Move everything away from the sides of the track (including yourselves while collecting data) so there is no interference with the beam from the sensor. 4. To ensure good data, make any necessary adjustments to the track and pulley so that a) the track is level, b) the string travels across the pulley in a straight line, and c) the string is parallel to the track. Constant Mass 1. Put two of the slotted masses in the cart and the third on the mass hanger. 2. Hold the cart on the track such that the hanger sits just below the pulley over the edge of the table. 3. Click the Record button then release the cart; data collection will stop automatically. 4. The slope of the Velocity vs. Time graph is the acceleration of the system. Using the Curve-Fit tool in the graph window, fit the data to a Linear function. 5. Repeat for a total of three trials and calculate the average. 6. Transfer one of the slotted masses from the cart to the mass hanger and repeat the procedure. 7. Transfer the second slotted mass from the cart to the mass hanger and repeat. 8. Plot a graph of acceleration vs. force. Constant Force 1. Start with an empty cart and two slotted masses on the hanger. 2. Determine the acceleration of the system three times and calculate the average. 3. Put one of the load masses on the cart and repeat the procedure. 4. Place the second load mass on the cart and repeat. 5. Plot a graph of acceleration vs. inverse mass. 2

3 Data Sheet Constant Mass Mass of system (kg) Force on Acceleration Average System Acceleration (N) (m/s 2 ) (m/s 2 ) Constant Force Force on system (N) Mass of Inverse Acceleration Average System Mass Acceleration (kg) (kg 1 ) (m/s 2 ) (m/s 2 ) 3

4 Analysis Constant Mass 1. What is the relationship between acceleration and force? 2. Does you graph confirm this relationship? Why or why not? 3. Use the slope of your line to determine the mass of the system. Compare (%) this to the known mass. 4

5 Constant Force 1. What is the relationship between acceleration and mass? 2. Does you graph confirm this relationship? Why or why not? 3. Use the slope of your line to determine the force on the system. Compare (%) this to the known force. 5

6 Pre-Lab: Newton s 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? 6