Kinematics. Become comfortable with the data aquisition hardware and software used in the physics lab.

Transcription

1 Kinematics Objective Upon completing this experiment you should Become comfortable with the data aquisition hardware and software used in the physics lab. Have a better understanding of the graphical analysis of one-dimensional motion. Apparatus Dynamics track, Track supports, End stop, Table clamp, Rod, Track clamp, Constant velocity cart, Low-friction cart, Motion sensor, Computer, Pasco 550 interface, Capstone software. Theory By now you are familiar with the basic kinematic equations describing the linear motion of an object that has a constant acceleration. x = ( vo + v 2 ) t (1) x = x o + v o t at2 (2) v 2 = v o 2 + 2a(x x o ) (3) v = v o + at (4) Here, x is displacement, v velocity, a acceleration, and t time. Setting a = 0 yields applicable equations for an object with constant velocity. In this experiment you will use the Pasco 550 data acquisition interface to acquire the position of a moving object as a function of time. The accompanying software uses this data to determine velocity and acceleration as functions of time. You will then analyze the motion in the context of the equations above. Procedure Mount the motion sensor at the free end of the dynamics track and connect the output leads to Digital Channels 1 and 2 (yellow lead in Channel 1) of the 750. Turn on the computer and 750 interface. In all procedures: The switch on top of the sensor should be set to narrow beam, and the face of the sensor should be angled up slightly from perpendicular. 1

2 The motion sensor is ultrasonic and subject to interference - keep all objects away from the track while you are collecting data. Constant Velocity 1. Open Capstone and the activity entitled Linear Motion. 2. Level the track if necessary. 3. Place the constant velocity cart on the track in front of the motion sensor - rubber wheels closest to the sensor. The speed of the cart is controlled by a knob on top of the cart; set it to roughly half speed. 4. When ready to collect data, click the Record button then turn on the cart. The sensor will automatically record the appropriate data. After the cart hits the end stop, pick it up and turn it off. 5. Make sure the Position tab is active. You will see a data table on the left side of the page and a graph on the right. If there is no data displayed, click on in the table and on the graph toolbar. In both cases select Run #1. 6. Use the Curve-Fit tool to fit the data to a Linear function. What is the equation returned from the curve-fit, and to which Equation (1-4) from the Theory section does it correspond? 7. What is the slope of the line? For this value, as well as all subsequent values - do not forget to include units! What does it represent? 2

3 8. What is the y-intercept? What does it represent? 9. In a position vs. time graph, why does a straight line signify constant velocity motion? 10. Select the Velocity tab. Describe the graph below. Is it what you expected? Why or why not? 11. Use the Coordinates tool to determine the velocity of the cart. Obviously, you want to place it such that the vertical location best represents the velocity of the cart. What is this value? 12. In the table, use the Statistics tool to display the Maximum, Minimum, and Average values. What are these values? How does the average velocity compare to the value in Step 7? Step 11? 3

4 13. Go back to the graph and use the Area tool to determine the area under the curve. What is this value, and what does it represent? 14. Does the value returned seem reasonable based on what you did in the procedure? Why or why not? 15. Select the Acceleration tab. What rate of acceleration do you expect for the cart? What is the average value from the table? Can you determine a value from the graph? 16. Keep the data you have collected, and repeat the procedure with the cart at maximum velocity. Describe how the position vs. time graph is different now that the velocity is higher. Answer also for the velocity vs. time graph. Positive Acceleration 1. Remove the supports from the track. 2. Attach the table clamp to the side of the lab table. Using the track clamp and rod, attach the dynamics track to the table clamp such that the sensor end is suspended above the table. [The bolt on the track clamp slides into the channel on the side of the track.] Adjust the height of the track such that the upper end is between 20cm-25cm above the table. 4

5 3. Delete any previous runs so that you are starting with empty graphs and tables. 4. Place the low-friction cart on the track in front of the motion sensor. Proceed as in the previous procedure; click Record then release the cart. 5. Select the Position tab. On the graph, fit the data to a Quadratic function. What is the equation returned from the curve-fit, and to which Equation (1-4) from the Theory section does it correspond? 6. Using the Slope tool determine the slope of the curve at three different points - one near the beginning of the motion, one near the midpoint, and one near the end. Record these values below, in this order. 7. According the slope values above, what is happening to the velocity of the cart as it moves down the track? Is it decreasing, constant, or increasing? Is this what you expected? Why or why not? 8. Select the Velocity tab. On the graph, fit the data to a Linear function. What is the equation returned from the curve-fit, and to which Equation (1-4) from the Theory section does it correspond? 5

6 9. What is the acceleration of the cart according to this graph? 10. What is the y-intercept? What does it represent? 11. Determine the acceleration of the cart from another graph or table. Record this value below, and explain how you obtained it. 6

7 Pre-Lab: Kinematics Name Section Answer the questions at the bottom of this sheet, below the line - continue on the back if you need more room. Any calculations should be shown in full. 1. Rewrite Equations 1-4 from the Theory section when a = 0 (constant velocity). 2. On a graph of position (m) vs. time (s), what are the units of the slope? What does the slope represent physically? 3. You plot the position vs. time for an object moving with a constant velocity. Will the slope be constant or not? Why? 4. On a graph of velocity (m/s) vs. time (s), what are the units of the slope? What does the slope represent physically? 5. You plot the position vs. time for an object moving with a constant acceleration. Will the slope be constant or not? Why? 6. You plot the velocity vs. time for an object moving with a constant acceleration. Will the slope be constant or not? Why? 7