PASCO scientific Physics Lab Manual: P05-1 Experiment P05: Position, Velocity, & Acceleration (Motion Sensor) Concept Time SW Interface Macintosh file Windows file linear motion 30 m 500 or 700 P05 Position, Velocity, Acceleration P05_POSI.SWS EQUIPMENT NEEDED Interface string motion sensor track, 2.2 meter (optional) fan cart PURPOSE The purpose of this laboratory activity is to study the relationship between position, velocity, and acceleration in linear motion. THEORY The equation for position (x), given a constant acceleration (a), is x = x 0 + v o t + 1 2 at 2 where x o and v o are the initial position and velocity. Note that if x o and v o equal zero, the equation is a parabola. The first time derivative (which corresponds to the slope of the graph) of this equation, d dt x = v 0 + at = v is the well-known equation for velocity under constant acceleration. This equation is linear; the slope of the line is the acceleration. The second time derivative is the constant acceleration. PROCEDURE d 2 dt 2 x = a For this activity, use a motion sensor to measure the position of a fan cart as it moves away from the motion sensor. The program plots the cart s position (x), velocity (v), and acceleration (a). dg 1996, PASCO scientific P05-1
P05-2: 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 motion sensor s phone plugs to Digital Channels 1 and 2 on the interface. Plug the yellow-banded (pulse) plug into Digital Channel 1 and the second plug (echo) into Digital Channel 2. 3. Open the file titled as shown: Macintosh Windows P05 Position, Velocity, Acceleration P05_POSI.SWS The document has a Graph display of Position (m), Velocity (m/sec), and Acceleration (m/sec/sec) versus Time (sec). 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.) Full size Close box Zoom box Control-menu button Restore button Minimize button Maximize button Macintosh Reduced size Windows P05-2 1996, PASCO scientific dg
PASCO scientific Physics Lab Manual: P05-3 PART II: Sensor Calibration and Equipment Setup You do not need to calibrate the Motion Sensor. 1. Place the motion sensor and fan cart on a flat horizontal surface. Make sure that there is nothing to obstruct the signal going from the front of the motion sensor to the fan cart, or the returning echo from the fan cart back to the motion sensor. (If you have a PASCO dynamics track available, use it.) To Interface Fan Cart Motion Sensor Position, Velocity, and Acceleration of a Fan Cart 2. Tie a string to the fan cart so that you can hold the fan cart before releasing it without interfering with the motion sensor. PART III: Data Recording 1. Hold the string so that the fan cart remains stationary about 40 cm in front of the motion sensor. Turn the fan on. Make sure that the fan cart is pulling away from the motion sensor! 2. Click the REC button ( ) to begin data recording. 3. Release the fan cart. 4. When the cart has traveled the length of the space available, (generally less than two meters is best), click the STOP button ( ) to end data recording. Run #1 will appear in the Data list in the Experiment Setup window. ANALYZING THE DATA 1. Select the Graph display to make it active. 2. Click the Statistics button ( ) in the lower left corner of the Graph to open the Statistics area. Click the Autoscale button ( ) to resize the Graph to fit the data. dg 1996, PASCO scientific P05-3
P05-4: Physics Lab Manual PASCO scientific 3. Click the Magnifier button ( ). The cursor changes to a magnifying glass shape. Use the cursor to clickand-draw a rectangle around a relatively small region of the plot of position versus time that shows a smooth parabolic curve. Try to surround about five or six data points with your rectangle. The Graph will rescale to fit the region you selected. (The velocity and acceleration plots will change as well.) 4. Use the mouse to click-and-draw a rectangle around only two consecutive points of the position curve. 5. Click the Statistics Menu button ( ) in the Statistics area of the position versus time plot. Select Curve Fit, Linear Fit from the Statistics menu. A best fit line will be drawn through the two points in your selected region. The coefficient a2 in the linear equation the Statistics area is the slope of the line through the points. 6. Click the Smart Cursor ( ) button. The cursor changes to a cross-hair when you move the cursor into the display area. Move the cursor/cross-hair to the midpoint of the line segment joining the two points in the region you selected for the position curve. Smart Cursor P05-4 1996, PASCO scientific dg
PASCO scientific Physics Lab Manual: P05-5 The coordinates of the cursor are shown next to the vertical and horizontal axes. 7. Compare the slope given in the position plot Statistics area with the value of velocity at that same time. Hold down the Shift key and move the cursor vertically into the plot of velocity versus time. Y-coordinate is velocity The velocity at that point is the Y-coordinate shown in the area next to the vertical axis. 8. Repeat the data analysis process for several points on the position plot. OPTIONAL In the plot of position, click anywhere outside your small rectangle to clear the selection. Click the Autoscale button to rescale the Graph to fit the data. In the Statistics area of the position plot, click the Statistics Menu button and select Curve Fit, Polynomial Fit in the Statistics menu. In the Statistics area of the velocity plot, click the Statistics Menu button and select Curve Fit, Linear Fit in the Statistics menu. In the Statistics area of the acceleration plot, click the Statistics Menu button and select Curve Fit, Linear Fit in the Statistics menu. In the plots of position and velocity, the chi^2 value indicates how well the data fit the selected curves. In the acceleration plot, examine the value of a2, the slope of the line of best fit. QUESTIONS 1. What are the appropriate units (in MKS) for the slopes of the position and velocity plots? 2. Why is the acceleration plot so much "noisier" than the other plots? (Hint: Use the analysis method in Analyzing the Data to compare the slope of the line segment between any two points on the velocity plot with the value on the acceleration plot that corresponds to the midpoint on the line segment in the velocity plot.) dg 1996, PASCO scientific P05-5
P05-6: Physics Lab Manual PASCO scientific OPTIONAL QUESTIONS 1. How close does the plot of position fit a polynomial curve? (Remember, the closer chi^2 is to zero, the better the fit of data to the curve.) 2. How close does the plot of velocity fit a linear curve? 3. Is the acceleration nearly constant? (Remember, a slope of zero indicates a constant value.) P05-6 1996, PASCO scientific dg