Use the slope of a graph of the cart s acceleration versus sin to determine the value of g, the acceleration due to gravity.
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1 Name Class Date Activity P03: Acceleration on an Incline (Acceleration Sensor) Concept DataStudio ScienceWorkshop (Mac) ScienceWorkshop (Win) Linear motion P03 Acceleration.ds (See end of activity) (See end of activity) Equipment Needed Qty Equipment Needed Qty Acceleration Sensor (CI-6558) 1 Dynamics Cart (inc. w/ Track) 1 Angle Indicator (inc. w/ Track) 1 Meter stick 1 Base and Support Rod (ME-9355) m Track System (ME-9429A) 1 What Do You Think? When a sled accelerates down a snow-covered hill, on what does its acceleration depend? You may want to consider the height of the hill, the slope of the hill and the mass of the sled. How does its acceleration depend on the variable(s) you selected? Take time to answer the What Do You Think? question(s) in the Lab Report section. Background A cart on an incline will roll down the incline as it is pulled by gravity. The direction of the acceleration due to gravity is straight down as shown in the diagram. The component of the acceleration due to gravity which is parallel to the inclined surface is gsin where is the angle of the incline. Neglecting friction, this is the acceleration of the cart. SAFETY REMINDER Follow all safety instructions. For You To Do Use an Acceleration Sensor to measure the motion of a cart as it moves down an inclined track. Use an angle indicator to measure the angle of the inclined track or determine the sine of the angle (sin ) from the height of the track and the length of the track. sin ø opposite side hypotenuse height length of track Use the slope of a graph of the cart s acceleration versus sin to determine the value of g, the acceleration due to gravity. NOTE: This activity is easier to do if you have a partner to run the computer while you release the cart. P PASCO scientific p. 13
2 Physics Labs with Computers, Vol. 1 Student Workbook P03: Constant Acceleration A PART I: Computer Setup 1. Connect the ScienceWorkshop interface to the computer, turn on the interface, and turn on the computer. 2. Connect one end of the cable to the Acceleration Sensor and connect the other end into Analog Channel A on the interface. 3. Open the file titled as shown: DataStudio ScienceWorkshop (Mac) ScienceWorkshop (Win) P03 Acceleration.ds (See end of activity) (See end of activity) The DataStudio file has a Workbook display. Read the instructions in the Workbook. The file has a Graph display of Acceleration versus Time, a Table display of Acceleration and sin (theta), and a Graph display of Acceleration versus sin (theta). Data recording is set for 50 measurements per second (50 Hz). See the pages at the end of this activity for information about creating a ScienceWorkshop file. PART II: Sensor Calibration and Equipment Setup You do not need to calibrate the sensor for this activity. 1. Carefully measure and record the overall length of your track. 2. Level the track by setting the cart on the track to see which way it rolls. Adjust the leveling screw at the end of the track to raise or lower that end until the cart placed at rest on the track will not move toward either end. Record the height of the end of the track that does not have the end-stop. 3. Mount the Acceleration Sensor onto the cart. Use the large thumbscrew to attach the short leg of the bracket to the sensor. p PASCO scientific P03
3 Name Class Date Use the small thumbscrew to attach the long leg of the bracket to a threaded hole in the top of the cart. 4. Set the SENSOR RESPONSE switch to SLOW. 5. Use the base and support rod to raise the end of the track without an end-stop so that it is 20 cm higher than its position when level. 6. Mount the angle indicator onto the raised end of the track. 7. Use a pencil to put a mark near the midpoint of the track. Let the midpoint mark be your starting point for the cart release during data recording. Preparing to Record Data Recording data involves the following steps: Measure and record the height of the track (or record the angle of the track). Tare the sensor. Start data recording. P PASCO scientific p. 15
4 Physics Labs with Computers, Vol. 1 Student Workbook P03: Constant Acceleration A Release the cart. Catch the cart and stop recording data. Repeat the process for several heights (several angles). PART III: Data Recording 1. Determine the angle of the track. (Hint: Use the angle indicator, or measure the height of the track and use the height and length of the track to calculate the sine of the angle.) 2. Put the cart at the starting point on the inclined track. Press the TARE button on the sensor to zero the sensor. 3. Start recording data (hint: click Start or click REC ) and then release the cart so it moves down the track. 4. Catch the cart when it reaches the end of the track and stop recording data. 5. Lower the raised end of the track by four centimeters. 6. Repeat the procedure at the new height. 7. Continue to repeat the procedure until the raised end is at 4 centimeters. p PASCO scientific P03
5 Name Class Date Analyzing the Data The first part of analyzing the data involves the following steps for each different height: Determine the sine of the angle. (Hint: Use the measurement from the angle indicator and then find the sine of the angle or calculate the sine of the angle based on the height and length of the track.) Examine the Graph display of Acceleration versus Time to determine the average acceleration. Enter the average acceleration and the sine of the angle into the Table display of Acceleration and sin (theta). Repeat the analysis procedure for the each height. 1. Determine the sine of the angle and record the value in the Lab Report section. 2. In the Graph display, click-and-drag the cursor to highlight that section of the data that corresponds to the motion of the cart down the track. 3. Use the Graph s built-in analysis tools to determine the average ( mean ) of the acceleration. Hint: In DataStudio, click the Statistics menu button ( ) and select Mean. In ScienceWorkshop, click the Statistics button ( ) to open the statistics area. In the statistics area, click the Statistics menu button ( ) and select Mean. 4. Enter the sine of the angle and the average acceleration for that angle into the Table display. For the second part of analyzing the data, use the Graph display of Acceleration versus sin (theta). 1. Find the slope and y-intercept of the best-fit line through your data. Hint: In DataStudio, click the Fit button and select Linear from the menu. In ScienceWorkshop, click the Statistics menu button and select Curve Fit, Linear Fit from the submenu. 2. Record the slope as the acceleration due to gravity, g. Hint: In DataStudio, the slope m is shown in the Linear Fit legend on the Graph display. In ScienceWorkshop, the slope is the coefficient a2. Record your results in the Lab Report section. P PASCO scientific p. 17
6 Physics Labs with Computers, Vol. 1 Student Workbook P03: Constant Acceleration A Lab Report - Activity P03: Acceleration on an Incline What Do You Think? When a sled accelerates down a snow-covered hill, on what does its acceleration depend? You may want to consider the height of the hill, the slope of the hill and the mass of the sled. How does its acceleration depend on the variable(s) you selected? Questions 1. What is the percent difference between your measured value for g and the accepted value for g? Remember, percent diff erence measured accepted accepted 100% 2. If the mass of the cart is doubled, how are the results affected? Try it. p PASCO scientific P03
7 Name Class Date P PASCO scientific p. 19
8 Physics Labs with Computers, Vol. 1 Student Workbook P03: Constant Acceleration A Appendix: Set Up ScienceWorkshop Create a ScienceWorkshop file to measure acceleration. Set Up the Sensor In the Experiment Setup window, click and drag the analog sensor plug to Channel A. Select Acceleration Sensor from the list of sensors. Click OK to return to the Experiment Setup window. Set the Sampling Options Click the Sampling Options button in the Experiment Setup window or select Sampling Options from the Experiment menu to open the Sampling Options window. Under Periodic Samples click the right arrow to set the sample rate at 50 Hz (50 measurements per second). Set Up the Display In the Experiment Setup window, click and drag the Graph display icon to the Acceleration Sensor icon. Select Acceleration (m/s/s) from the list of calculations and click Display. Analyzing the Data After you have recorded data and determined the sine of the angle and the average acceleration for each trial, use the Experiment Notes window to enter your data into a new Graph display of Acceleration versus sin (theta). Enter the Data 1. Open a Notes window. Use the following format to enter your data pairs of the sine of the angle and the average acceleration for each angle: sine of angle <TAB> average acceleration <RETURN> p PASCO scientific P03
9 Name Class Date 2. Pick Select All in the Edit menu and then pick Copy in the Edit menu. Result: The data pairs in the Notes window are highlighted. 3. Click the Experiment Setup window to make it active. Pick Paste from the Edit menu to paste the data into the Data list. Result: The Enter Data Cache Information window opens. Enter Acceleration as the Long Name and m/s/s as the Units and click OK. Result: Import appears in the Data list in the Experiment Setup window. Display the Data 1. In the Graph display, select Data Cache, Acceleration from the Data Input menu. Result: The data pairs are plotted. Note that the horizontal axis label is Time (s) but the x values correspond to the sine of the angle. P PASCO scientific p. 21
10 Physics Labs with Computers, Vol. 1 Student Workbook P03: Constant Acceleration A p PASCO scientific P03
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