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Return to Honors Physics Lab Overview (Revised 07-17-02)
Lab 4: Speed and Acceleration
Purpose: What is the relationship between a uniform increase in velocity with time, and how can this relationship be represented graphically?
Materials: (List them)
Procedure:
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Students will work in groups of four per lab station. Part I and Part II of the procedure are preparatory tasks which should be completed at the same time by a pair of students.
Part I: The Cart
(Record the identifying number written on your cart)
1. String of sufficient length must be attached to the front on the cart so that when the cart is positioned on the table, the mass which is attached to the opposite end of the string can suspend freely below the smart pulley (Fig. 1). The cart's starting point should be about 125 cm from the pulley. The cart must move a horizontal distance equivalent to three revolutions of the Smart Pulley, which is about 46 cm (second tape in Figure 1). The remaining distance is the region where the cart must be brought to rest WITHOUT striking the pulley (Fig. 2). The technique needed to stop the cart will be discussed in lab. The height of the pulley must be adjusted to permit the string to run parallel to the table top. The string must be placed in the groove of the smart pulley in such a manner that as the pulley turns, no noticeable friction encumbers the pulley's rotation.
2. Place a piece of masking tape on the table top to mark the "Start" position of the cart's front wheels where the cart's original velocity (VO) is zero (Fig. 3).
3. With a 20 gram mass attached to the free end of the string, pull the cart back to its labeled starting point. Place a tiny piece of tape on one spoke of the pulley (Fig. 4 ), and place that spoke in a vertical position as illustrated. Carefully examine the open region between the spokes located 90 degrees to the right of the marked spoke. You should see the photogate's IR sensor. Data is collected each time the IR sensor receives the beam of light (which is periodically cut off by a passing spoke). Very slowly, and while still holding the cart, allow the cart to roll forward exactly three revolutions of the pulley. Mark this position with a line drawn on a piece of tape. Measure this distance using a metric stick and record the distance on the masking tape. Allow the cart to continue rolling forward to complete the fourth revolution. This tape should be long enough to cross the intended path of the cart (Fig. 2). This point will represent the "End" position, or the cart's final velocity (VF).
4. Before velocity/time data are collected by the procedure below, use a stopwatch to determine the average time (tEXP) taken by the cart to accelerate over the marked distance. The cart moves very quickly, so take ten trials for time. This data must be recorded and displayed as part of this lab.
Part II: The Smart Pulley Photogate, CBL, and Calculator
5. Attach the Pasco Smart Pulley Photogate to the edge of the lab table using the support clamp. The support shaft of the pulley-photogate apparatus must be positioned vertically (Fig. 5).
6. Connect the Pasco Smart Pulley Photogate to the CH1 input on the CBL using the adaptor (Fig. 6).
7. Use the black link cable to connect the CBL unit to the TI 83 Plus calculator. Firmly press the cable ends.
8. Turn on the CBL unit and calculator.
9. Press the applications key (APPS) on the calculator, select the PHYSICS program, and proceed to the MAIN menu.
10. Once on the main menu, select "SET UP PROBES". Select ONE as the number of probes. Scroll to MORE on the SELECT PROBE menu, until you find and select PHOTOGATE. The Smart Pulley Photogate should already be connected to Channel 1, so press ENTER.
11. Proceed to the TIMING MODE menu. Select MOTION. Select SELECTION DEVICE from the MOTION TIMING menu. Select SMART PULLEY from the SELECT DEVICE menu. Select 10 SPOKE INSIDE from the SMART PULLEY window.
12. In the MOTION TIMING menu, select COLLECT DATA. Enter "4" for the number of revolutions as prompted by the calculator. Your cart must move far enough to rotate the pulley four revolutions or the CBL will not end data collection.
13. The window now asks you to PRESS [ENTER] TO ARM the pulley's photogate. NOTE: Final adjustment of the cart at the "START" marker should be now be made. WITHOUT MOVING THE CART, press the ENTER key. The READY... message indicates that data will commence once the Smart Pulley begins to rotate through the Photogate. Movement of the cart at this time will produce extraneous data points. Data will be collected by the CBL for the number of revolutions specified in the previous step. Gently release the cart and allow it to proceed unencumbered along its assigned path.
14. Be patient! The calculator will present lists of data (Fig. 7) for Time (L1) and Velocity (L5). Press ENTER.
15. On the SELECT GRAPH screen, select VELOCITY. A relatively straight-line graph appears on the screen (Fig. 8). Press NEXT, then for "REPEAT?", select NO. Select "RETURN TO MAIN", then on the MAIN MENU screen, select "ANALYZE". On the ANALYZE MENU screen, select CURVE FIT.. On the CURVE FIT screen, select LINEAR L1, L5. Take note of the graph's slope (M =) and y-axis intercept (B =). Press ENTER. A graph with data points is displayed (Fig. 9). Press ENTER, and QUIT. Instead of performing graphical analysis using the calculator, you will transmit data to the computer where Vernier's Graphical Analysis for Windows has been installed.
16. On the TI 83 Plus calculator, clear the screen by pressing the "2nd function" and "Quit" keys.
17. Disconnect the black calculator-CBL link cable from the calculator. Connect the calculator to the computer using the gray link cable
18. On the calculator, press the "2nd function" and "Link" keys.
19. On the SEND/RECEIVE screen, select LIST.
Part III: Graphical Analysis on the Computer
20. If Graphical Analysis for Windows has not been opened on the computer, do so by clicking on Start, then follow Programs to Vernier Software. On the computer screen you should see blank data table and graph windows. Next under "File", click on "Import From TI Calculator". An information box will appear with a "Waiting on Serial Port 2...." message.
21. On the SELECT/TRANSMIT screen of the calculator (Fig. 10), select L1 (press ENTER), scroll down, select L4 (press ENTER) and L5 (press ENTER). Toggle right to highlight TRANSMIT and press ENTER.
22. A data stream should fill three data columns on the computer screen.
23. Highlight the Graph Window, then click on "Graph" on the menu bar. Select "Point Protectors"; deselect "Connecting Lines"; and select "Background Grid".
24. Highlight the Data Table Window. Double click on "L1" heading the left column to access "L1 Options". Type "Time" for the New Name and type "sec" for the New Units. Double click on "L5" heading the right column. The New Name is "Velocity" and the New Unit is "m/sec". Take note that the graph's y-axis becomes "Velocity" and the x-axis becomes "Time". L4 is "Distance" with "m" as the unit.
25. On the Data Table Window, click on "Data Set 1: Data" to highlight both columns. With both data columns highlighted, click on the "Graph Window" bar heading the Graph Display, then click on "Analyze" on the menu bar. Scroll down to "Regression" and click. A floating box of regression data should be displayed. You can click and drag this box to a convenient location. Print a copy of the data table alone. Once the graph display is highlighted and maximized, select "Selected Display" under the Print option to gain a copy of the graph. Identify the graph and data table by writing "50 g mass" at the top of each page.
26. Repeat the procedure to generate a second set of data by replacing the 20 gram mass on the string with a 50 gram mass. Identify the graph and data table by writing "20 g mass" at the top of each page.
Part IV: The Coefficient of Kinetic Friction of an Accelerating Wood Block (Record the identifying number written on your block)
27. Replace the cart with a wood block (Fig. 11 ). Measure the combined mass of the wood block and one kilogram cylinder using the digital platform balance. Do not assume "1000 g" as the mass of the cylinder. For the first trial, the block and its load will be pulled by a 500 g mass attached to the free end of the string. Record the average time for the motion of the block over the marked path, repeating the "time" procedure at least three times.
28. Collect velocity/time data and print a copy of the resulting data table and graph. Caution: "Distance data (L4) must be transferred from the calculator to Vernier Graphical Analysis, along with time (L1) and velocity (L5).
29. Repeat the procedure, replacing the 1000 g load on the block with a 400 g mass, and replacing the 500 g mass on the string with 400 g. Remember to identify all pages by writing "1000 g mass" or "500 g mass" on the appropriate pages.
Part V: Math Calculations - Cart
30. For each of the two trials, select two data points on the graph (Fig. 12a and Fig. 12b) that rest directly on the line; their point protectors should appear to be bisected by the regression line. The two points selected have been elected as representatives of the slope, so be careful. Try to select two points that are widely separated (Fig. 9). Use the mathematical expression shown below to calculate the slope, aGRAPH:
ΔY / ΔX = slope
(V2 - V1) / (T2 - T1) = aGRAPH
31. Use S = Vo· T + 1/2 · a · T2 to calculate aMATH, where "S" is the distance between the tape marking the "zero" or rest position and the tape marking the end of the third revolution, and "T" is the average time taken by the stopwatch.
32. Use the appropriate formula(s) to calculate the time (T") and distance (S") related to the motion of the cart from rest to the point where the CBL began to display data as the first data point (Fig. 13).
Part VI: Math Calculations - Wood Block
33. Calculate the μ K for the wood block in each of the two trials. Use FNET = M · a to solve for Fk, using the slope of the line indicated in the floating box on the graph display. "M" represents the mass of the wood block and the load placed on it, NOT the mass attached to the end of the string. You must record the precise sum of these two masses, which represent "M". Use μ k = Fk/Fn to determine the coefficient of sliding friction. Use V2F(math) = Vo2 + 2 · a(graph) · S(exp) to calculate VF(MATH). In the formula, S(exp) is the distance from rest to the tape marking the end of the third revolution. VF-EXP can be estimated from the data table by moving down the "Distance" column to the distance which most closely approximates the actually measured distance between the tape markers.
Graphs: A completely labeled graph, with data table, must be included for each of the required runs. "Completely labeled" will be clarified in class. Each graph must include an appropriate graphical analysis of the slope, which designates x-axis and y-axis origins of data points used. Any values taken specifically from the data table for plotting points on the graph, as opposed to values taken directly from the background grid of the graph, must be circled on the data table. It is essential that data points representing the slope, rest perfectly on that line.
Sample Calculations:
You must show all math steps for each of the following, including labeled diagrams:
Cart - aGRAPH, aMATH, S", T"
Block - Fk, μ k, and VF
Conclusion:
(Delineate your answers; do not write your answers as sentences in a long paragraph)
1. What aspect of the cart’s motion is being graphically represented? Explain its meaning. What does the shape and orientation of the slope indicate?
2. State the values for “a1” and “a2” relative to the cart, and “a1” and “a2” relative to the bloc, as obtained from the floating data boxes.
3. Compare/contrast “a1” and “a2” for the cart, then for the block. For each pair, explain the differences quantitatively and in terms of Newton’s Second Law of Motion.
4. Referring to the “a2” graph for the cart, explain the mechanism that allows for the unaccounted time (T').
5. Compare a(graph) and a(math) for one of the cart's runs. Explain any discrepancies.
6. Relate each of the terms in the equation, y = mx + b, to the motion formula(s) used in class, and to the graph produced during the motion of the cart.
7. Under what condition(s) is the distance between the two pieces of tape important? Explain.
8. State the coefficient of sliding friction values for the block's two trials. What relationship should exist between these values? Explain. What effect should the weight placed on the wood block have on the coefficient of sliding friction between block and table top? Explain.
9. Examine the data points displayed on one of the wood block's graphs. What effect would choosing two data points randomly have when calculating the block's acceleration, using ΔY / ΔX = slope.
Three Potential Sources of Lab Error: (State the specific source of error and what variables are affected)
Practice Problems: