PART 2: KINETIC FRICTION COEFFICIENT FROM ACCELERATION & NEWTONS 2ND LAW Pair of Surface Materials Used: Cart Mass (g): Motion Detector String Pulley Hanging Mass (g): Cart Trial # Acceleration (m/s') Slotted 1 Masses on Hanger Track with Friction 2 3 4 5 Mean 6. Using the setup shown, draw free body diagrams for the hanging mass and the cart assuming there is friction acting on the cart. 7. Beginning with Newton's 2"d Law and using your knowledge of the free body diagrams, derive an equation for calculating the coefficient of kinetic friction. It should only include terms for masses, acceleration, and gravity. Coefficient Of Kinetic Friction = (Materials: Compare your value here to what you obtained in Part 1 for the kinetic coeff. Which method gave a larger value? Think carefully about the setup for both parts, and what we added to Part 2. Which Part would you expect to give a larger value?Copy this Data onto the relevant tables of your worksheet. Approximate Speeds Low speed (m/s) NJ 3 4 6 Felt Object on Aluminum Track This Table already has the total object (cart) total mass N static kinetic mass entered for the 5 trials of data taken (g) (N) (N) (N) and supplied in this file. The Normal force is also already calculated. 728 7.13 2 1228 12.03 You need to complete this table by entering the Static Friction Force, and Kinetic Friction 3 1730 16.94 Force for each trial. To do this follow the 4 2233 21.87 instructions on these tabs: Procedure 1.0 5 2733 26.76 Analysis 1.0 6 Completing this table is needed in order for 7 the graph on tab "Analysis 1.1" to properly display.Analysis, Part 1: In the graph toolbar, click on the black triangle in the Statistics tool _ _, and make sure Max is turned on. Click on the Statistics icon. The value of the F maximum force should appear in the upper left. Record this value in the 1.6 0.10 static column of the Cork bottom tray table on the Data 1.0 page. Click the Part 1 - Trial 1 Statistics tool again to turn it off. 0.09 2. 1.4 Click on the Highlight Range tool and drag and reshape the highlighted box so that the region where the force is roughly constant (where velocity is 0.08 also roughly constant) is in the box. Click on the triangle in the Statistics tool box and turn Mean on. Click on the Statistics to ol. The mean force. while the 1.2 Object moves at constant speed. should appear in the middle left of the 0.07 highlighted box. Record this value in the kinetic column of the table on the Data 1.0 page. Turn the Statistics tool off. Select the Highlight box and click the Graph Delete Active Element button to turn off the Selection tool. 1.0 0.06 3. Enter the total mass of the cork plus one 500 g mass in the first column of 0.05 the Cork Bottomed Tray table under the Data 2 tab. A Force (N) 0.8 A Velocity (m/s) 4. Click on the Delete Last Run Button on lower right. 0.04 5. No w repeat Procedure 1.0 steps 2-6 and Analysis 1.0 steps 1-4 adding a 0.6 single 500 g mass each time until you have a total of 5 trials recorded in the 0.03 tables on the Data 1.0 page. Try to use about the same slow speed as before. 0.4 0.02 0.26 Use the graph at the right and the graph menu 0.01 bar tools to complete the Analysis for all 5 Trials 0.2 0.00 of Part 1. 0.00 You can cycle between displaying different Trials 0.0- by clicking the down arrow next to the Data -0.01 Summary icon in the graph tool menu. 0 1 3 4 5 6 7 8 9 10 2.14 Time (s) Applied ForceAnalysis, Part 1: I HADEX-AAN- XXX NEXT 1 . On the Friction Force vs Normal Force graph to the right, use the Curve Fit tool from the graph toolbar to best fit a straight line and determine the slope for both the static and kinetic date. First click on the static date icon in the box near the top of the graph to highlight the static data. Then click on the triangle in the Curve Fittool and select static kinetic Proportional. This forces the line to pass through the origin. W does this make sense? Set I Now click anywhere on the graph outside of the black box to get rid of the black box. 6. You can click on and drag the Proportional box if it covers your data. What is the physical meaning of the slope (A)? Repeat the process for the kinetic data. How well does your data fit straight lines? Record your information on your worksheet. 5- Effect of Contact Surface Area on Friction From the Force graphs to the right, you should see that as normal force (weight) increases Force (N) the force of friction between the object and surface increases. However, it increases at a constant rate. or rather the ratio of the friction force to normal force remains constant. This is the coefficient of friction- it remains constant. But what if we increase the surface area over 3 - which the normal force interacts between the surfaces? 1. Attach a second friction block behind the first. Use all four 500 g masses split between the two friction blocks. This is the same normal force as your heaviest trial before, it is just pushing down on twice the surface area. 2. Repeat Procedure 1 steps 2-5 with two 500 g masses in each cart. As before, determine the maximum static force and the kinetic force at constant velocity. 3. Since we already know the relationship will be a ratio giving us a constant coefficient of friction, we will only use one data point and assume a zero intercept (0.0) as our second point. Calculate the coefficient of friction for the "larger area". Remember it is a simple ratio between the two forces. Record this on your worksheet. 0 6 8 10 12 14 16 18 20 22 24 26 28 N (N) Frictional Force vs Normal ForceProcedure, Part 2: 1. Hold the cart in the starting position. Click RECORD and release the cart. Stop recording data just before or after the hanging mass touches the floor. 0.7 F 1.2 2. Look at the graph to the right. You should clearly see that the force remains constant as the mass falls 0.6 Part 2 - Trial 1 and the cart object moves. A constant force implies a constant acceleration. Looking at the velocity you 1.0 should also see the velocity increases at a constant rate. or rather the slope of the velocity data is constant. 0.5 The change of velocity over time is acceleration. 0.4 Linear 0.8 mt + b A Velocity (m/s) 3. In the graph windowselect the velocity data. Use the Highlight Range . tool to select the region of 0.3 m = 0.402 + 0.0042 0.6 velocity data that is increasing at a constant rate. Then use the Curve Fit tool to make a Linear Fit. Copy 0.2 b = -0.387 + 0.0068 0.4 the slope of this fit to the data table below as the acceleration of the system. Click the Delete Last Run button at the bottom right of the screen to delete unwanted runs. 0.1 r = 0.998 0.2 4. Repeat this procedure until you have five runs. 0.0 0.0 0.1 5. Use the mean acceleration to determine a new value for the coefficient of kinetic friction. The standard deviation of your five trials will be the uncertainty of your mean acceleration. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Record your information on your worksheet. Time (s) Average Constant Acceleration of the cart and hanging mass system with friction on the cart Use the graph above and the graph $15 0 A part 2 - Trial 1 X 0.0-+ 0.00 0.00 0.04 123 E -P & B 20 menu bar tools to complete the Analysis for all 5 Trials of Part 2. Set #2 Acceleration You can cycle between displaying (m/s=) different Trials by clicking the down arrow next to the Data Summary H 0.402 icon in the graph tool menu. N You may need to use the green W Playback menu buttons at the 4 bottom of screen. The "End" button should display all data for a Trial in 5 the graph. Video playback may not Mean 0.402 work properly. Std. Dev