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COEFFICIENT OF FRICTION
Introduction Friction is the force that resists the sliding of one surface against another. The coefficient of kinetic friction is defined as the ratio of the frictional force to the normal force while the object is sliding,
μk =
Fk
Fn
The coefficient of static friction is defined as the ratio of the maximum frictional force to the normal force before motion,
μs =
Fs ,max
Fn
In this lab you will explore some of the properties of friction and use different methods to measure the coefficient of friction. Equipment Smart cart, hook, mass set, string, aluminum track, meter stick, wooden block. Preliminary questions a. How does μk and μs usually compare in magnitude? b. How do you expect μk to depend on the size of the contact area between the two sliding surfaces? c. How do you expect the coefficient of friction to depend on the normal force? For example, do you expect μk to increase, decrease, or remain constant as the normal force increases?
PART 1 – Static vs Kinetic Friction Open the file: “ v-t_F-t.cap ” contained in the T:\Capstone folder, which display graphs of the velocity vs time and force vs time. Procedure Step 1. Place the large felt side of the block on the table. Step 2. Place at least 500 g of mass on the block. Step 3. Place a hook on cart. Attach the force sensor to the block with a string. Step 4. Before each measurement, press record. Step 5. Looking at the force vs time graph as you very gradually increase the tension in the string. Try to achieve the largest possible force before the block starts sliding (this may take a few tries). Step 6. Keep pulling the block and, by looking at the velocity vs time graph, try to make it move at a constant speed,
1. The maximum force required to start the block moving, is larger than, smaller than, or the same as the force required to keep it moving at constant speed? 2. Do your results support your response to the preliminary question a? Step 7. Place the block with the small area felt side down. Step 8. Place the same mass on the block as in the previous. Step 9. Measure the force required to keep the block moving at constant speed and compare with what you got with the large felt side down. 3. Are your results consistent with your answer to question b?
8. How do your measurements compare with your answer to the preliminary question c? 9. Calculate the mean value of the coefficient of kinetic friction Mean μ¯ k 10. Calculate the standard deviation and the error. You can use the formula below or excel or your calculator or any online resources. σT =
N − 1
⋅∑ i = 1 N di^2
1 2 = _____ σ (^) average = σT √ N
= _____
11. Record the final answer for your calculation of the coefficient of kinetic friction. μ k = μ¯ k ± σaverage = _______ ±_______ 12. In a plot of μk vs Fn ( Fn on the horizontal axis) which kind of curve would suggest that μk is independent of the normal force? Use Excel to plot Fk as a function of Fn and fit the data to a straight line to determine the slope. Plot Step 1. Open Excel, on column A insert the value of Fn and on column B insert Fk (Excel plots the first column on the x -axis and the second column on the y -axis). Step 2. Using left-click on the mouse, select all your data. Then click the tab Insert, Scatter, (Scatter with only Markers). Step 3. Then right click on one of the point displayed on the graph, Add Trendline …, choose Trend/Regression Type as Linear and mark Display Equation on chart. Click close. Step 4. The linear fit equation should appear on the plot, if not try again to follow these steps or ask for help to the TA. You will also have to use Excel for plots on following labs, so take a chance to learn how to use it. 13. What is the numerical value of the slope and what does it represent? Label your axes in Excel and include an appropriate plot title. Print the Excel graph.
PART 3 – Incline Plane and Forces of Friction. Assume that friction can be neglected. Suppose you shove a cart so that it rolls up an incline plane, and then it comes back down.
14. Draw two free body diagrams: as the cart moves up and as it moves back down. Indicate on the diagrams the net force acting on the cart. 15. Compare the magnitudes of the net forces. Should they be the same? If not, which one is greater? 16. Sketch the expected position and velocity of the cart as a function of time. Assume the coordinate system has origin located at the bottom of the incline; the x axis is parallel to the incline and points upward the incline plane. Now assume that friction is present. Suppose you shove a cart so that it rolls up an incline plane, and then it comes back down. 17. Draw two free body diagrams: as the cart moves up and as it moves back down. Indicate on the diagrams also the net force acting on the cart. 18. Compare the magnitudes of the net forces. Should they be the same? If not, which one is greater? 19. Sketch the expected position and velocity as a function of time. 20. Are your predicted curves the same with and without friction? Explain.
PART 4 - Incline Plane and Coefficients of Friction. Procedure Step 1. Place the block on the track (large felt side down). Step 2. Very gradually, raise one end of the track until the block begins to slide.
29. Consider the block on the incline plane. At first the block is at rest, if you increase the angle θ the block will start to fall. Draw on the two figures below the free diagrams for the block when it is at rest and when is in motion. (a) block at rest (b) block in motion For the case of static friction θ = θs 30. Write the Newton 2nd^ law relative to the x- axis. 31. Write the Newton 2nd^ law relative to the y- axis 32. Divide the two equations, which expression do you find for μs as a function of θs?
μs =
33. Determine the minimum angle θs at which the block begins to slide: measure the elevation of one end of the track, the length of the track and use trigonometry.
θs = _____
34. Calculate the coefficient of static frictions μs = _____
For the case of kinetic friction a similar calculation can be done if the track angle is adjusted so that the block slides down at a constant speed, in that case we find μk = tan( θk )
35. Determine the minimum angle θk necessary for the wooden block to slide down the incline: measure the elevation of one end of the track, the length of the track and use trigonometry.
θk = _____
36. Calculate the coefficient of kinetic frictions μk = _____
37. How do your values of μk compare with those found in PART 1 and PART 2 (the % difference)? Summary Questions 38. In part 1, you were told to pull the cart at constant speed to measure Fk and μk. Why is this important? What effect would it have on your results if the block was speeding up? 39. Do Fk and μk depend on how fast the block moves? 40. Indicate the errors present that had a large effect on the measurements conducted during this lab Human errors: Instruments errors: Others source of errors:
