Reading Assignment: McGinnis (2005), pp. 23-26. ARIZONA STATE UNIVERSITY KIN 335 BIOMECHANICS LAB #6: Friction Introduction: When one body moves or tends to move across the surface of another, a friction force develops. This force acts in a direction parallel to the plane of contact and opposes the motion or the tendency to move. The maximum friction that can develop between two surfaces (i.e., the limiting value of friction or maximum static friction, f max ) is dependent on two factors: the force holding the two surfaces together (often referred to as the normal force or normal reaction force, R n ) and the nature of the surfaces (material type, smoothness, etc.). Note that the area of contact between the two surfaces is not a factor that affects the friction force directly. If the overall normal force happens to increase or decrease with area of contact (keeping the nature of the surfaces constant), then friction will change, but the change is not due to contact area, per se; rather it is due to the change in the overall normal force R n. The maximum static friction force is represented mathematically by the following relationship: f max = µ s R n (1) where f max represents the maximum static friction force, µ s is the coefficient of static friction (an index representing the nature of the two surfaces in contact under static conditions), and R n is the normal force. Remember that R n reflects the net force directed perpendicular to the plane of contact between the surfaces. As we slowly increase the force trying to cause sliding between two surfaces, we know that at the instant of impending motion (that instant when sliding is just ready to begin) the actual friction force acting between the two surfaces reaches its maximum value (i.e., maximum static friction) and that it is equal in magnitude but opposite in direction to the net force attempting to produce sliding. Once sliding occurs between the surfaces, a similar relationship exists between the dynamic friction force (f d ), the coefficient of dynamic friction ( µ d ) and the normal force R n : f d = µ d R n (2) The value of µ d is usually less than the value of µ s and remains approximately constant throughout a range of velocities. Purpose: The purposes of this lab are (1) To investigate the various factors affecting frictional forces under controlled conditions and (2) to determine the coefficients of static and dynamic friction between selected footwear soles and a variety of surfaces. Procedures Part 1--Incline Plane Figure 1a is a schematic of a block sitting on an incline plane. Figure 1b is a free body diagram of the block and characterizes forces W and R acting on the block. The weight of the block (W) can be resolved into two components just as the upward reaction force from the surface (R) can be resolved into two components. These components are Figure 1a shown in Figure 1b. W represents the weight of the block. W n and W t are the components of the weight normal (i.e., perpendicular) and tangential (i.e., parallel), respectively, to the surface. R represents the surface reaction force while R n and R t are the components of R that are normal and tangential to the surface, respectively. If the block is in equilibrium (i.e., not accelerating), then the resultant force on the block is zero. Figure 1b W n W t R W R t R n F1
Hence W (down) is exactly canceled out by R (up). The components of W and R must also add up to zero all directions. W n and R n, which are equal in magnitude, but opposite in direction, each represent the magnitude of the force pushing the surfaces together. W t represents that component of the weight that is trying to cause the block to slide down the slope. R t is the actual friction force that opposes sliding. Under equilibrium conditions, W t, W n, R t, and R n are dependent on the angle of incline () since R t = Rsin, R n = Rcos, W t = Wsin, and W n = Wcos. And, at the instant sliding begins to occur: W t = R t = f max = µ s R n Hypotheses: Before taking any measurements, predict the effect of the force holding the surfaces together, the roughness of the surfaces, and the area of contact between the surfaces on f max and µ s. Base your hypotheses on the theory presented above and on the discussion presented in McGinnis (2005). [This is not to be turned in.] If we double the normal force R n without changing surface types or area (A vs. B), how will f max and µ s be affected? If we change the roughness of one surface without changing R n or area (A vs. C), how will f max and µ s be affected? If we double the area without changing the roughness of the surfaces or the normal force R n (B vs. D), how will f max and µ s be affected? Directions: Using the incline plane apparatus, slowly increase the slope of the incline plane until sliding just begins to occur. Measure the angle of the plane when sliding just begins for each of the following conditions and record the angle in Table 1 below (and on p. F5). Complete five trials for each condition, then compute and record the mean angle for each condition. [Note: These results and your calculations are to be turned in.] Condition Description Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Mean W =, area =, rough Table 1 From the mean results above, calculate the magnitude of the maximum static friction force (f max ), normal force (R n ), and the coefficient of static friction (µ s ) for each of the four conditions and write your results in Table 2 below (and on p. F5). You may use the space below for your calculations. Do you see a simpler way to calculate µ s? [Hint: sin/cos = tan.] Condition f max (N) R n (N) µ s =f max /R n Table 2 F2
Part 2--Footwear Soles and Playing Surfaces Figure 2 shows the testing apparatus for the second phase of testing for the laboratory. Several combinations of shoe surface types, playing surface types, and shoe loading will Load be studied. The general procedures are as follows: Select Load Pull a horizontal playing surface (the experimental surface ). spring scale Board Place the board so that the footwear sole is in contact with Surface Friction the surface. Place some weights on top of the board. The total weight of the board + added weights should be Figure 2 recorded. Attach the spring scale to the hook provided and exert a horizontal pull on the spring scale (see Figure 2). The pull should be slowly increased until the board just begins to slide. Note the magnitude of the force shown by the spring scale at the instant that sliding occurs. This force that is causing the block to slide is equal in magnitude to f max at the instant that sliding is initiated (Why?). Record that force in Table 3. Notice that as soon as the sole begins to slide, the force needed to maintain sliding is less than that needed to initiate sliding. Continue to pull on the scale so that sole moves with a constant velocity (why?) and record the scale reading. This second reading is equal in magnitude to the dynamic friction force.(f d ). Record this value in Table 3 as well. Experiment A Altering Normal Force: Repeat the above procedure for one or two selected footwear soles on the experimental surface. Gradually increase the normal force by adding additional weights to the top of the board. Measure the maximum static and dynamic frictional forces after each additional weight is added. Record all values in the attached preliminary table. Experiment B Playing Surfaces: Repeat the above procedure for each footwear sole on a variety of playing surfaces, both indoors and outdoors. Record all values in Table 3. Experiment C Surface Conditions: Repeat the above procedure for one or two selected footwear soles using a variety of substances to contaminate the experimental surface. Carefully clean both the footwear sole and the experimental surface after each test. Record all values in Table 3. Hypotheses: Make some predictions about the outcomes prior to completing the testing. [Note: These are not to be turned in.] How will the increased normal force affect friction? How will sole type and floor surface type affect friction? How will surface contaminants affect friction? Calculate the coefficient of static and dynamic friction (µ s and µ d ) for each condition. Use the space below to show some representative calculations and write all results in Table 3. F3
Discussion Questions. Consider each of the following questions: [Note: these are not to be turned in.] 1. Based on results from parts 1 and 2, what effect on f max was produced by a) changing the nature of the surfaces, b) changing the normal force, and c) changing the area of contact between the surfaces? Be sure to cite specific results that support your responses to parts a-c. 2. The magnitude of f max between contacting surfaces is frequently of great importance in athletic activities. Excluding footwear changes and playing surface characteristics, provide two examples in which an athlete attempts to manipulate friction (either increase or decrease) to his or her advantage and describe what the athlete does to affect friction (i.e., provide an indication whether change in the coefficient of friction or the normal reaction force is primarily responsible for the observed change). 3. Cross-country skiing offers an interesting example of friction. What alternatives does a cross-country skier have in an attempt to prevent the ski from slipping backward during the kick phase of the skiing cycle (i.e., what can the skier do to ensure that maximum static friction is sufficient to keep the ski from slipping)? NOTE: There is NO FORMAL LAB REPORT for this lab. However, you are to complete Tables 1, 2, and 3 on the following pages and turn them in before you leave the lab period. Part of your score will be participation in this lab and part will be your completed work. On your own, you should answer all the discussion questions to help you learn the material and prepare for your upcoming exam(s). F4
Name Complete each of these tables and turn in at the end of lab period. Show example calculations on the back of this page. Condition Description Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Mean W =, area =, rough Table 1 Condition f max (N) R n (N) µ s =f max /R n Table 2 Sole Surface Contamination Normal Force, R n f max (N) f d (N) µ s µ d Table 3 (continued on next page) F5
Name Sole Surface Contamination Normal Force, R n f max (N) f d (N) µ s µ d Table 3 (continued) F6