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Sam Poole Ava Ridge, partner Friction Lab Physics 101 30 February 1980 For this lab, the coefficient of static friction was determined by two methods and the results compared to determine if there was a statistically significant difference between them. This is a limited test of whether or not the friction relation f = μn is correct for varying normal force n. In the second part, pulling horizontally with varying mass, we also check one experimenter’s results against another to see what kind of variation exists between different investigators with the same technique. Method A : Inclined plane method For this method, an inclined plane is tilted until the block starts to move and the angle is recorded. The force balance is then used to determine the coefficient from the data. The force diagram is: The resolution of the weight vector gives: Balancing forces normal to the ramp gives n – w cos() = 0 (no acceleration) so n = w cos() Just before the block moves on the tilted ramp, the static friction has reached its maximum value, s n, and the block is not yet accelerating. Balancing the forces along the ramp gives w sin() – fs = 0 (not yet accelerating) which gives w sin() = fs = s n substituting for n from the vertical force balance, w sin() = s w cos() sin() = s cos() s = sin()/cos() s = tan() Method A data and results: angle 30.0 0.577 31.0 0.601 30.4 0.587 29.7 0.570 30.2 0.582 avg 0.583 std dev. 0.011 Method B : Friction and Normal Force. In method B, each lab partner measured the force needed to just begin moving the block with various added masses on the horizontal ramp. A best fit line to each series of data was then used to determine the coefficient of friction from the data. The force diagram is: Balancing forces gives: Vertical : n–w=0 n=w Horizontal pull – f = 0 pull = f Using the formula for maximum static friction f = s n and substituting gives pull = s n Substituting for n from the vertical force balance gives pull = s w This means that plotting the pull needed to just move the block versus the weight of the block gives a line with slope s . Method B data and results: weight of block (N) 1.23 11 20.82 30.61 40.41 Pull ( partner1) (N) 0.71 6.2 11.78 17.3 22.9 Pull ( partner2) (N) 0.81 7.03 13.41 19.58 25.95 Graphing the friction force (= pull) versus the weight (= normal force) gives: static friction 30 friction (N) 25 20 15 10 y = 0.5663x - 0.0089 Pull 1 y = 0.6413x + 0.0076 Pull 2 5 0 0 10 20 30 normal force (N) 40 50 The slopes give values of 0.57 and 0.64 for the coefficient of static friction. Only 2 digits are kept due to the force measurements being steady in the second digit, the third digit varying throughout the pull. Comparison of results: The results for the different methods are summarized in the table below: method A B avg B partner1 B partner2 std 0.583 0.605 0.57 0.64 0.01144 0.049497 Results from methods A and B seem quite different. Trying to get a reproducible force for part B was difficult and may contribute to such a difference. This is also consistent with the fact that the results in method B for the two partners bracket the result for part A. The percent difference between the results for methods A and B is calculated below. Since neither is a theoretical or accepted value, the difference is compared to the average of the two experimental values. 0.605 – 0.583 x 100% = 0.93% ½ (0.605 + 0.583) The small percent difference indicates that the apparent difference between the results of the two methods is obvious because of precision in the results, not large differences in the values. Comparing the results from methods A and B using a t test gives the following information, calculated from the website http://www.bio.miami.edu/rob/Students_t.html T score = 1.0548 Method A P value = 0.170 Method B P value = 0.34 The T score indicates that the two values are different by a bit more than 1 standard deviation. This means that there is only a 65% chance of them being different, not enough to say that the difference is significant. The results for partners 1 and 2 in method B differ by about 1.5 standard deviations. This is likely to be statistically significant. If so, this would indicate that the two experimenters were not consistent with each other. Other questions: To measure the coefficient of kinetic friction, method B could be used, but now pulling to keep the block moving at a constant velocity. The same data analysis using a linear fit will give the coefficient of kinetic friction.