Friction and The Inclined Plane Lab Report

Experiment 5 Friction and the Inclined Plane Abstract The purpose of this experiment was to measure the coefficient of friction using two different methods and determine the various factors that influence the coefficient of friction. It was found that surface area has no effect on the coefficient of friction, and the angle required for the block to slide down the incline plane decreased as the weight of the block increased. More testing must be performed to prove that the coefficient of friction decreased as the block moves up an incline at an increased angle since there are some inconsistencies with materials and measuring devices. Introduction Friction is the force between two objects that opposes the relative motion when one object slides over another object. This type of friction is better known as kinetic friction. Static friction is the friction that occurs between a stationary object and the surface on which it’s resting. Friction acts in the opposite direction of the motion and parallel to the surface which the object is sliding across. An important factor of friction is the nature of the material of the objects in contact. The area of contact between the surfaces of the objects is independent to the coefficient of friction. Theory The coefficient of friction is the ratio between the force needed to overcome friction and the normal force. The normal force acts at 90 degree angles to the plane of the surface of contact between two objects, and represents the reaction force to the objects weight. The equation for the coefficient of kinetic friction is f μk = k N Where μk is the coefficient of kinetic friction, f k is the force needed to overcome kinetic friction in newtons, and N is the normal force in newtons. The equation for the coefficient of static friction is f μs = s N Where μs is the coefficient of kinetic friction, f s is the force needed to overcome kinetic friction in newtons, and N is the normal force in newtons. The Incline Plane To determine the second method of the coefficient of friction, a machine called the incline plane will be used. Using the angle ( θ ) of the incline plane and determining the point which the block moved down the incline plane at a constant speed, the coefficient of kinetic friction ( μk ) is calculated from the ratio of the height (h) to the base (b) of the incline plane. This ratio is called the tangent of the angle θ between the incline plane and the horizontal. h μk = =tanθc b If we slide an object up a frictionless plane, the exerted force needed would have to be equal to the weight (W) times the sine of the angle that the plane makes with the horizontal ( θ ). P=W sinθ When a body slides down an inclined plane at a constant velocity, the weight component that is parallel to the surface of the incline plane, P, just balances the frictional resistance, f. The angle of uniform slip or angle of repose is the angle which the incline plane makes with the horizontal, θ . The weight component that is perpendicular to the plane is just balanced by the normal for N. At the angle of uniform slip, the coefficient of friction becomes W sinθ h = μ= b N with h being the height of the end of the plane above the table top and b the length of the base of the plane along the table top. If the object is going up an incline plane, the total force would be Fup=W sinθ+ f While if the object is going down the incline plane, the total force would be Fdown=W sinθ−f Experimental Procedure The procedure of the experiment consists of two parts. In Part A of the experiment, it was required to measure the wooden block in grams. Then place the block on the incline plane with the wide side facing down. The plane was then set to 0 degrees parallel to the table top. Weights were added slowly to the string of the pulley system until the block moved with a constant velocity once it had been pushed to overcome static friction. A 500 gram mass was added to the block and the same procedure was executed. Then an additional 500 gram black was added, for a total of 1 kilograms, and the same procedure was executed once again. The steps were then repeated using the narrow side of the block. Next the block was placed back on its wide side and angles of the incline plane were increased to 15 degrees, 30 degrees, and 45 degrees. The previous steps were repeated for each of these angles. In part B of the experiment, the wooded block was placed on its wide side. Then the incline plane angle would be slowly raised until the block moved down the incline plane at a constant velocity once it had been pushed to overcome static velocity. The height and base of the incline plane would then be recorded. These steps would then be repeated using the 500 gram and 1 kilogram masses placed on the block. Data Part A Table 1. Object Moved Weight W(dynes) Side Used Angle ( θ ) Pulling Force F(dynes) Coefficient of Friction f μk = N Block only Block + 500g Block + 1kg Block only Block + 500g Block + 1kg Table 2. Object Moved 189,336 679,336 1,169,336 189,042 679,042 1,169,042 Wide Wide Wide Narrow Narrow Narrow 0 0 0 0 0 0 49,000 166,600 279300 49,000 166,600 279,300 .259 .245 .239 .259 .245 .239 Pulling Force F(dynes) Angle ( θ ) Normal Force N=W sinθ Parallel Force W sin θ Frictional Force f = F - Wsin θ Coefficient of Friction f μk = N Block only Block only Block only Part B 98,000 137,200 172,420 15° 30° 45° 182,884.53 163,969.79 133,880.77 49,003.76 94,668.00 133,880.77 48,996.24 42,532.00 38,599.23 .268 .260 .288 Table 3. Object Moved Weight W(dynes) Angle ( θ ) h (cm) b (cm) μk = Block only Block + 500g Block + 1kg 189,336 679,336 1,169,336 17° 15° 14° 20 18 17 57.2 59.0 59.0 .3497 .3051 .2881 h b μk =tanθc .3057 .2679 .2493 Analysis COEFFICIENT OF FRICTION PULLING FORCE VS COEFFICIENT OF FRICTION 0.27 0.26 0.26 0.25 0.25 0.24 0.24 0.23 0.23 0.26 0.25 0.24 0 50,000 100,000 150,000 200,000 250,000 300,000 PULLING FORCE (DYNES) PULLING FORCE (DYNES) Figure 1. Graph of Pulling Force vs Coefficient of Friction from Table 1. Using the f , as the pulling force of the block increases, the coefficient of friction equation μk = N decreases. ANGLE VS PULLING FORCE 200,000 172,420 137,200 150,000 98,000 100,000 50,000 0 10 15 20 25 30 35 40 45 50 ANGLE (�) Figure 2. Graph of Angle vs Pulling Force from Table 2. As the angle of the incline plane increases, the pulling force required to move the block up the incline at a constant velocity increases. COEFFICIENT OF FRICTION ANGLE VS COEFFICIENT OF FRICTION 0.3 0.29 0.29 0.28 0.28 0.27 0.27 0.26 0.26 0.25 0.25 10 0.29 0.27 0.26 15 20 25 30 35 40 45 50 ANGLE (�) Figure 3. Graph of Angle vs Coefficient of Friction from Table 2. Using the equation f μk = , the trend line shows that as the angle of the incline plane increases, the N coefficient of friction increases. ANGLE (�) WEIGHT VS ANGLE 18 16 14 12 10 8 6 4 2 0 17 15 0 200,000 400,000 600,000 14 800,000 1,000,000 1,200,000 1,400,000 WEIGHT (DYNES) Figure 4. Graph of Weight vs Angle from Table 3. As the weight of the block increases, the angle required to move the block down an incline at a constant speed decreases. Discussion of Results From Part A of the experiment, the coefficient of friction from the wide side of the block was equivalent to the coefficient of friction from the narrow side of the block. Given that these values are identical, it can be concluded that the surface area of the block in contact with the surface plane has no effect on the coefficient of friction. From the data in Figure 1, there seems to be a relationship between the pulling force and the coefficient of friction. As the pulling force of the object increases, the coefficient of friction decreases. From the data in Figure 2, as the angle of the incline plane increases, the pulling force required to move the block up the incline also increases. If we compare the data of the pulling force from Figure 1 and Figure 2, it could be expected that as the angle of the incline plane increases, the coefficient of friction should decrease. If extreme values for an angle such as a 90 degree angle were to be used, the friction between the incline plane and the block would be virtually nonexistent. Therefore, we can conclude that as the angle of the incline increases, the coefficient of friction decreases. The data from Figure 3 does not agree with this statement however. It seems that there is increasing trend between the relationships of the angle of incline verses the coefficient of friction. There most likely was an error of measurement when testing at a 45 degree angle, we should expect a low value of friction for a higher angle, but instead a high value of friction was the result for a higher angle. In Part B of the experiment, the angle required for the block to slide down the incline plane decreased as the weight of the block increased. Since weight and pulling force are directly proportional, we should expect opposite trends from Figure 2 and Figure 4. Given that the block in Figure 2 was moving up the incline and the block in Figure 4 was moving down the incline, it can be concluded that the angle required for the block to slide down the incline plane decreases as the weight of the block increases. The surface of the block and the incline were not perfect, so it can be assumed that there may be some calculation and measurement errors within the experiment. For example, in Part A were it was asked to increase the angle of the incline plane, it was expected that the coefficient of friction would decrease, however the returned value for the coefficient of friction was highest at the largest angle. It is possible that during the testing at that angle, the inconsistency of the materials of the block and the incline place played a major role in returning a high coefficient of friction value. Also there was a human error when measuring the base of the apparatus in part B of the experiment. In Table 3, the base measurement of Block + 500g and Block + 1kg are equivalent. Since the angle of the incline and the height of the apparatus have different values for each block weight, the base of the apparatus should not have equivalent measurements. This error could be due to the fact the meter stick used to measure the base was only precise to the 10th of a centimeter. Conclusions From the experiments taken place in this lab, the errors lie within the quality of material the block and apparatus had, as well as the measuring devices. In order to analyze these problems more in depth, more testing must be performed using different apparatuses and block materials, as well as more precise measuring devices. Although these errors may have occurred, through consistent trends of the experiment, it can be concluded that the surface area of the block in contact with the surface plane has no effect on the coefficient of friction, and the angle required for the block to slide down the incline plane decreases as the weight of the block increases. More testing must be performed to prove that the coefficient of friction decreases as the block moves up an incline at an increased angle since the results of that test did not agree with its theory.