How the Lab Report Might Look (Formal Report)

Transcription

1 How the Lab Report Might Look (Formal Report) Title Page: Friction Lab Date Name Name of Partners Purpose In this laboratory we investigated the kinetic and static friction forces acting on a wood block and on other materials. In Experiment 1, we attempted to find the relationship between the friction force and the normal force on the block as is slid along a wooden plank, and we calculated the coefficient of kinetic friction between the two wooden surfaces. In Experiment 2, we tested how the surface area of contact between the block and the plank affected the friction force. In Experiment 3, we calculated the magnitude of the force of static friction on the block as it rested on an incline. We calculated the coefficient of static friction, and investigated whether this coefficient depends on the load on the block. We also calculated and compared the coefficient of static friction for various materials. Set up & Theory For experiments 1 and 2, the experimental set-up looked like this: We used a hanging mass to exert a force on the block. The hanging mass was connected to the block using string draped over a frictionless pulley. By trial and error, we found hanging masses so that the block moved along the plank at constant speed. To find an expression for the friction force, we analyzed the forces on the sliding block and the hanging mass.

2 M 1 M 2 W 1 = weight of sliding block = M 1 g (This includes any weight added to the block to increase the load.) N = normal force on block T = tension in the string f = friction force on M 1 W 2 = weight of mass 2 = M 2 g a = acceleration of the system along the string We used coordinates along the string and perpendicular to the string to analyze the forces. For motion along the string, using F net = ma, we have T f = M 1 a (for the block) W 2 T = M 2 a (for the hanging mass) Combining these we get: So: W 2 f = (M 1 + M2)a M 2 g f = (M 1 + M2)a f = M 2 g (M 1 + M2)a The friction force can be calculated from this if we also measure the block s acceleration. To simplify matters, we chose masses so that the system moved at constant speed. In that case the acceleration was zero, so we have: f = M 2 g We can use this to calculate the friction force on the block. We did this for several values of M 1 and M 2. To find the coefficient of kinetic friction, we use the basic definition of the friction coefficient: μ = Friction force/normal force find: Since the normal force on the block (N) equals the weight of the block and any added mass, we μ = M 2 g/m 1 g = M 2 /M 1

3 We will use this to calculate the coefficient of kinetic friction. We will also graph our results for the friction force vs. the normal force. The coefficient will be the slope of this graph. In Experiment 2, we performed the same procedures as above, except that we set the wood block on its narrow edge. We looked for a difference in the coefficient of friction because of the smaller area of contact between the surfaces. In experiment 3, we placed the block or other material on the wood plank while the plank was horizontal. We then slowly lifted one end of the plank until the block began to slide from rest. We then fixed the plank in place and measured its inclination angle with an inclinometer. θ Expressions for the force of static friction, the load, and the coefficients of static friction were determined as follows. From the free body diagram for the block W = weight of block = Mg (includes any weight on the block) N = normal force on block F s = static friction force on M 1 and considering the components of its weight parallel and perpendicular to the incline we have: Mgsinθ = f and Mgcosθ = N (= load) The coefficient of static friction is then: μ s = f/n = Mgsinθ/Mgcosθ = tanθ

4 Data & Analysis Experiment 1: Kinetic Friction From the data and graph below, we find that the friction force has magnitude of slightly more than ¼ the weight of the block, or of the load on the block. The coefficient of kinetic friction was roughly constant over all loads, with an average value.267 +/-.07, or a 2.6% deviation. On our graph, most points (4 out of 5) fell very close to a straight line of slope.273, very close to our average value. The very close fit of most points to the line indicates that our value for the coefficient is fairly precise. We conclude that we are justified in writing: f = μ K N. Mass of block: Weight of block: 253 grams 2.48 N Trial M 1 W 1 M 2 W 2 μ K dev. (grams) (Newtons) (grams) (Newtons) Average coefficient & average deviation : Graph: Friction force vs. Normal Force

5 1.4 Kinetic Friction Force (Newtons) Y-Values Slope of graph:.273 (μ K ) Normal Force (Newtons) Experiment 2: The Effect of Surface Area Trial M 1 W 1 M 2 W 2 μ K (grams) (Newtons) (grams) (Newtons) Average coefficient:.268

6 We found an average coefficient of.268 in this case, essentially the same value as for the wide face of the block (0.4% difference). We conclude that the force of kinetic friction does not depend on the area of contact, at least in this case. Experiment 3: Static Friction on an incline. Limiting Angle for Wood Block Weight of wood block: 2.48 N Trial Limiting Angle (deg.) μ S deviation Averages: The average maximum force of static friction = 2.48N * sin(23.2) =.977 N. This is about 43% of the load, or about 39% of the weight of the block The average coefficient of static friction = tan(23.2) =.429 with an average deviation of.028 (6.5% deviation). There is a fairly wide range of variation in our values. According to the Handbook of Chemistry & Physics, the coefficient of static friction usually ranges anywhere from 0.25 to Our value does fall within this range, but it does not appear to be very precise. Coefficient vs. Mass on block: Wood on Wood Added Mass Limiting Angle deviation in the angle (grams) (degrees) (degrees)

7 Averages: =.038 radians Average value for coefficient = tan(21.7) =.398 Here we are trying to determine whether the coefficient is the same for varying loads on the block. The limiting angles vary widely, but they seem to vary around an average value. To determine our uncertainty in the coefficient we use: Δμ S = d(tanθ)/dθ Δθ =.044 Thus our best value for the average coefficient is μ S =.398 +/-.044, or 11% deviation Coefficient for various materials on wood Material Limiting Angle (deg) μ S Wood Glass Aluminum Brass Iron Lead The metals had lower coefficients than the wood, while the glass had the greatest. Conclusions For kinetic friction, we found that the kinetic friction force varied in direct proportion to the normal force on the block. Its magnitude turned out to be about ¼ the weight of the block and load, with an average coefficient of.268 +/ For static friction, we found that the coefficient was greater than that for kinetic friction:.398 +/ This means the force of static friction was about 40% of the load on the block. We also find that the coefficient of static friction varies with the material. Metals turned out to have lower coefficients than wood, and glass had a higher coefficient.