Lab 6; Friction (Report on Part 3 & 4 for Sandpaper)

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Dec 6, 2023

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Lab 02: “Friction”; Part 3 and 4 for Sandpaper Date Performed: Oct 21, 2023 Date Submitted: Oct 24, 2023 Student: Kyra Pell (Ann) USM ID: w10132479 TA: Shwe Oo

Purpose Friction is defined as the force resisting the relative motion of objects sliding against each other, whether they be solid surfaces, fluid layers, or material elements. The purpose of this experiment was to determine the forces and coefficients of static and kinetic friction of a sandpaper friction block against a wooden board, as well as calculate the maximum angle of repose of the sandpaper block. The measured physical quantities of this experiment are the mass of the block (g), the kinetic frictional forces F k (N), the static frictional forces F s (N) and finally the angles at which the sandpaper friction block starts to slide down a wooded board. The physical quantities that are calculated are the total weight of the block and hanging weight (N) (also known as the normal force), the average static and kinetic frictional forces of three trials, their corresponding coefficients ( μ s ) and ( μ k ), the maximum angle of repose, the average angle of repose regarding three trials, and finally, the precent difference (%) of said angle. The physical principles used during this experiment are the properties of friction and frictional forces. Introduction As previously stated, the purpose of this experiment was to determine the forces and coefficients of static and kinetic friction of a sandpaper friction block and its maximum angle of repose. To do this I first needed to measure the mass (g) of the sandpaper friction block, add the mass of a 100 (g) hanging weight, then convert the total to kilograms (see equation 1) and calculate its weight (see equation 2). I then set the sandpaper block flat on a wooden board. After this, I set the 100 (g) hanging weight in the center of the block and connected the block to a spring scale set at zero. I then measured, in newtons, the kinetic friction force and the static friction force three times each. After words I took these values and then proceeded to calculate the corresponding avg forces (see equation 3). Using these values, I then calculated the correlating coefficients (see equations 4 & 5). Then using the static friction coefficient, I calculated the maximum angle of repose for the sandpaper friction block (see equation 6). Then after removing the weight, and placing the block in the same starting position, I lifted the wooden board until the friction block just started to slide, and measured the angle using a protractor, a string, and a small hanging weight. I repeated this step three times. Using these measured angles, I then calculated the avg angle of repose (see equation 3). Finally, I calculated the percent difference between the predicted maximum angle of repose and the average measured maximum angle (see equation 7). The physical assumptions of this experiment are that I made accurate measurements with my scale, and protractor. Also, that I made accurate calculations. Equation 5 Equation 6 Equation 1 Equation 2 Equation 4 Equation 7 Equation 3

A force that acts parallel to the surface 1 Friction A force that acts perpendicular to the surface 2 Normal A force that increases as applied force increases up to some maximum value 3 Static friction Magnitude depends on the interacting materials 4 Coefficient of friction A force that is constant regardless of the applied force 5 Kinetic friction Data, Calculations, and Questions Physics 111L Friction Final Report Student Name Kyra Pell Student ID 291291 Lesson Friction Institution University of Southern Mississippi Session Fall 2023 Course Physics 111L Instructor Sidney Gautrau Test Your Knowledge Match each term to the best description.

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1 N 2 f 4 mg sinθ 3 mg cosθ 1 2 4 3 Static friction μ k Kinetic friction μ s Label the force arrows on the free-body diagram. Label the force versus time graph.

Categorize each statement as True or False. True False 1 2 Static friction is caused by molecular Kinetic friction is caused by molecular bonds. bonds. Friction between objects increases Friction does not always increase the thermal energy of both objects. temperature of interacting objects. Increasing in the normal force between Increasing the surface area of two objects increases the friction force interaction between two objects between them. increases the friction force between them. Exploration The force of friction always acts parallel to the surface of interaction. True False When the objects are moving relative to one another, the speed of the moving object affects the magnitude of what is known as the kinetic friction force. True False The force of static friction is always equal to the coeﬃcient of static friction multiplied by the normal force. True False

The force of kinetic friction for a particular pair of interacting objects is always the force of static friction. less than greater than equal to None of the above Static friction is caused by molecular and kinetic friction is caused by molecular . attraction; bonds attraction; repulsion bonds; attraction None of the above The coeﬃcient of static friction is related to the maximum angle of repose by . μ s =sin θ ma x μ s =tan θ max μ s = θ max None of the above The coeﬃcient of kinetic friction is found from the equation: . μ k = F app F N F N μ k = z app μ k = F app × F N None of the above

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rce up to some maximum value. With this said, once an object starts to slide along the surface of another object, the friction force between the objects be e nature of the interaction), the normal force (which is related to the weight of the object and the angle of the surface) and the properties of the surfaces orce needed to move the block in either position is the same as well. Since we know that surface area has no direct effect on the forces of friction, this le e greater the static force needed to indicate movement. This in turn, effects the static friction coefficient, meaning that the less surface area between the The force of friction is always represented as a horizontal arrow in a free- body diagram. True False Exercise 1 Explain the difference between static friction and kinetic friction. Discuss the relationship between friction, normal force, and surface area. Compare the static and kinetic friction forces and coeﬃcients determined for the ﬂat wooden friction block and the wooden friction block on its side that were recorded in Data Table 1. What was the relationship of surface area to the force and coeﬃcient of friction

d the greater the kinetic frictional force needed to continue movement between the objects. This has led me to believe that the static and the kinetic forc of the magnitude of a frictional force divided by the normal force’s magnitude. Meaning that the greater the normal force, the greater the static friction c This is most likely due to human error on my part, I may have misread my spring scale. raphs, The Static frictional coefficient was always greater than its corresponding kinetic frictional coefficient. In most cases, the coefficient of static frictio a higher force to overcome the interlocking irregularities. Once the object is in motion, the surfaces slide more smoothly, resulting in a lower resistance to inetic coefficient is the more accurate. This is because I made my graph using the excel software. In many cases, computers with good software are more between the objects? Compare the forces of static and kinetic friction and the coeﬃcients of static and kinetic friction that were determined for the ﬂat wooden friction block as the weight (and normal force) of the block changed, as recorded in Data Table 2. What was the relationship between the normal force and the forces and coeﬃcients of friction between the two Materials? Do your experimental results support the background statement that the coeﬃcient of kinetic friction is always smaller than the coeﬃcient of static friction for the same two materials? Explain your answer by referencing your data and graphs. Compare the average coeﬃcients of static and kinetic friction found for the wooden friction block to the coeﬃcient of static and kinetic friction found from the graph. Do the values match? If not, which method provides a more accurate calculation of the actual coeﬃcient? Explain your choice.

her surface than all of the materials leading to the highest coefficients. Note that smooth surfaces tend to have fewer points of contact on a molecular level than rough surfaces. Molecular bonds form where the surfaces do to happens with a constant velocity. During the scenario the kinetic frictional force can be directly measured under the conditions where it is in equilibrium se, it is necessary to measure the applied force just before the block begins to move. This allows us to determine the maximum force of static friction tha tion opposes motion and manifests in various ways, such as static friction that keeps an object at rest, kinetic friction that acts on moving objects, rolling Which material among the four you tested has the largest coeﬃcients of static and kinetic friction? Which material has the smallest? Does this make sense? Why or why not? When attempting to determine the coeﬃcient of kinetic friction, why is it necessary to move the block with constant velocity? When attempting to determine the coeﬃcient of static friction, why is it necessary to measure the applied force just before the block moves? Are these two scenarios (constant velocity and almost in motion) the only scenarios when friction is present? Explain your answer.

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Mass (g) Weight (N) F k Trial 1(N) F k Trial 2 (N) F k Trial 3 (N) Average F k (N) μ k Flat 5.18 1.40 1.30 1.35 1.35 0.26 Side 5.18 1.30 1.40 1.35 1.35 0.26 Weight (N) F s Trial 1(N) F s Trial 2(N) F s Trial 3(N) Average Fs (N) μ s Flat 5.18 1.90 1.80 1.85 1.85 0.36 Side 5.18 2.00 2.10 2.00 2.03 0.39 Data Table 1: Friction and Surface Area Data Table 2: Friction and Normal Force Weight (N) F k Trial 1 (N) F k Trial 2 (N) F k Trial 3 (N) Average F k (N) μ k calc. μ k calc. avg. μ k graph 5.18 1.40 1.30 1.35 1.35 0.26 0.24 0.28 1.26 0.30 0.35 0.30 0.32 0.25 0.77 0.20 0.15 0.15 0.17 0.22 Weight (N) F s Trial 1 (N) F s Trial 2 (N) F s Trial 3 (N) Average F s (N) μ s calc. μ s calc. avg. μ s graph 5.18 1.90 1.80 1.85 1.85 0.36 0.36 0.36 1.26 0.50 0.40 0.50 0.47 0.37 0.77 0.30 0.25 0.25 0.27 0.35 28.6

Graph 1: Static Friction Graph 2: Kinetic Friction Data Table 3: Friction and Surface Material Material Weight (N) F k Trial 1 (N) F k Trial 2 (N) F k Trial 3 (N) Average F k (N) μ k

Wood 1.26 0.30 0.35 0.30 0.32 0.25 Glass 1.53 0.15 0.15 0.10 0.13 0.08 Sandpaper 1.53 0.70 0.75 0.70 0.72 0.47 Paper 1.27 0.30 0.25 0.30 0.28 0.22 Weight (N) F s Trial 1 (N) F s Trial 2 (N) F s Trial 3 (N) Average F s (N) μ s Wood 1.26 0.50 0.40 0.50 0.47 0.37 Glass 1.53 0.25 0.20 0.20 0.22 0.14 Sandpaper 1.53 0.90 0.80 0.85 0.85 0.56 Paper 1.27 0.50 0.50 0.55 0.52 0.41 Data Table 4: Maximum Angle of Repose material θ (°) calc. θ (°) Trial 1 θ (°) Trial 2 θ (°) Trial 3 θ (°) Average % Difference Wood 20.3 30.0 27.0 29.0 28.7 8.6 Glass 8.0 13.0 15.0 13.0 13.7 13.1 Sandpaper 29.2 30.0 30.0 34.0 31.3 1.7 Paper 22.3 25.0 26.0 24.0 25.0 2.9 Competency Review The friction force is proportional to the normal force on an object. inversely directly quadratically None of the above The inﬂuences the magnitude of the static friction force. normal force

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coefficient of static friction applied force All of the above The coeﬃcient of static friction for a certain pair of materials is greater than the coeﬃcient of kinetic friction for the same pair of materials. True False Smooth surfaces have more points of contact on a molecular level than rough surfaces. True False The friction force as represented in a free-body diagram always has the same length as the applied force. True False A box of tools rests in the back of a pickup truck. The truck accelerates to the north and the box remains at rest in the truck. The direction of the friction force on the box of tools is . north south zero None of the Above A block of mass 10 kg rests on an incline of 20°. The magnitude of the friction force on the block is N.

98 92 34 None of the above If a go-kart's specifications indicate it can climb a slope of 35°, the coeﬃcient of static friction between the go-kart tires and the ramp is . 0.8 0.6 0.7 None of the above A block of mass 10 kg is pulled by a 30 N force at a constant velocity along a ﬂat surface. The coeﬃcient of kinetic friction between the block and the surface . 0.31 0.47 0.33 None of the above Extension Questions In the sport of curling, large smooth stones are slid across an ice court to land on a target. Sometimes the stones need to move a bit

erefore increasing the friction. Another method would be to increase the mass of the stone or to increase its weight. A way to decrease the kinetic friction farther across the ice and other times players want the stones to stop a bit sooner. Suggest a way to increase the kinetic friction between the stone and the ice so that the stone stops more quickly. Next, suggest a way to decrease the kinetic friction between the stone and the ice so that the stone slides farther along the ice before coming to a stop. Me and my lab project

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My Calculations

Results During my experiment I had to calculate the total measured mass of the sandpaper friction block, 56.08 (g) and a 100 (g) hanging weight in (kg). This led me to a result of 0.15608 (kg). Using this value and the acceleration of gravity, 9.8 ( m s 2 ), I then calculated the corresponding weight of 1.53 (N). I then proceeded to measure the kinetic frictional forces and the static frictional forces of three trials. Resulting in the kinetic frictional forces of 0.70 F k (N), 0.75 F k (N) and 0.70 F k (N), along with the static frictional forces of 0.90 F s (N), 0.80 F s (N), and 0.85 F s (N). Using these values, I then calculated the correlating avg force values, leading me to the result of 0.72 F k (N) and 0.85 F s (N). With these average values and the correlating total weight value, I then calculated the coefficients of the static and kinetic friction, with the results being 0.47 ( μ k ), and 0.56 ( μ s ) respectfully. After this, using the static friction coefficient value I calculated the maximum angle of repose giving me the value of 29.2 degrees. I then measured the angle at which the sandpaper friction block started to slide down the board, three times, giving the resulting values of 30.0 degrees, 30.0 degrees, and 34.0 degrees respectfully. Using these values, I calculated the avg maximum angle of repose giving me the value of 31.3 degrees. Finally, I calculated the precent difference of the predicted maximum angle of repose value and the calculated avg maximum angle of repose, resulting in the value of 1.7 %. Given the precent difference value is less than 5% I can conclude that this experiment is valid. Conclusion Since this exercise is considered valid, I can assume that my previous assumptions are correct. These assumptions being that I made accurate measurements with my scale and protractor and that I made accurate calculations. I can also assume that I used the understood properties of friction and frictional forces. As the data shows, my static force and coefficients are higher than my kinetic ones. Also, while my predicted maximum angle of repose value, found using my static coefficient, was not exact, it was close enough to be considered valid. Thus, once again making this experiment valid.