Friction Lab

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Arizona State University *

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122

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Mechanical Engineering

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Feb 20, 2024

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(1 point) Title of the Experiment: Friction Student’s name: Anjana Shyam Section SLN: A TA’s Name: Ayush Kumar Singh Week of the experiment: 4
Objectives: (3 points) The objective of this lab is to calculate the frictional force in different situations and determine the coefficients of static and kinetic friction from the calculated frictional force. Calculating the static and kinetic frictional forces can help determine a distinction between the two forces on objects. Static friction acts in the opposing direction on objects at rest and has a larger coefficient of friction than kinetic friction which acts in the opposing direction on objects in motion. Experimental Data (3 points): Kinetic Friction on Horizontal Plane
Kinetic Friction on Horizontal Plane Run 2:
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Kinetic friction on an inclined plane 1
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Kinetic Friction on an Inclined Plane 2:
PART 1. Static Friction 1a) Cart on the horizontal track Mass of the cart, M = 0.25 kg + 400 g = 0.65 kg Mass of the hanger, m = 0.05kg Mass on the hanger, m w = 0.07 kg Total mass of the hanger m h = 0.12 kg
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1b) Cart on an inclined plane Mass of the cart, M = 0.25 +0.4 = 0.65 kg Trial Critical angle (Θ) 1 10.3 2 10.3 3 10.3 PART 2. Kinetic friction 2a) Cart on the horizontal track Mass of the cart, M = 0.25 +0.32= 0.57 kg Mass of the hanger, m = 0.05 kg Mass on the hanger = 0.01 kg Total mass of the hanger m h = 0.06 kg Run acceleration, a 1 -0.02 m/s^2 2 0.13 m/s^2
2b) Cart on an Incline plane. Run 𝜭 acceleration, a 1 0.02 m/s^2 2 -0.32 m/s^2 Data Analysis (10 points): PART 1. Static Friction 1a) Cart on the horizontal track. The experimental value of the coefficient of the static friction µ s calculated as follows: T = s max = μ s N ? T = W h = m h g μ s F n = m h g μ s Mg = m h g μ s =m h /M μ s = 0.184615 ~ 0.18
The discrepancy between the experimentally determined µ s and its actual given value has been calculated to be: % discrepancy = |( = |(0.184-0.18)/0.18| *100 ?𝑥??𝑟𝑖???𝑡𝑎? − 𝑡ℎ??𝑟?𝑡𝑖𝑐𝑎?)/𝑡ℎ??𝑟?𝑡𝑖𝑐𝑎?| * 100 = 2.22% 1b) Cart on an Incline plane The experimental value of the coefficient of static friction µ s is calculated with equation (4) as follows: Mgsin( 𝜃 )= μ s Mgcos( 𝜃 ) μ s = tan( 𝜃 ) tan( 𝜃 ) = tan(10.3)=0.18173 μ s = 0.18173 Determine the discrepancy between the above-calculated value and the given one to compare them: 100%* ( | calc. value– expect. value | / expect. value). % discrepancy = |( ?𝑥??𝑟𝑖???𝑡𝑎? − 𝑡ℎ??𝑟?𝑡𝑖𝑐𝑎?)/𝑡ℎ??𝑟?𝑡𝑖𝑐𝑎?| * 100 (0.181-0.18)/0.18*100 = 0.56% PART 2. Kinetic friction 2a) Cart on the horizontal track For run 1 the coefficient of kinetic friction μk is calculated as follows:
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W h - f k = (M + m h ) a W h - 𝛍 k F N = (M + m h ) a m h g - 𝛍 k F N = (M + m h ) a m h g - 𝛍 k Mg = (M + m h ) a 𝛍 k = (m h g - (M + m h ) a)/Mg (0.05*9.8 -(0.62)(-0.02))/(0.57*9.8) = 0.0899 For run 2 the coefficient of kinetic friction μk is calculated as follows: 𝛍 k = (m h g - (M + m h ) a)/Mg (0.06*9.8 -(0.63)(0.13))/(0.57*9.8) = 0.0906 The average values of coefficient of kinetic friction μk from both runs is: (0.08994+0.0906)/2 = 0.09 The discrepancy between the experimental and theoretical values is: (0.09-0.09)/0.09*100 = 0% 2b) Cart on an Incline plane. For run 1 the coefficient of kinetic friction μk is calculated as follows: W h - 𝛍 k F N = (M + m h ) a m h g - 𝛍 k Mgcosθ = (M + m h ) a -Mgsinθ + 𝛍 k Mgcosθ = Ma 𝛍 k = (gsinθ+ a)/gcosθ
(9.8*sin(5) + 0.02)/9.8cos(5) = 0.0895 For run 2 the coefficient of kinetic friction μk is calculated as follows: 𝛍 k = (gsinθ+ a)/gcosθ (9.8*sin(7) + (-0.32))/9.8cos(7) = 0.0899 The average values of coefficient of kinetic friction μk from both runs is: (0.0895 + 0.0899)/2 = 0.09 The discrepancy between the experimental and theoretical values is: (0.09-0.09)/0.09 * 100 = 0% Results (3 points) Friction Force Lab Section Experimental Value Theoretical Value Discrepancy 𝞵 s 1a 0.184 0.18 2.22% 𝞵 s 1b 0.182 0.18 0.56% 𝞵 k 2a 0.09 0.09 0% 𝞵 k 2b 0.09 0.09 0%
Discussion and Conclusion (10 points): The experiment involved a mass-cart system to determine the coefficient of kinetic friction and static friction on a horizontal plane and inclined plane. The equations for the coefficients of static and kinetic friction determined by free body diagrams of the hanging mass and the cart were used to determine the experimental coefficients of kinetic and static friction and theoretical coefficients were given in the lab manual. The coefficient of static friction varies depending on the force applied to resist motion. The coefficient of static friction has a maximum value corresponding to a maximum static frictional force that the applied force in the opposite direction has to exceed in order for the object to begin moving, which is why the coefficient of static friction is always larger than the coefficient of kinetic friction. In the experiment, the coefficient of static friction for the cart on a horizontal plane was determined by the theoretical equation for which was determined to be the ratio of the hanging mass to the mass of the cart. The theoretical was calculated to be 0.184 and the theoretical coefficient of static friction was 0.18 resulting in a discrepancy of 2.22%. The coefficient of static friction on an inclined plane was determined by three trials to calculate the critical angle(the angle of the inclined plane that would allow the cart to begin motion). Using the calculated critical value 10.3° and the equation for determined by the free body diagram on the cart( ) the coefficient of static friction = 𝑡𝑎?(𝛉) was determined to be 0.182 resulting in a discrepancy of 0.56%. The coefficient of kinetic friction on a horizontal plane was calculated from the quadratic fit performed on the position time graph of the cart’s motion and the linear fit performed on the velocity time graph of the cart’s motion which was used to calculate the acceleration of the mass-cart system. The acceleration for Run 1 was -0.02 m/s^2 and the acceleration for Run 2 was 0.13 m/s^2, and the equation for 𝛍 k was the weight of the cart divided by the difference between the weight of the hanging mass and net force of the mass cart system. The average of the coefficients of kinetic friction for both runs (0.0899 and 0.0906 respectively) was 0.09, which resulted in an experimental discrepancy of 0% against the theoretical value 0.09. The accelerations for the cart on an inclined plane of 5° and 7° were 0.02 m/s^2 and -0.32 m/s^2 respectively. The equation for 𝛍 k using free body diagrams and Newton’s Second Law was (gsin( ) + acceleration of the 𝛉 cart)/gcos( ), resulting in a coefficient of 0.0895 for Run 1 and 0.0899 for Run 2. The average of 𝛉 the two coefficients was 0.09 which resulted in an experimental discrepancy of 0%. The equations of the coefficients of static and kinetic friction determined by the free body diagrams of the cart- block system and the cart on an inclined plane were confirmed by this experiment, and the fact that the coefficient of static friction is always larger than the coefficient of kinetic friction was confirmed by this experiment(0.18>0.09). In conclusion, the objectives of this experiment were achieved. The principles of friction force were confirmed through Newton’s Second Law, and the frictional force to resist motion is always greater than the frictional force when the object is already in motion.
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(Follow the general directions given in the Syllabus where it is describing how the Discussion and Conclusion section should be composed. In particular explain how the values of the coefficients of the kinetic and static friction compare to each other; what does the frictional force depend on, explain the nature of the frictional forces, also explain the reasons for discrepancies between your experimental and theoretical results).