22-Mar-2017: Modeling Friction Forces

Lab 7: Modeling Friction Forces
Kevin Nguyen
Lab Partners: Kevin Tran, Jose Rodriguez
Date of lab performed: 22-Mar-2017

Statement/ Purpose: The purpose of this lab is to teach students about modeling friction forces, including static and kinetic friction. Students performed several experiments in order to see what role friction plays on the object that is sliding over different types of surfaces.

Theory/ Introduction: This section will cover each five parts of the friction lab separately.

(1) Static Friction - In the first part of the lab, we  need to determine the coefficient of static friction between the block and the table. In order to do so, we use the equation

Coefficient of static friction = (maximum force of static friction) / (normal force)

This equation means that the maximum amount of force required to get the object to slide divided by the normal force exerted on the object will give a dimensionless ratio (since two forces are divided). To find the coefficient of static friction, we need to find the maximum force of static friction and the normal force exerted on the object. Using the apparatus that we have developed (shown in the summary section), we ran four trials to get the data for normal force (mass of the block * g) and static friction force (Mass of the hanging mass * g). After getting the values, we plotted our data points on logger pro. We plotted normal force on the x-axis and maximum force of static friction on the y-axis so that when we made a line fit of the plot, the slope gave us the coefficient of static force.

(2) Kinetic Friction - In the second part of the lab, we are required to measure the coefficient of kinetic friction between the block and the table. To do this, we use the equation

Coefficient of kinetic friction = (Force of kinetic friction) / (Normal force on the object)

This equation means that we must find and divide the force required to keep an object moving by the normal force exerted on the object by the surface it's on in order to solve for the coefficient of kinetic friction. In order to solve for the coefficient of kinetic friction, we use the apparatus (shown in the summary section) in order to measure the force of kinetic friction and normal force on the object. After running four trials, we plotted the data on the graph. We took the mean value the pulling force in the interval when the block moved horizontally at constant speed (because having acceleration will alter the results of this experiment). We plotted the average kinetic friction force we found on the y-axis and the normal force on the x-axis and made a line fit of the plot since the slope of the line gives the coefficient of kinetic friction.

(3) Static friction from a Sloped Surface - In the third part of the lab, we found the coefficient of maximum static friction between the block and the surface using a sloped surface. First, we placed the block on a horizontal surface. We slowly raised one end of the surface to tilt it until the object starts to slip. We  recorded the angle at which it slips to find the coefficient of maximum static friction. We found the coefficient of maximum static friction by setting the direction the block slips as the x-axis and made the y-axis perpendicular to the x-axis. Using the angle we recorded, we found the forces in the x and y-direction and solved for normal force and maximum static friction force. We divided the maximum static friction force by the normal force in order to find the coefficient of maximum static friction.

(4) Kinetic Friction From sliding a Block Down an Incline - This experiment is similar to the 3rd part of the lab except we placed a motion detector at the top of the incline. We raised the surface to the angle at which the the block starts slipping in order to measure its acceleration as it falls to the bottom of the surface. We used the angle of the surface and the acceleration of the block to find the coefficient of kinetic friction by setting the direction of acceleration of the block as the x-axis and set the y-axis perpendicular to the x-axis. Then, we solved for the horizontal and vertical forces to find normal force and kinetic friction force. We divided the kinetic friction force by normal force in order to find the coefficient of kinetic friction.

(5) Predicting the Acceleration of a Two-Mass System - We set up the apparatus similar to part 1 of the lab except we placed a motion sensor behind the object in order to record the acceleration for the block when enough mass is placed on the hanging mass to get the block to begin moving. We solved for the coefficient of kinetic friction by setting the direction of acceleration of the block as the x-axis and set the y-axis perpendicular to the x-axis. We solved for the horizontal and vertical forces in order to find the kinetic friction force and normal force. We then divided the kinetic friction force by normal force in order to find coefficient of kinetic friction. We then compared our experimental results to our model.

Summary/ Introduction:
For the first part of the lab, we set up the apparatus like the picture below.

For different trials, we added more mass to the block in order to see how much more mass the hanging mass needed to be in order to get the block to slip.

For the second part of the lab, we set up the apparatus like so. 

 We attached a force sensor to the end of the string so that when we pulled the block, the force sensor reads the force that is used to pull the block. For each trial, we added 200g of mass on the block and recorded how much force was required to pull the block with the added masses.

For the third part of the lab, we set up the apparatus like so.

Taped on the high edge of the board is the motion detector (that we used for part 4) and a phone that is used to measure angle of the surface.

For part 4 of the lab, we used the motion detector on top of the incline in order to measure the acceleration of the block when it falls down.

For part 5 of the lab, we set up the apparatus like so. 

The reason why we taped a notecard to the block was because it makes the block easier to detect for the motion sensor when the block accelerates away from the motion detector.

Table of Measured Data:

Part 1

Part 2

We used the mean value from the white boxes

Part 3

Angle of the slope when block began to slip: 26 degrees

Part 4

Acceleration of block at 26 degrees = 1.697 m/s^2 

Part 5

Mass of block = 0.188 kg

Mass of hanging mass = 0.09 kg

Acceleration = 0.7627 m/s^2

Calculated Results:
Part 1

The slope gives the coefficient of maximum static friction = 0.6025

Part 2

Slope of the coefficient of kinetic friction = 0.2786

Part 3

Mu static = 0.488

Part 4

Mu kinetic = 0.295

Part 5

Mu kinetic = 0.3704

Explanation of Graphs/ Analysis:

This was explained in the Theory/introduction section.

Conclusion:
The value of Mu static from part 1 is greater than the value of Mu static from part 3. This difference of result may have came up because the experiment in the first part of the lab tends to be inconsistent. This means that although the mass of the block stays the same (meaning no mass added), the block will fall with different masses added on the hanging mass. The inconsistency of the first experiment contributed to the differences of results.

The value of Mu kinetic from part 2 is closer to Mu kinetic of part 4 than part 5. The large difference between the results from part 2 and part 5 may have came about because the notecard on the block in experiment 5 may have created air resistance, preventing the block from reaching its maximum acceleration.

Although no two Mu static or kinetic values are the same, one consistency that happened was that the results of parts 1 and 3 (Mu static) were both greater than the the results from parts 2, 4, and 5 (Mu Kinetic), making these experiment and labs valid.