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. 

15-Mar-2017: Lab 5 Trajectories

Lab 5: Trajectories
Kevin Nguyen
Lab Partners: Kevin Tran, Jose Rodriguez
Date of lab performed: 15-March-2017

Purpose: The purpose of this experiment was to help us understand projectile motion and guide us to use calculations to predict the point where the ball will land.

Theory/ Introduction: We set up the apparatus so that we could find the velocity of the ball when it left the v-channel. We first found the position where the ball landed so that we could place the paper and carbon paper on its impact point and measure its position. We launched the ball 5 times in order to see if the ball landed on the same spot. We measured the height of the ball when it left the v-channel and the distance in the horizontal direction the ball traveled. We used our measurement of height and distance and found the launch speed of the ball. We also took to account the unpropagated uncertainty of our measurement tools (metric ruler has an uncertainty of 0.01 m).

Next, we attached an inclined board at the edge of the table and measured the angle at which the board is placed. This angle is used to find the x and y-component of the diagonal distance the ball hits the board. We then launched the ball so we know where the impact point is on the board. After attaching paper and carbon paper on the impact point of the board, we launched the ball 5 times to see if the ball lands on the same spot. We measured the diagonal distance the ball landed from the launch point. The reason why we needed this distance is because we compared the measured distance to the predicted distance that we calculated using kinematics.

Then, using the horizontal and vertical distance we calculated using the angle and the theoretical diagonal distance, we solved for the propagated uncertainty for the theoretical diagonal distance.

Summary:
First, we set up the apparatus like this.

We set a plumb bob in order to identify x=0m as well as determining the height.

After setting up the apparatus, we placed the ball on top of the inclined ramp (and made sure to put the ball on a place that can be easily identified as the starting point) and had a test run to see where to place the paper and carbon paper.

After we placed the paper and carbon paper, we ran the test five times. After the 5th trial, we lifted the carbon paper to measure the distance. 

After finishing our measurements, we attached a metal board to the edge of the lab table. We placed a weight at the end of the inclined board in order to keep it from moving. We then measured the angle the board is placed in.

We ran a test trial first to see the impact point of the ball. Once we attached the paper and carbon paper over the carbon paper, we ran 5 trials. After the 5th trial, we lifted the carbon paper to measure the distance from the v-channel (where the ball left) to the impact point.

Measured Data:

Distance (in the horizontal and vertical direction) the ball traveled

Height: 0.9430 plus or minus 0.0001 meters

Distance (horizontal direction): 0.9110 plus or minus 0.0001 meters

Diagonal distance the ball traveled (distance from end of V-channel to impact point on board)

=0.481 plus or minus 0.001 meters

Alpha = 24.6 plus or minus 0.1 degrees

Calculated Results:

Velocity of the ball when it leaves the V-channel

Calculated value of theoretical diagonal distance

Calculated propagated uncertainty of the theoretical diagonal distance

Explanation:
This is covered in the theory/ introduction section of the blog.

Conclusions: Although the theoretical diagonal distance was very similar to the experimental diagonal distance, they were not within their respective propagated uncertainty ranges. This error may have resulted from the inaccuracy of the angle measuring tool. When we used our phones to measure our angle, we gotten the different value from the value given by the angle measurement tool. Although we decided on using the angle given by the angle measurement tool, the phone may have given a more accurate value, resulting in error of results.

13-Mar-2017: Modeling the fall of an object falling with air resistance

Lab 4: Modeling the fall of an object falling with air resistance

Name: Kevin Nguyen

Lab Partners: Jose Rodriguez, Kevin Tran

Date of lab performed: 13 March 2017

Statement/ purpose: The purpose of this lab was to determine the relationship between air resistance force and speed and to create a model on excel that will be able to determine the terminal velocity of the falling objects that matches our experimental data. 

Theory/ Introduction: In the first part of the lab, we assumed that the air resistance force on an object can be modeled by the equation below.

Air resistance force = kv^n

We used this equation because this equation takes into account the physical characteristics of the falling object when air resistance force is acting on the object. In this equation, "k" is the term that takes into account the shape, material, and area of the object. "n" is the slope of the function and "v" is the velocity of the object. In this case, since we don't know "k" and "n" and "v" is the independent variable, we measured the unknown variables by first video capturing the objects falling inside the design building. In this experiment, we captured 5 instances of the object falling to the ground. 

For each instance, the amount of coffee filters dropped increased by one. So, for example, on drop 1, only 1 coffee filter dropped. On drop 2, 2 coffee filters stacked together dropped. We recorded these videos in order to find "k" and "n". We did this by recording the terminal velocities for each drop. To find the terminal velocity, we set a position vs time graph (where position is in the y-direction and time is in the x-direction) and found the slope of the line fit of the last few points. After finding the terminal velocities, we plotted these points on logger pro and made a power line fit, where terminal velocity is plotted in the x-direction and weight of the coffee filter (m*g) is plotted in the y-direction. The values of "k" and "n" is given from the equation of the power line fit. 

In the second part of the lab, we used the mathematical model of air resistance force used in part 1     (Air resistance force = kv^n) in order to predict the terminal velocity of the falling coffee filters. In order to do so, we need several values. These values are ∆t, the change in time, "m", the mass of the coffee filter(s) dropped, "g", gravity, "k" and "n", the variables defined in part 1, ∆v, the change in velocity, v, the velocity, "a", the acceleration of the falling coffee filters, ∆x, the change in position, and x, the position of the object from the release point. These values are used to make a model on excel in order to predict the terminal velocity of the falling filters, which is determined by the variable "v" and "a", since once acceleration is 0 m/s^2, the velocity will be constant. 

Summary: For part 1 of the lab, we went to the design building in order to record the coffee filters falling from their release point. 

After video capturing the drops, we found the terminal velocity by plotting the position of the falling coffee filter each 3rd of a frame (not pictured). After plotting the points, we made a line model of the last portion of the plot and used its slope to find the terminal velocity. The reason why we made the line model at the end of the graph was because we needed the maximum velocity of the object (maximum velocity = no more acceleration). 

Drop 1

Drop 2

Drop 3

Drop 4

Drop 5

After finding the terminal velocities of each drop, we made another plot on logger pro. We plugged in the values for terminal velocity (before anything, we used the absolute value of these values since the power model can not use negative values) and weight of the coffee filters and got this.

Power model

For part two of the lab, we set up our excel spread sheet similar to this model.

We plugged in our values in the relevant boxes.

After plugging in the necessary values, we set up the variables (t, ∆v, v, etc...) in the spreadsheet so they have the following equations. 

After putting in the following equations into their respective boxes, we "filled" the information down in order to get our answer for terminal velocity.

The highlighted portion represents the terminal velocity of 1 falling coffee filter at ∆t = 0.01 seconds.

We also found the terminal velocities of the 2nd, 3rd, 4th, and 5th drops by changing the mass so it matched their respective drops.

Terminal velocity for the second drop

Terminal velocity for the third drop

Terminal Velocity for the 4th drop

Terminal Velocity for the 5th drop

Table of Recorded Data:

Data collected for the First part

Data needed for the Second Part

Calculated Results:

Calculated "k" and "n" for part 1

Shown below is the calculated terminal velocities (highlighted yellow) for drops 1, 2, 3, 4, and 5 for part 2 of the lab.

Predicted terminal velocity for Drop 1 is 1.50 m/s

Predicted terminal velocity for Drop 2 is 1.97 m/s

Predicted terminal velocity for Drop 3 is 2.31 m/s

Predicted terminal velocity for Drop 4 is 2.58 m/s

Predicted terminal velocity for Drop 5 is 2.82 m/s

Explanation of graphs:

This is explained in Theory/ introduction section.

Conclusion:

The velocities that we recorded from the video capture were slightly different from the values that we predicted using the spread sheet. For drop 1, the velocity prediction had a 1.3% error from the terminal velocity recorded. For drop 2, the velocity prediction had a 2% error from the terminal velocity recorded. For drop 3, the velocity prediction had a 2.5% error from the terminal velocity recorded. For drop 4, the velocity prediction had a 3.7% error from the terminal velocity recorded. For drop 5, the velocity prediction had a 2.7% error from the terminal velocity recorded.

The reason why these predicted values may have had a percent error ranging from 1.3% to 3.7% was because during the video capture, we set the frames per dot to be 3 frames. If it was a smaller value, it may have lowered the percent error of the predicted values since the recorded values may be more accurate.

08-March-2017: Non-Constant acceleration problem/ Activity

Title of Lab: Non-constant acceleration problem/ Activity
Kevin Nguyen
Lab Partners: Kevin Tran, Jose Rodriguez
Date of Lab performed: 08-March-2017

Purpose: The point of this lab is to learn how to solve a physics problem by using excel spread sheets.

Theory/ Introduction: In this lab, we were presented with a problem pictured below.

To solve for the distance the elephant travels before coming to rest, we could either take the analytical approach (which takes a massive amount of time) or we could take the numerical (arguably faster) approach. In the numerical case, we need several variables in order to create a spreadsheet. We used total mass of elephant plus the rocket on it, which was 6500 kg, the initial velocity of the elephant, which was 25 m/s, the burn rate of the rocket, which was 20 kg/s, the total force exerted on the elephant (in the opposite direction) initially, which was 8000N, and the change in time, which we can arbitrarily change, in order to solve for the position of the elephant using values of acceleration, average acceleration, change in velocity, average velocity and change in position. From Newton's second law, we used an acceleration function a(t) = net force / (total mass minus burn rate multiplied by time) in order to solve for the variables needed to find the position of the elephant.

Summary
At first, we set up the spreadsheet so it can look like the picture below.

Then we plugged in the values corresponding to their boxes. We then entered the function into the box below "a" and used the value given to solve for the other variables such as a_avg, ∆v, v, v_avg, ∆x, and x. After we finished setting up the values, we "filled" the information down. We changed the value of ∆t to 1 second, 0.1 second, and 0.05 second, showing the values below.

∆t = 1 second

∆t = 0.1 second

∆t = 0.05 second

To solve for the position of the elephant, we filled the information down and looked where velocity approximately equaled zero to find where did the elephant ended up.

The highlighted portion shows the position of the elephant when velocity equals zero.

After finding where velocity approximately equaled zero, we found that at t = 19.65 to 19.70 seconds, the position of the elephant was at approximately 248.70 meters.

Table of measured data:

Table of calculated results:

Calculated results for ∆t = 1 second

Explanation of analysis:

Addressed in the theory/ introduction section.

Conclusion:
Using the numerical approach actually made this physics problem much easier and faster than if we were to solve this problem using the analytical approach. We also got the same answer as the answer given in the lab manual.

Questions
1. We found our answer and compared the result we got to the answer in the lab. We confirmed that the answer we got matched the answer in the lab, confirming that the numerical approach also works in finding the answer to the problem.
2. We knew when the time interval was small enough when only the thousandths digit of the x value was changing each ∆t.
3.

Using the numerical approach, the answer that we got was 164.04 meters.