September 25, 2014- Modeling Friction

Purpose: The Purpose of this lab is to find a model for static friction though an experiment produced in class. This Will be done by pulling a mass up until the point that the friction breaks and the mass starts to move.
Apparatus: A Pulley, a string, a block of wood(mass), a cup, and water. I know it may sound like an off set up but this is how we set it up to record the data we were looking for.

How This Was Used: First we weighed the block to determine the mass of the block. Next we tied the mass to a string, revolved it around the pulley, and tied the other end to the cup. After we inserted water into the cup until the block started to move. Once we found the breaking point we weighed the cup full of water and recoded all of this data. We repeated the process for the mass of 2 blocks, 3 blocks, and four blocks and recorded all of the data.

What we did with this data: We used this data to find the normal force between the table and the block. We also used this data to determine the maximum static friction between the block and the table.

We then plotted this data in logger Pro by making a maximum static friction Vs. Normal force graph. This graph determined the coefficient of static friction.

static friction=.38

Part B:Kinetic Friction With Force Sensor:

What we did: We tied the sting from the brick and attached it to the force sensor. We then opened up logger pro and and recorded our data. in order to make this work we had to make the force on the force sensor be as close to constant as possible. We would pull on the sensor up untill the static friction broke. after it broke the friction reduced and we kept it as constant as possible. We took the recording of this information and it automatically graphed onto logger pro. In order to get a kinetic friction we took the data on the whole interval at which we tried to keep the force constant and got the average of it.

Apparatus Used: Force sensor

Part c:Static Friction from an angle to get it Sliding:

We Set up a ramp and placed the Blockk onto the ramp. We tried to get the angle at which the static friction broke. We gradually raised the ramp until the brick began to slide. The angle that made the block slide was 20 degrees. After taking several calculations and manipulating formulas we found that 

Ms=Tan(theta)

Part D: Finding Kinetic Friction on a Ramp: 

We used the same process as the one mentioned above, but this time solved for kinetic friction.  The formula we obtained this time was

Mk=(mgsin(theta)-ma)/(mgCos(theta))

Mk=gsin(theta)/gcos(theta)

Part E: Finding acceleration with friction: 

Motion sensor positioned at the top of the ramp.

We set up the ramp at a steeper angle and positioned the motion sensor on the top of the ramp. The Motion sensor sends a sound wave to determine the distance traveled during each time interval. Once again we recorded the block sliding down the ramp using logger pro and it automatically graphed our data. It made a velocity vs  time graph. We got a linear fit on the data we needed and it gave us a formula. This formula was in the form Y=Mx+b  Our M was valued at .8966. In conclusion Our acceleration is equal to .8966 since the derivative of this graph gives us our acceleration.

Acceleration=.8966

Conclusion: After following the instructions of lesson 7 ( Modeling Friction) we were able to come up with the formulas needed to find kinetic and static friction. This lab helped up visualize how to find kinetic and static friction and realize how it works.  We were also able to find acceleration using logger pro.We were able to get familiar with  two new apparatus the force sensor and the motion sensor. Once again we used  logger pro and we are getting  closer to proficiency with that cpu program.   

September 20, 2014-Measuring the Density of Metal Cylinders.

 Purpose: The Purpose of this lab was to learn how to find the density of an object and find the propagated error, while learning how to use different tools that you could find in the classroom.

Apparatus used: We used a scale to find the weight of an object We also used  a vernier calipers to help us find the diameter and height of our cylinder.

 vernier calipers

What we  Did: We found the diameter, the height, and the mass of three cylinders. One of aluminum, one of copper, and one of steel. We then used this information to determine the density of each cylinder using the density formula. After obtaining the density we listen to Professor wolf lecture about propagated error and how we would derive it. Below are the main notes that I needed to find the propagated error.

We used the formula above and plugged in the information we needed to find out the propagated error. Each of our lab members took it upon themselves to find the propagated error of 1 cylinder. I was given the duty to find the density and propagated error of the copper. I found that the coppers density was 2246.13 kg/m and the propagated error was + or - 33 kg/m.


Conclusion: We were able to used the derived formula provided by professor Wolf to find the propagated error for our three objects. My object in particular had a propagated error of + or - 33kg/m which made my density look like 2243.13,+- 33 kg/m

September 15-2014- Trajectories

Purpose: To understand projectile motion and predict the impact point of a ball on an inclined board.

Materials: Aluminum V channels, a steel ball, a wooden board, a ring stand, a clamp, paper, and carbon paper.

What we did: We first set up our run for the steel ball to travel through. We stood up the ring stand and taped the V channel onto one of the extending post. We then connected the bottom of that V channel to another  horizontal V channel. Next we placed our steel ball onto the top of the ramp and tried to find out where the ball landed off the table. Once we had an idea of where the ball landed we taped our carbon paper that was sandwiched between two regular papers in the area where the ball landed. Finally we put the ball back to its original testing point and allowed it to roll off the table and land onto the carbon paper. This left an imprint of carbon on the back side of the white paper in which we would use to calculate the distance the ball traveled in the horizontal direction. We used the height of the table as the distance traveled in the vertical direction.

 Our ramp

 This is the end of where the ball flew off of.

This is the carbon paper that took an imprint of the ball when it landed.

What we did with this information that we obtained: With our first run we were able to obtain valuable initial information information.

IN THE X DIRECTION                      IN THE Y DIRECTION

Delta x= 64.5 cm(.645m)                      Delta Y=93cm (.93 m)

a=0                                                        a=G=9.8 m/s^2

We are able to calculate Time using the variables in Y. 

DeltaY=(1/2)(g)(t^2)

After calculating for time we find that T is equal to .44seconds.
Time is very important because it is uniform on both the x and y direction. This provides us with the third  of five unknowns on both sides of the kinematic equations.

Pic of calculations

PART II:
Making a prediction of where the ball would land on a plank of would at the given angle: First we grabbed a piece of wood and randomly placed it in an angle from the floor to the table. (Photo Below)

Angel is equal to 50

We found that our angle was equal to 50 degrees. We also determined that the height (Delta Y) was equal to 93.5 cm. Next we found time since we know that acceleration in the y direction is equal to g. We then created different kinematic equation and came up with these unknowns.

In order to make our prediction we had to use a new formula to find t at the moment it hit the wood. Our team determined that it would take .356seconds. We multiplied the time t by the velocity in the x direction and came up with a horizontal distance of 52cm from the table. We 2 meter sticks to make a right angle one parallel to the table and the other perpendicular to the floor and the meter stick at 52 cm. We marked the spot where the perpendicular stick crossed the wood and placed the carbon paper on top of it. Finally we let the ball launch off the table to hit the wood with the carbon paper and found that the ball traveled 51 cm in the x direction.

Conclusion: After studying projectile motion we put it to the test. After careful analysis we were able to predict the position of the steel ball and predicted the landing1cm or .01m too far from the actual position. We Learned that velocity in the x direction is always constant and as long as we have velocity and a time we could figure out the position in the x direction. This lab taught us how to use and manipulate all the kinematic equations to find what we need to find.

September 13,2014- Air Resistanc

Purpose:  To model reality and develop a formula that takes air resistance into consideration. In order to do so we must find the relationship between air resistance and speed. We know that air resistance on any object is dependent on the objects speed. We are given the formula
F(air resistance)= kv^n
Where v is the velocity an we are suppose to find K and N.

Apparatus: We used lagger pro to obtain all of our data. We used a special feature that captures pictures in time intervals of .1 seconds. This feature allowed us to find the coffee filters displacement at a given time. We would first record the drop of the filter rack and then use lagger pro to plot Blue dots of time and displacement as the picture below shows.

A picture of my lab Partners before our first drop.

After recording the drop we used the plot option in the video capture section to graph the drop of the filter after each time interval. As you can tell the displacement is getting longer as time moves forward. Eventually the displacement and velocity stays constant. When this happens, the filter has reached terminal velocity.

How we are going to obtain our data: We went to the Design Technology Building to capture all of our filter drops. We were asked to drop and record 5 different drops using video capture. The first drop would consist of one filter(About 1 gram). On the second drop, you would drop 2 filters.(About 2 gram) On the third drop, you would drop 3 filters(About 3 gram). On the fourth drop, you will drop four filters(About 4 gram). Finally on your fifth drop, you will drop 5 Filters(About 5 gram). The purpose of dropping and recording a different amount of filters is so that we could have data on the drop of 5 different masses. The Goal was to get these filters to reach terminal velocity one by one. 

How we are going to use this data: Once we captured all of of video footage onto lagger pro, we returned back to our classroom where we recorded our data. We did exactly what the photo above demonstrates on all 5 of our drops. We plotted the blue dots which in return gave us a position vs. time graph. Our goal was to choose a section of the graph that would give us a linear fit. This linear fit will help us find our terminal velocity as well as our k and n values. Below are the photos of what the capture feature on logger pro recorded and plotted. The slope is equal to its Terminal Velocity.

One Filter:Terminal Velocity is Equal to -1.142m/s

 Two Filter:Terminal Velocity is Equal to -1.834 m/s
 Three Filter:Terminal Velocity is Equal to -2.065 m/s

 Four Filter:Terminal Velocity is Equal to -2.156 m/s

Five Filter:Terminal Velocity is Equal to -2.894m/s

Using our data above we created a spreadsheet of the force and velocity of each drop

This is a picture of an objects mass and its terminal velocity 

We then created a graph of Force vs. velocity. This graph had the section of 4 Filters struct in order to ge tumor accurate information.

4 Filters Struct

In order to be able to perform a power fit, we had to strike one of our data points to be able to come up with a model for our equation F(air resistance)= kv^n. Our graph is put in the  form of F=av^b. The Graph gives us the Variables that we are looking for. a=.007563 and b= 1.764

Summary: We were able to record our drops using video capture and obtain the data needed to come up with our formula. The key to this Lab was to obtain the terminal velocity of each mass and plot it using a mass vs velocity graph. In order to get the information we needed we had to struck one of our points in order to insert a power fit. In doing so we came up with our formula.

F(air resistance)=.007563(v)^1.764

Now that we have obtained our formula we can now find the terminal velocity of an object depending on its mass or find the mass of an object depending on its terminal velocity.

September 11,2014- Non-Constant Acceleration

Purpose: We were given a problem involving a 5000 Kg elephant that was rolling down a hill in skates and we were asked to figure out how far the elephant rolled before coming to rest. This lab was created so that we could learn to solve kinematic equations of non-constant acceleration analytically and numerically.

Apparatus used: We did not use any apparatus in this lab. We were simply asked to find the answer to the problem given by the professor using calculus and then solve it using excel.

How we approached the problem Mathematically: This was by far one of the most difficult problems I have been exposed to. Thankfully the professor Wolf solved the problem step by step with us. Initially I was overwhelmed by how easily and how fast the professor knew what to do since, I knew i would not have been able to come up with the answer so easily. I was relived of some stress when the instructor told us not to fret if we aren't sure how this whole process that was being unfolded. He reassured us that he was able to breeze through the problem since he had solved it several times.(more than 5 times) After arriving to an answer we began part two of the lab. Solving the equation using excel.

How we approached the problem numerically: The second part of the lab had us use excel to see if our answer that we would obtain using the formulas derived onto our excel spread sheet would match up to the answer we obtained analytically.
Our hand out had us enter information for 6 different variables as well as with 6 different formulas for each column. These variables were as followed.

1. t= Time
2. a=Acceleration 
3. a_avg= Average acceleration
4. Delta V= Change in Velocity
5. V=Velocity
6. X=Distance the Elephant Traveled. 

After we developed our excel spreadsheet we were asked to fill them down far enough to figure out the distance the elephant traveled. We used three different time intervals. We used the time intervals of .01 seconds, .5 seconds, and 1 second. Our data/excel spread sheet look as followed.

 Time Interval of .01 

 Time Interval of .05 

 Time Interval of 1 second

what this data shows: This data is telling us that it takes between 19-20 seconds for the elephant to reach a final distance of 248 feet.

summary: We were able to obtain consistent Numbers using our numerical approach of excel to get a total distance of 248 m. which took between 19-20 seconds. To be more accurate we would use the time interval of .01 seconds which tells us it takes between 19.6-29.7 seconds to reach a distance of 248.69m. The data that we obtained numerically is consistent with the number we obtained analytically. With this lab we come to realize that there are several approaches one can take to solve a problem. However, you must always be careful when computing your data. One wrong number or rounding error in both the numerical or analytical approach can really fudge your answer.

We were also asked how would we know if the time interval we chose for the integration or excel small enough? We know that the results are correct if the numbers converge to a specific number. 

September 5th, 2014 Lab 2: Free Fall- Determination of Gravity

Purpose: To use a spark generator to determine that a free falling object will accelerate at a rate of 9.8 m/s^2 .

Apparatus used:

 This is the top of our device. The electromagnet holds our object into place. Once it releases the object, the spark generator records the distance the object travels onto a strip of paper. It generates a spark every 1/60th of a second at 60 Hz.

The over all height of the Apparatus is 1.86 meters tall.

How we obtained our data: The apparatus above used a 60 Hz spark every 1/60th of a second. A spark sensitive tape would record the distance the object traveled at each time interval. (Photo below)

Spark Sensitive Tape next to a meter stick. Each dot is where the object was located at every time interval of 1/60 seconds.

What we did with this Data: We measured 15 dots and obtained the total distance it traveled from the top of the spark sensitive tape. We then created an excel worksheet which consisted of time, distance, the change of distance relative to time(Delta D), mid-interval time, and mid interval speed.

OUR DATA 

This information from the excel spread sheet was then used to make a POSITION VS TIME graph . Which is the photo below

Velocity V.Time Graph

Question for Analysis: Describe how you get the acceleration due to gravity from your velocity time graph? Your acceleration due to gravity can be found by obtaining the slope of the velocity versus time graph. Above is our velocity versus time graph. The slope on our graph is 939 cm/s^2. This converts to 9.39 m/s^2 which is not quite acceleration due to gravity.

Conclusion: Our efforts to conclude that acceleration due to gravity is equal to 9.8m/s^2 fell short. With our data we concluded that gravity was equal to 9.39 m/s^2 which is incorrect. 

• Using the formula for absolute difference (Experimental value-Accepted value) we determined that we were off by -.41m/s^s(9.39-9.8=-.41) 
• Using the formula for relative difference (Experimental value-Accepted value divided by accepted value times 100%) we determined that we were off by -4.1%

Reasons for error: What may have happened

• We measured or dots incorrectly
• The distance of the drop of the object (1.8 m) may have not be a long enough period. 
• We inserted the data or a formula incorrectly in our excel spread sheet.
• Human Error.
  
  Information obtained from group 1-9
  The closest to obtain g=9.8m/s^2 was group 6 who came up with 9.75. This graph shows that every group came up with a G that is lower than it should be which is known as a systematic error.