Lab 7 - Centripical Force

Objective: 
To verify Newton's second law of motion for the case of uniform circular motion.

Procedure: 
The equipment used for this lab are as follows:
1. Centripetal force apparatus
2. Metric scale
3. Vernier Caliper
4. Stop Watch
5. Slotted weight set
6. Weight hanger
7. Triple beam balance


The idea of this lab was to manually spin the centripetal force apparatus so the weight is close to the marker, time 50 rotations for each weight to figure the velocity using Newton's second law.   After a few practice runs with the apparatus, we were ready to begin.  While one of the lab partners counted, one manually spun the apparatus another used the stop watch to track the time it took for 50 rotations.  The hard part of spinning the apparatus is that the weight had to match with the indicator post on the apparatus as it spun.  Spinning it too fast would make the weight pass the post, while spinning too slow would not reach the post.  This was repeated 4 more times for a total of 5 runs.  With all of this data, we were able to calculate a relatively accurate average of the velocity.

The cetripetal force apparatus also had another post that would let us calculate the cetripetal force of the bulb by attaching weight to a string until the bulb was even with the indicator post.  The amount of weight that was attached to the bulb to get it to center over the indicator post was .6kg.  This is illustrated below.



Apparatus with the weight to measure the Centripetal force needed to center the bulb over the indicator post

After the first set of runs, we added another .1kg of weight to the bulb and started the experiment over.  In the end, we had data to calculate the cetripetal force for a .5 kg and .6 kg bulbs, along with the measured centripetal force that it took to center the bulb over the indicator post.

Data: For both of the experiments, the information was entered into Excel to do the calculations.

Data captured from the experiments and information derived from formulas used

Trial - The number of the trial out of the 5
Time - The amount of seconds that it took for 50 revolutions
LDT - 2PIr - 2*pi*.1754 measured in meters
Mass - the mass of the spinning bulb
Radius - The measurement from the center of the spinning pole to the center of the indicator post
Average Velocity - LDT / Time measured in m/s
Calculated Centripetal Force - (mass - Velocity ^2) / Radius measured in Newtons
Measured Centripetal Force - the mass of the weight it took to hold the bulb over the indicator post * 9.8(gravitational measurement) measured in Newtons
Percent Error = Absolute value of ((Measured C force - Calculated C force) / Measured C Force )* 100

Possible Sources Of Error:  Timing was the key with this experiment.  If the person spinning the bulb could not keep the bulb over the indicator post, the timing would be off.  If the bulb spun too fast, the time would be less, and if the bulb spun too slow the time would be too much.  In addition, the timer had to be paying attention to the person counting the rotations to ensure that the stop watch was started and stopped at the correct times.  This was the cause for most of the trials that were done a second time.  We tried to ensure that the count was correct by having 2 of the lab partners counting at the some time.  This prevented us from starting over at least 2 times.

Questions:
1. Calculate this force and compare with the centripetal force obtained in part 3 by finding the percent difference.  This was completed with the excel data.  The percent difference at .5 kg was 1.42, and at .6 kg it was 1.95.
2. Draw a force diagram for the hanging weight and draw a force diagram for the spring attached to the hanging mass.

Conclusion:  I feel that the lab overall was successful.  We were very close to the measured centripetal force with very little difficulty.
The purpose of this lab was to verify Newton's second law of motion in a uniform circular motion using the formula F = (mv^2) / r.  Using this formula I was able to calculate the centripetal force of the bulb as it spun on the apparatus.  This was a great way to see the calculations that we do in the problems in action with the spinning bulb.
If the force and radius are the same, and only the weight changed, then the only other variable that effect the net force is the velocity of the spinning bulb.

Lab 5 - Working with Spreadsheets

Objective:  To become familiar with electronic spreadsheets by using them in some simple applications.

Procedure: Starting with a clear Excel spreadsheet, we followed the instructions and entered 5 in column A, and a 3 in column B and PI/3.  The columns were labeled Amplitude, Frequency and Phase, to look like this:


Step 1 - adding headers and data

 

The next set of instructions were to add another column, label it X and put a 0 in the first field of the column.  In the next column, label it f(x) and enter the formula "A2*sin((B2*D2)+C1)".  This is what the spreadsheet now looks like:

Step 2 - adding more columns and the formula

 

The next step was to add a series of values in the X column ranging from 0 to 10 Radian, step by .1.  The idea was to use Excel to do this, so after the first .1 was entered, the rest of the column could be added from the previous field.  When this was completed, it looked like:



Step 3 - Getting familiar with Excel

Using Excel, the X column was extended to 100 radians.  The f(x) formula was extended to cover the range from 0 to 100.  This information was cut from Excel and inserted into the Graphical Analysis, where a graph of the data was created.  Using the program to analyse the data that was entered with the data set function, the following data was created:

 

Step 4 - importing the data to the graphical analysis program





Using another equation [f(t) = r0 + v0(t1-t0) + 1/2a(t1-t0)^2], setting up the series in Excel:





Step 5 - Creating the new data sheet

What the data looked like with the curve fit when it was imported into the Graphical Analysis software:

Step 6 - Adding new data to the computer software

Data:  All of the data was provided in the procedure.  No additional data needed.

Possible Sources of Error:  Unless the numbers were keyed incorrectly into Excel, or the graphical analysis program, there were not other sources of error.

Questions:
1. How do these compare with the values that you started with in your spreadsheet? The data from the curve fit matched the data that was used to create the series of numbers that were pasted into the graphical analysis program.

Conclusion: I can see how using MS Excel when working with the lab experiments can be a huge advantage.  Excel can be used to calculate data like series or formulas to verify or use the numbers with the lab software that is used for the lab experiments.  In future experiments, I will be using this software to assist with gathering and analyzing the data.



Lab 6 - Drag force on a Coffee Filter

Objective:  To study the relationship between air drag forces and the velocity of a falling object.

Procedure: Using coffee filters as the falling object, we were to track the velocity using the logger pro software and the motion detector.  To do this, we started with 9 of the coffee filters about a meter and a half above the motion detector and let them fall freely until they hit the floor.  The motion detector and the logger pro software would track the position over time.  Using the curve fit for a sample in the graph that was created, we were able to determine the velocity of the falling filters.  Then with excel, we tracked this motion for 5 trials and determined an average velocity of the 9 filters.  One of the filters was removed from the stack and the procedure started all over.  After the five trials were captured, another filter was removed and the same procedure followed. This continued until there was only 1 filter, and five trails were completed.  A copy of the excel sheet is posted below.

The information that was used to populate this table was pulled from the position versus time graphs that were created with the logger pro software, and the curve fit that was used to get the

Questions:
1) In the formula F-drag = K V^n, what should the n be?  The n should be a 2.  The velocity would be parabolic in nature since it is being increased by the weight (f-gravity * mass) exponentially.  This  would be true until the object reaches terminal velocity where f-drag = weight.
2) Why is it important that the shapes stay the same? Since we are experimenting with the drag force, and this is directly effected by the cross section of the object, any change in the shape of the object is going to change the cross section and therefore have an effect on the drag of that object.
3) What should the position versus time graph look like? Explain. Since the object is falling over time, the graph should be a straight line representing the distance from the sensor as time goes by.  Therefore, the shape of the graph would be a slope.
4) What should this slope represent? Explain.  Once the object can no longer accelerate, where f-drag = weight, then the object has reached terminal velocity.  Terminal Velocity is where a falling object can no longer accelerate because the drag force and the gravitational force plus mass are in an equilibrium.
5)

PSOE:
1) As stated in question 2, the shape of the coffee filters should be relatively the same no matter the count used for the experiment.  Our set of filters were slightly worn, and no matter how much we tried to keep the shape consistent, they always seemed to lay out as flat again.  This lessened somewhat as the experiment went on, but it did seem to have an adverse effect and this was really seen in the average velocity over time chart that was published in the procedure.
2) As always, the tools and equipment that were used are not the most precise ones available.  This does not prevent us from doing the experiments, just makes our results a little fuzzy.
3) Try as much as I did, but I am sure that I was not able to drop the filters from the same position every single time.  For the trials where the numbers seemed extremely different from the other trials, the trial was repeated to try to minimize this as a source.
4) No matter how many times I explained to one of the lab partners that the motion detector picks up movement in a cone, he still insisted on waving the measuring stick in front of, and around the testing area.  This also lead to several of the trials being run again in an effort to remove this as a source.

Conclusion:
The experiment was a very time consuming one.  Between the number of trials that had to be ran again due to the sources of error that were explained, and the fact that there were 45 base trial runs, this turned into a lengthy experiment.  That is not to say it was a boring or tedious experiment, just a long one.  This ended up being one of the reason that some of the trials that needed to be redone were not.  We simply ran out of time and barely got the lab completed as class was ending.
One thing that should have been done was to control the area around the experiment a lot better.  I think that this might have helped tremendously with the numbers that were calculated from our trial runs.