Group5_6_ch5

toc =**Chapter 5 Group 5**=


 * Jake Greenstein,** **Joe Miller****, &** **Remzi Tonuzi**

Centripetal Motion:


Part A: Joe Miller/Remzi Tonuzi Part B: Jake Greenstein Part C: Joe Miller Part D: Joe Miller/Jake Greenstein

What is the relationship between system mass and net force? What is the relationship between speed and net force? What is the relationship between radius and net force?
 * Objectives**

We believe that (mass and net force) as well as (velocity and net force) will both be directly proportional and look something like this. We predict that (radius and net force) will be inversely proportional and will produce a curved graph.
 * Hypothesis:**

Cut a piece of string, approximately 1.18 meters. Feed it through a hollow plastic tube. On one end, attach a paper clip by tying a knot around the paper clip with the string. On the other end, tie a knot around a rubber stopper. Add mass (metal washers) to the paper clip. Holding the plastic tube, swing the rubber stopper above your head. Swing it so that it moves at a constant speed, indicated by the hanging mass not moving up or down. Record the time of revolution, and radius. Repeat experiment, changing the hanging mass.
 * Methods and Materials:**


 * Picture:**

media type="file" key="Movie on 2011-12-13 at 12.50.mov" width="300" height="300"
 * Video:**


 * Data & Graphs:**
 * //Our Data://**

A Link to our excel file:
 * //Our Graph://**

Our data collection for the graph above took us far longer than it should have. Initially we misunderstood the directions and collected about 40 minutes worth of useless data. What we did initially was we allowed more than one variable to change defeating the purpose of the experiment. Once we realized our mistake we basically restarted the lab and began to collect the data that we needed to. We then took the additional time we received in class to run one more trial and finalize this graph. We had just set up to begin our data collection for the next graph when the period ended. In the future we need to budget our time better, because we can get good results we just need to make sure we have time to get them. Because of this in order to complete the lab report we had to take data from a previous year. (below)
 * Explanation:**

//**Data from previous Years:**//

We were unable to get any data for this portion of the lab. By using the data from last year we were able to construct the reaming two graphs. From the Net Force Vs. Mass graph we can tell that mass and net force are directly proportional and create a linear graph. (like we predicted) The graph also has an r 2 very close to one so we can assume that the data is pretty accurate. The Net Force vs. Radius graph formed a curved line. The graph below shows an inverse relationship between radius and force. We found this because is equal to 1/R (1/radius). This graph also has an r 2 very close to one so we can assume that this data is pretty accurate.

Previous Year Excel file:


 * Sample Calculations:**




 * Conclusion:**

Our hypothesis for net force and mass was correct. We predicted that the two would be directly proportional, and the graph would appear as a straight line increasing positively. However, our other two hypotheses were incorrect: Our graph for net force and velocity was predicted to math the graph of net force and mass, however, this was not the case. While they both show an increase over time, the actual results yielded a curved graph, unlike the linear fit we predicted. With regards to radius and net force, we were partially correct. We were right in knowing that they would be inversely proportional, however the shape of the graph was inaccurate. The predicted graph had an extremely negative slope, making the line very steep. Our actual graph had a line that decreased over time, however did so at a slower pace, with a less negative slope.

We were able to obtain decent data for our Net Force vs. Velocity graph. However do to mistakes that cost us time and general time mismanagement we were unable to collect the needed data to create the other graphs. However thanks to Ms. Burns we were able to use data from a previous year. This made it possible for us to create the other two graphs and ultimately understand their relationships. In the trials that we did we found several factors that contributed to error. One of the biggest sources of error was the actual measurement of the radius. We were using an un-exact method and because of this we can not assume that this data is 100% accurate. Another source of error in data collection could have been the person timing the revolutions. It became slightly difficult to record the time accurately when the system got faster. We could have lessened our tendencies for error by doing a few things. As for the radius it is difficult to do a more exact method we could try several other measurement techniques to try to lessen the error. One possible option is to have multiple people measure. This would hopefully help us to get a more exact reading. As for the issue with time we could use a sensor that detects when an object passes it and once it passes ten times it gives you the time. You could also try to have multiple people time it. I do however think that the best way to lessen our chance for error would be to try and use a data studio force sensor. I think that the less we have to rely on with manually obtained results the better.

We can apply what the concepts that we learned in this lab to several situations in real life. One possible example would be that of a helicopter. The helicopters rotors move in a circular pattern which provides lift for the helicopter. The pilot may find the centripetal force of his or her helicopter's rotors, and the force they place on the helicopter itself. The blades of the helicopter move in a circular motion, generating a centripetal force. This motion ultimately pushes air down, allowing for the helicopter to fly.

Activity:
Joey Miller Jake Greenstein Remzi Tonuzi

__**Our data:**__

A link to our excel file:

__**Class Data:**__

__**Some Sample Calculations:**__


 * Example velocity calculation:**


 * Average Time Calculation:**
 * Theoretical:**




 * Percent Error:**


 * Tension:**


 * Percent Difference:**



**Analysis:** Throughout this lab, we noticed many instances of experimental error. With our Percent Error being so high at 44.64%, it is clear that the procedure allowed much room for mistakes. The first is the way in which we measured the tension. Our data assumes that tension is 0, which was impossible to actually achieve in the experiment. Swinging a string by hand and trying to maintain constant speed is nearly impossible for a human - which we figured out soon enough during this lab. While we tried to be as accurate as possible, we noticed that we had often been spinning the string too slowly, causing it to drop. To counter-act this, we would then begin spinning too rapidly in order to compensate. In reality, we had to spin with greater tension than 0 at the top, because too much tension allowed the string to continue spinning, while too little tension would cause it to drop. This lack of consistency made our data less accurate.

Conical Pendulum Lab:
Task A: Joe Miller/Jake Greenstein (class data) Task B: Joe Miller/Jake Greenstein Task C:Jake Greenstein/Joe Miller Task D: All

**Objective:** What is the relationship between the period of a conical pendulum and the radius?

**Hypothesis:**

The radius will increase when the period gets smaller. This is because when the radius increases the faster the object moves, so it takes less time to complete 1 revolution.

The first thing we have to do is to get fishing wire and cut a long piece of it. We should then tie the top of it to the ceiling and the bottom of it to the hanging weight. When the weight settles at its center, tape down three meter sticks. That will be helpful in both regulating the radius of the weight and help the timers to have a spot to start and stop their clocks. For each of the 4 different radiuses record the time for each of the three trials. We can than use the time from each persons clock to determine the average time for each revolution to occur.
 * Procedure: **


 * Data Table: **



Our excel file:

__**Sample Calculations:**__

**Experimental:** 

**Theoretical:**

<span style="font-family: Arial,Helvetica,sans-serif;">Note that Theta (third line) should read theta=15.32 degrees <span style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-family: Arial,Helvetica,sans-serif;">

<span style="font-family: Arial,Helvetica,sans-serif;">**Percent Error:** <span style="font-family: Arial,Helvetica,sans-serif;">

<span style="font-family: Arial,Helvetica,sans-serif;">__**Analysis/Discussion Questions:**__


 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">**Calculate the theoretical period.**
 * 2) 0.304
 * 3) 0.308
 * 4) 0.312
 * 5) 0.317
 * 6) <span style="font-family: Arial,Helvetica,sans-serif;">**Calculate the average experimental period for each radius.**
 * 7) 0.304
 * 8) 0.305
 * 9) 0.315
 * 10) 0.326
 * 11) **Discuss the accuracy and precision of your data.**
 * 12) The data we collected during this lab was very accurate. All of our percent errors are extremely close to 0. The highest source of error was the 1 meter trial which produced a still good result of 2.84% error. In this trial our experimental period (0.326) was slightly higher than the theoretical period (0.317). Our data was also precise because the theoretical values were pretty close to each other as seen in the data table about.
 * 13) <span style="font-family: Arial,Helvetica,sans-serif;">**Why didn’t we use the tangential axis at all in this lab?**
 * 14) We didn't use the tangential axis in this lab because we were primarily focusing on the horizontal axis. The tangential axis is not needed to do the calculations for this lab thus we ignored it. There were no forces on the tangential axis, so it did not appear on the free body diagram.
 * 15) **What effect would changing the mass have on the results?**
 * 16) It would have no effect, on the results of this lab. When we do the calculations mass is eventually canceled out which means that it would have no effect on our results.
 * 17) **How did period change as radius increased? Is this relationship linear? Why or why not?**
 * 18) As we predicted when the period got smaller the radius increased. One decreases as the other increases so thus they are inversely proportional. Based on this we can assume it will not form a linear graph.
 * 19) **What are some sources of experimental error?**
 * 20) The hardest part about this lab has to do with the radius. Its hard to measure the radius exactly every time and thus it is expected that there will be some error. We tried to cut down on this error by doing 3 trials (in one case 4) because the more trials the better the data when we go to average them together. Another source of error had to do with the timing. As seen in the data table above each person recorded a slightly different time and because of this the experimental period would be slightly affected. The final source of error is specific to this lab because if we did it again it most likely would never happen again. During the lab the ball snapped the string and because of that we had to reposition that ball which most likely resulted in a slightly changed string length (this would ultimately affect our calculations).

Horizontal Circle Lab:
Task A: Joe Miller Task B: Joe Miller Task C: Remzi Tonuzi/Joe Miller Task D: Joe Miller


 * Objectives:**
 * 1) What is the relationship between the radius and the maximum velocity with which a car make a turn?
 * 2) How does the presence of banking change the value of the radius at which maximum velocity is reached?
 * 3) How does changing the banking angle change the value of the radius at which maximum velocity is reached?

1. The larger the radius the higher the potential velocity will be 2. By banking the surface a higher max. velocity can be reached at a lower radius 3. Having a higher banked angle would created a higher maximum velocity at a lower radius. vice versa
 * Hypothesis:**

First we placed the 5 gram washer (used as the mass) on the rotational mechanism. The mechanism was a circle that was attached to a motor fed by a small power supply. Slightly above the circle was a photo-gate timer. We placed the washer on our radius (.2m). Then we connected the data studio portal to my computer. By increasing the voltage we were able to make the circle spin. We ran the circle until the washer flew off, at which point we stopped the data studio timer. We than did this several times. The data studio kept track of the time between gates. Using the information we acquired from these tests we were able to determine the maximum speed that the circle could move before the washer flew off.
 * Methods and Materials:**


 * Picture:**


 * Video:**

media type="file" key="12.mp4" width="300" height="300"


 * Data Table:**


 * Graph:**


 * Sample Calculations:**








 * Analysis:**



In above FBD F= F c

>>> If we were to run the same procedure on an angled/banked surface we could have expected a few things. We could have expected a higher velocity for each radius. Because of this our graph would change slightly. I believe that the graph would be much steeper than the current line. This is because the radius does not change but the velocity has grown so it will make the graph stretch into a steeper curve.
 * ANALYSIS:**
 * 1) Discuss the shape of the graph and its agreement with the theoretical relationship between R and v.
 * 2) We knew that because the object traveled in a circular pattern that the line would be slightly curved. We also assumed that the exponent would be fractional because if the exponent was 1 the line would have been linear. The theoretical exponent is actually 0.5. The exponent that we got from our graph was 0.4799 which is a good result (as it is very close to the theoretical).
 * 3) Derive the coefficient of friction between the mass and the surface.
 * 4) [[image:Screen_shot_2012-01-05_at_3.53.05_PM.png width="138" height="446"]]
 * 5) Compare your coefficient of friction with that of all groups doing this lab. (Be sure to post a data table with the class values.)
 * 6) [[image:Screen_shot_2012-01-05_at_4.05.56_PM.png]]
 * 7) [[image:Screen_shot_2012-01-05_at_4.15.55_PM.png width="453" height="190"]]
 * 8) A “car” goes around a banked turn.
 * 9) Find an expression for its maximum velocity, in terms of variables only.
 * 10) [[image:Screen_shot_2012-01-04_at_7.58.03_PM.png width="215" height="399"]]
 * 11) [[image:Screen_shot_2012-01-04_at_7.58.20_PM.png width="326" height="255"]]
 * 12) How do you think the graph would change if you performed the same procedure but with an angled surface, instead of the level surface we used?

**Conclusion:**

In our hypothesis we said that the larger the radius (of the turn) the higher the potential velocity would be. Using the data that we compiled on our own and with our classmates we discovered that this is true. This is because the further away the mass is from the center the more distance it can cover with the same number of revolutions. When it came to banking angles we hypothesized that by banking the surface a higher max. velocity can be reached at a lower radius. In this lab we didn't do any tests with banked turns so we were unable to determine if it was correct or not. However we can assume that it is correct and I'm sure with further research we could have confirmed this hypothesis. We also hypothesized that if there is a larger banking angle that higher velocities would occur at lower angles. This also we did not test but we can assume that it makes sense. Basically by banking the angle we are forcing the object toward the center at a velocity thats too slow so it would take a larger velocity in order for the mass to fly off of the circle table mechanism.

Our percent error for this experiment wasn't bad, at 4.02 percent error this is well within the acceptable range. The percent difference between our coefficient of friction and the one on the graph was only 8.36% which is good. The percent difference between our coefficient of friction and the class average was only 1.76% which also is good! One main source of error that could have occurred during this lab is related to the data collection. When we pressed the stop button on datastudio it is likely that our reaction time was slightly delayed from the actual value. Another source of error is that the voltage could have been turned up to quickly which would have also led to poor results. It is hard to fix a lab like this especially because most of the data collection is done automatically. However to improve the lab I think that best way would be to have 2 groups do the same radius to see if their results were similar. I also think that the more trials, the better.

This can be applied to real life in a few ways. Circles are all around us and influence every part of our life. One specific example that would relate to this lab would be a person driving in a car. The person goes around a curve (similar to the one in our experiment) too fast and loses control and skids off the road. This happens in everyday life. An example of this in real life with a banked turn would be a nascar race. The stadiums raceway is put on an angle. They do this to give the rider more traction to keep him from smashing into the wall. But like this experiment, occasionally someone goes around a turn too fast and bumps into the stadium wall.