Group6_4_ch5


 * Group 6 **

**Swinging Stopper Lab**
toc **D: Gabby**
 * A: Lauren **
 * B: Maddie **
 * C: Nicole **

**Objective:** **What is the relationship between system mass and net Force?** **What is the relationship between velocity and net Force?** **What is the relationship between radius and net Force?**

**Hypothesis:** **The centripetal force and the mass are directly proportional, so as the mass goes up so does the force. In addition, the velocity and the net force are also directly proportional. Finally, the radius and the net force are indirectly proportional.**

**Methods and Materials** **To set up this lab a piece of string was cut and strung through a grey tube. Then on one end, on the ground, a force sensor was attached. On the other end, black, rubber stoppers were attached. After it was set up, we spun the string changing the radius, mass, and velocity at separate times.**

**Video:** media type="file" key="Movie on 2011-12-16 at 11.36.mov" width="300" height="300"

**Data Table:** **Our results:** **- Due to lack of time, we were unable to obtain more than 3 points for changing the velocity, and did not get any results for changing the length of the radius.** **Graphs:** **Class results from 2010 (given by Ms. Burns)** **Graphs:**


 * Sample Calculations **

Tension was calculated through Data Studio



**Analysis**

Although we did not complete a changing radius graph due to lack of time, our other graphs turned out successfully.

Mass v. Force -- r^2 value is .98985, this results are very good considering all the possible error that can occur. The data proves that as the mass on the swinging string increased, the centripetal force also increased. Therefore the graph is a linear fit because centripetal force and mass are directly related. This is confirmed with the other class data, where it is also a linear fit.

Velocity v. Force -- r^2 value is 1. Because the r^2 value is so high, this graph is confirmed to be perfectly accurate. The data shows that this relationship is not as direct. In numerical order, as the velocity increased, the force decreased. However then the velocity increased again and the force increased as well. This relationship is exponential, meaning there is a power and the first value is squared. The y value is the force and the x value is the velocity however it is actually velocity squared. Confirmed with the class data, although it did not have as high of an r^2 valued, proves that the graph depicts the correct relationship.

Radius v. Force. --- class r^2 value is .98712. The class data shows that as the radius decreases, the centripetal force increases. Therefore the y value is the force again but the x value is 1 over radius. This relationship is depicted in an exponential relationship with a power on the graph, the first term is squared. Although we do not have a graph to confirm with, the class data has a very good r^2 value so it can be confirmed to be correct.

This lab allowed for the relationship between mass, velocity, radius, and net force to be determined. Our group originally hypothesized that centripetal force and mass, net force and radius, and net force and velocity, are all directly proportional. These were all proven correct with this experiment. First, this lab proved that as mass increases, so does net force, illustrated in the above graph which demonstrates a constant, linear relationship. The equation F=ma allowed us to draw this conclusion, because it shows that as m, or mass, increases, F, or force, will always increase as well. This lab also proved that as velocity increases, so does net force. The graph above also demonstrates this concept, the increasing relationship between force and velocity in a parabolic fashion.The equation F=mv^2/R illustrates this, as well, because as F increases v, or velocity, does as well, and that the two variables have a parabolic relationship. Finally, this lab proved our last hypothesis correct, that as radius increases, the net force will decrease. Both our graph above, showing a decreasing relationship between radius and force, and the equation F=mv^2/R, illustrate that these two variables are inverses of one another. Although our data and graphs show that this lab was successful, there is a wide range of error that could have occurred. First, due to time constraints, we were unable to obtain more than 3 points for changing the velocity and didn't record any results for changing the radius. Therefore, we used Mrs. Burns data to fill in the rest of our chart. In addition, the possibility that error occurred within our experiment is very likely. This experiment left room for many sources of human error to get in the way. First, we assumed that the radius would be constant for some of the trials after we measured the string. However, it was extremely easy for the string to shift in length during the course of the experiment, altering our results. In addition, the length of the string ended up not being the only component we couldn't fully control. It proved impractical that one of the group members could maintain a constant speed throughout all of the trials, and it was only natural that they would speed up or slow down at some point. This had an effect on our results that relied on the fact that velocity would remain constant. Finally, the fact that it was also up to a group member to time each trial resulted in the possibility of error, since it is very likely that they either pressed "stop" too quickly or too slowly after the trial was finished. This small difference once again alters any results that counted on the accuracy of the time. Since this was a simple physics experiment that took place in a short period of time with few materials available, it makes sense that we would face these errors. However, if we could change the experiment to make it as accurate as possible, using some sort of mechanical device that spins the string would allow for the velocity to be kept constant and would prevent the radius from shifting. It would also mechanically time each trial, allowing us to observe for ourselves when each reaches its full conclusion.
 * Conclusion **

**Minimum Speed Activity**
**Maddie, Nicole, Lauren**

Setup :

media type="file" key="Movie on 2011-12-19 at 11.15.mov" width="300" height="300"


 * Free Body Diagram**
 * Sample Calculations**




 * Class Data**

There are several factors that could have caused such a high percent error of almost 93 percent. Theoretically, the velocity would have been constant; however, since we were just approximating and trying to keep the speed constant, it's likely that it changed throughout rotations. Therefore, the results would be impacted by this error. Additionally, we assumed that the mass was moving at the slowest possible speed with the least amount of tension, thus in our calculations tension was set to equal zero. But, it's possible that it could have moved at a much slower rate, and therefore the tension s we performed the activity was not in fact zero, which would have made our results incorrect, as well.
 * Conclusion**

January 6, 2012 Lauren- Conclusion Nicole- Analysis Maddie- Excel ** Lab: Moving in a Horizontal Circle **
 * __PRELAB:__**
 * __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?

__**Hypotheses**__: 1.) On a level surface, as the radius (of a turn) increases, the maximum velocity for which a car can make a turn will icnrease, as well. Therefore, the radius and maximum velocity are directly proportional.

2.) Banking enables there to be a smaller radius for which the maximum velocity can be reached. This is because the friction force points towards the center, balancing the force of gravity of the car, as well as momentum (into the turn), which leads to a higher possible maximum velocity. The centripetal force is this friction force, which is made by the presence of banking.

3.) There is an inverse relationship between the banking angle and the value of the radius at which maximum velocity is reached. As the angle of banking goes up, the radius at which maximum velocity is reached will go down, and vice versa. This is because with a larger velocity, larger normal and friction forces are needed to balance the weight and momentum (into the turn), which are making the car move in a straight path, tangential to the circle. When these two forces increase, the centripetal force increases, enabling the car to make the turn successfully.
 * Prelab Assignment:**



FBD:


 * //Variables// || //Constant or Variable// || //How to Acquire information// ||
 * N || constant || multiply mass* 9.8 ||
 * R || constant || given ||
 * g || constant || 9.8 m/s/s ||
 * maximum velocity || variable || take the square root of µ*g*R ||

In this lab, a rotational turntable with a power supply and hooked up a photo gate to a computer. Then a mass was placed on a particular radius, which was .35 meters. Then slowly, the power supply was turned on and the voltage was raised. Before the rotational turntable began to spin, in a data studio activity, the start button was pressed. Then when the mass began to move; the turntable was stopped. After eight trials were completed, the data from the "in between the photo gate" data column was used to find other calculations, such as the velocity. After the velocity was found, a Radius versus Velocity graph was made.
 * Methods and Materials:**

media type="file" key="Movie on 2012-01-06 at 11.26.mov" width="300" height="300"
 * Video:**


 * Data:**
 * Personal Data:**


 * Class Data:**


 * Graph:**



Excel Sheet:

>> >
 * ANALYSIS:**
 * 1) **Discuss the shape of the graph and its agreement with the theoretical relationship between R and v.**
 * The shape of the graph is a positive curve, with a powerfit needed to properly display the data. Theoretically, as the radius increases, the velocity should also increases. Our r squared value .9912, which is very good showing that as class our data is a good description of the coefficient of friction between the coin and the surface. The equation of the graph reads as follows:
 * [[image:Screen_shot_2012-01-07_at_5-1.01.44_PM.png align="left"]]
 * [[image:Screen_shot_2012-01-07_at_5-1.01.49_PM.png]] & [[image:Screen_shot_2012-01-07_at_5.01.47_PM.png]]
 * [[image:Screen_shot_2012-01-07_at_5.35.20_PM.png]]
 * 1) **Derive the coefficient of friction between the mass and the surface.**
 * [[image:Screen_shot_2012-01-07_at_5.02.01_PM.png]]This value should be close to the value on the class average experimental value of µ. The values are similar ( .5445 vs. .551) However, the value we calculated is much more accurate because a powerfit and graphical examination of data is stronger and more precise than a calculation of an average when dealing with data.

> If the same procedure was performed but with an angled surface instead of a level surface, a higher velocity would be able to be reached at a lower radius. Since the graph has the radius on the x axis and velocity on the y axis, the line would appear much steeper on a graph with a banked angle, since a particular radius would be able to have a larger velocity.
 * 1) **Compare your coefficient of friction with that of all groups doing this lab. (Be sure to post a data table with the class values.)**
 * Personal coefficient of friction = .518 (Theoretical and Experimental) --> 0% error
 * Class average coefficient of friction = .551
 * Class coefficient of friction (from graph) = .5445
 * % error (Personal to class average) = 1.28%
 * % difference (Personal to class average) = 5.99%
 * % error (Personal to class Graph) = 5.12%
 * % difference (Personal to class graph) = 4.87%
 * SAMPLE CALCULATION:
 * 1) [[image:Screen_shot_2012-01-07_at_8.10.13_PM.png width="440" height="132"]]
 * A "car" goes around a banked turn. Find an __expression__ for its maximum velocity, in terms of variables only.**
 * A "car" goes around a banked turn. Find an __expression__ for its maximum velocity, in terms of variables only.**
 * 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?**

We hypothesized that the radius and the maximum velocity were directly proportional; in other words, as the velocity increases, so will the radius, and vice versa. Our personal as well as the class results both support this hypothesis, but a little more precisely, for the radius is actually directly proportional to the //__**square root**__// of the velocity. This is portrayed by our graph: as the radius increases, do does the velocity at which the mass will turn. The graph's equation is y=2.231x .4764, which is a power function, following the equation y=Ax B. The "y" value represents maximum velocity, the "A" value (2.231) represents the slope, which is the square root of µ*g, the square root of the radius is the "x" value, and B represents the power of the radius. This theoretical value is 0.5, since we are trying to get the square root of g*µ*R. Our value for this, however, was slightly less.This can be due to multiple possible areas of error. Overall, our results were pretty accurate, as none of our results were under a 6% error. The lowest percent error of ours was personal coefficient of friction- we had a zero percent error from our theoretical to experimental. But, when comparing this value to the class data (using the graph), there was a larger percent of error, which was approximately 5.12%. Due to our sample calculations and analysis, as shown, above, our other two hypotheses were proven correct, as well. A source of error could be due to the turntable itself. The apparatus runs on a motor, which can be inconsistent at times, and thus not move at constant speeds when supposed to. A way to resolve this problem would be to test the consistency of the turntable before using it. Additionally, it took a very long time for the table to speed up, which caused us to use much higher voltages than we should have, since we didn't realize how fast this speed would truly be initially. Due to this, the voltage may have increased too rapidly for an eligible and accurate velocity to be used. Another source of error could have been the placement of the mass; although the mass itself is insignificant, the radius is very important, and if the mass was placed in slightly different locations each trial, this would have damaged the results as well. The mass has a hole through its center, and for some trials, this hole may have been above, below, or in the middle of the .35 meter mark, where our radius was. In order to prevent this mistake in future cases, one should pick one specific spot to place the mass, and keep this consistent throughout all of the trials. A final source of error could be due to human reaction time. Since the mass was placed extremely close to the edge of the turntable, almost instantly after beginning to move, it would fly off of the device. Therefore, it was very difficult for one person to yell "stop" just as it began to move, before at least on second had passed. Although we used the second to last period on DataStudio to account for this error, it's possible that this period, too, was inaccurate, depending on how much time passed before the person stopped the trial. Using a different program that has the ability to somehow stop automatically as the mass begins to move could prevent this source of error in future trials. This lab activity can be applied to everyday life in many ways, driving in particular. This is because when approaching a curve in the road, or needing to make a turn, each vehicle has a maximum velocity for which it can make this turn successfully. Therefore, the driver must not go too fast, or else he or she may spiral out of control; this is exemplified in this activity, for once the mass reached the maximum velocity, it flew off of the turntable. Also, banked turns are present when exiting a highway.
 * CONCLUSION:**