Group2_6_ch5

= = toc =Centripetal Motion Lab = Task A: Molly Task B: Julie Task C: Rachel Task D: together

**Objectives**:
 * 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?

**Hypothesis:** .
 * Mass and net force are directly proportional, forming a linear graph.
 * Speed and net force are directly proportional, forming a linear graph


 * Radius length and net force are directly proportional, forming a linear graph

**Materials and Methods:** In this lab we will be using a string, a meter stick, paperclip, stopwatch, weighted masses, hollow plastic tube, and a rubber stopper. The string will be strung through the hollow tube and attached to a paper clip with several masses on one side and rubber stopper at the other. After ensuring that the radius of the circle does not change through experimentation, use the meter stick to measure the length of the radius, which will be the distance of the string from the hallow tube to the rubber stopper. The stopwatch will be used to measure the amount of time it takes for the stopper to make a full circle. As the experiment progresses, more masses will be added on to the paperclip to shorten the radius and more stoppers to increase the system mass to see how different variable effect the relationship between net force and radius, speed, and mass.

**Procedure:** media type="file" key="Movie on 2011-12-13 at 13.25.mov" width="300" height="300" This is a video of us doing one of our trials.
 * Attach a rubber stopper to one end of a string and a paper clip at the other end
 * Feed the string through a hollow tube
 * Attach several masses onto the paper clip
 * Hold onto the tube allowing paper slip and masses to hang straight down
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Swing the rubber stopper around in circles in a horizontal motion and make sure that the masses remain in place without moving up or down
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Change one of the following variable while allowing the others to remain constant at one time:
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Add more system mass(more stoppers)
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Change the length of the radius
 * Increase speed

<span style="font-family: Tahoma,Geneva,sans-serif;">**Sample Calculations/Data:** Velocity- Time-

<span style="font-family: Tahoma,Geneva,sans-serif;">**Our Results:** <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">This is the graph for net force vs. speed. The graph is polynomial because as the speed increases so does the force. To find speed you need to use the equation avg v = 2 πr / t.
 * Our Results:**

This was our graph for Net force versus radius. Our calculations proved to be very wrong. We tried to change the radius while keeping each other component constant, but that did not work. The changes in the radius were very small and they should have been larger. Also, the velocity changed with the radius and we wanted to keep velocity the same while doing this portion of the lab. Overall our results were bad and unusable. Our graph came out bad and wrong. Below is what it should have looked like. This is the previous results for changing the radius and keeping mass and velocity constant. The graph of this proved to be a power graph showing that as the radius decreased the force increased. This is very different and basically our graph flipped. This data is good because the radius changing in bigger intervals than ours did and also the velocity was much closer together.
 * Previous Results:**

We were not able to test or get any data down for this part of the lab due to troubles with the other parts. This graph shows the relationship between Net force and mass while keeping velocity and radius the same. The graph is linear with an r 2 value of .99, which is very good and shows that results were accurate. the relationship between net force and mass is that as the mass increases so does the net force, which is why the graph is linear.
 * Previous Results:**

<span style="font-family: Tahoma,Geneva,sans-serif;">**Conclusion:**

Our hypothesis for the relationship of Net Force vs. Mass was correct, while our other two for Net Force vs. Radius and Net Force vs. Speed were not. We thought that all the graphs would look the same since we thought that they had the same relationship, that they were mass, radius, and speed were directly related to Net force. Through experimentation we proved that net force was directly proportional to the system mass because as the mass increased so did the net force. However, net force was not directly proportional to both radius and speed as we predicted. Net force did not turn out to be directly proportional to the speed. As one increased, the other did too, however not at a constant rate. The graph proved to be polynomial instead of linear as we had hypothesized. Net force and radius also proved not to be directly proportional. As the size of the radius decreased, so the net force increased, resulting in a power graph instead of a linear one as we had predicted.For the data that we were able to collect, there turned out to be very little error, which we can determine this by looking at the strong r2 value of the polynomial curve. For the Speed vs. Net force graph we got a high r 2 of .99 which shows that our data was consistent and good. However, for the data we collected for the net force vs. radius graph there was a very large percent error. This was because as we changed the radius, the other two components, mass and speed, were not kept constant. We ended up with a graph that was flipped upside down, therefore our collection of data was very off and so we can conclude that our percent error was very large. We are unable to determine the amount of error for the net force vs. mass graph however because we were unable to finish the lab in time. If we were to redo this lab there are many different thing that we would change in order to obtain more accurate results. There were also many things that we did wrong that could be fixed if we did this lab another time. While testing for the radius, we would make sure that the other two components remained the same throughout, making sure that the changing radius would be the only variable, since it is very important that only one value changes at a time otherwise the data would not be correct. Also, we would have used radiuses with larger differences so that our the changes would have been more evident and we would have been able to determine the relationship between these two items. Another source of error was that the tape was pushing up against the hollow plastic tube causing another added force which we were unable to calculate. This could have altered our results to make them impractical and wrong. To change this each run we would need to ensure that the tape was not up against the tube. Another source of error may have came from different people holding the hallow tube and making the system mass rotate. In the future we would make sure that one person does this so that it is more constant. We also had difficulty recording an accurate measurement of the radius, resulting in some error. We could have fixed this by making sure the ruler is held horizontally rather than in a slant. In addition, our reaction time with the stop watch was delayed or early because a separate person was timing than spinning the apparatus. To make this more accurate we could have had the spinner hold the stop watch so they can time and come up with more accurate readings. We also had trouble counting ten complete rotations. This could have been fixed by using the force sensor. An additional source of error was that the hanging mass was not always still. This error does not ensure a constant velocity, which is necessary to complete the lab properly.In order to ensure a constant velocity we must make sure the hanging mass is completely still at all times.

=Activity= Minimum speed at top of circle

Data table

During this activity, we encountered many sources of error. We had a lot of difficulty spinning the rope at constant speed as well as keeping total control over the string at all times. The radius also kept changing because of where we held our hands on the string. The main source of error we encountered was that our experimental values were affected by tension. The reason our percent error was so high was because our calculations assumed zero tension. As well, our string continued to get caught in our hands.

=Lab: Conical Pendulum=
 * Objective-** What is the relationship between the period of a conical pendulum and the radius?


 * Hypothesis-** We hypothesize that the smaller the period is, the larger the radius should be. We can predict this from analyzing our results from the centripetal motion lab. We observed that as period length shrank, the radius was larger because the faster it was going around the circle, the more perpendicular it gets to the center, making the radius extend out to its maximum.

<span style="font-family: Arial,Helvetica,sans-serif;">**Procedure:** <span style="font-family: Arial,Helvetica,sans-serif;">First you cut a long string that will withstand a heavy weight. After tying that in a steady place attach the weight to the bottom of the string. Then, tape down measuring sticks starting at the center of the circle to be able to measure the radius when you start your trials. After that is taped down you will start the experiment. Choose a radius and make sure that the weight is swinging around in a circle with the constant radius that you have chosen. Use a stopwatch to measure the time the weight takes to make one full rotation, then record this time. Do this three times for each radius. After that, move on to the next radius and repeat the steps above. Once all the data is collected you are then able to find the average time the weight take to make one rotation for each different radius, which will then allow you to find the experiment period.


 * Class Data-[[image:Screen_shot_2011-12-20_at_6.48.11_PM.png]]**



Analysis:
 * 1) Calculate the theoretical period. (on graph)
 * 2) Calculate the average experimental period for each radius. (on graph)
 * 3) Discuss the accuracy and precision of your data.
 * 4) Our results proved to be more accurate than precise. This is because everyones times that were collected were very spread out and not centered around one specific time. Although this is true our results were accurate because we found to have very small percent errors for each radius.
 * 5) Why didn’t we use the tangential axis at all in this lab?
 * 6) We do not use the tangential axis because it is not helpful when solving for the horizontal circular motion of the mass because there are no forces on the tangential axis, all the forces affecting this lab are on the horizontal axis.
 * 7) What effect would changing the mass have on the results?
 * 8) The change in mass would not have any affect on the results of this lab. After problem solving, mass is canceled out, making it have no affect on the results.
 * 9) How did period change as the radius increased? Is it a linear relationship? Why or why not?
 * 10) The period decreased as the radius increased as we had predicted. The relationship between radius and period us not linear because they are not directly related, they are indirectly related.
 * 11) What are some sources of experimental error?
 * 12) For the person that had to make the mass move it was hard to them to ensure that the ball was at the raduis they wanted at all times and that the speed was constant. Also,for the timers it was hard to ensure that you were timing one full rotation, starting and ending the stop watch at the same time. Another source of error is timing the masses roation after it had lost some energy so the radius would not longer be the length you wanted and the data you collected would be wrong.

=Horizontal Circles-= Objective-
 * 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?

Hypothesis-
 * The Bigger the radius the bigger the maximum velocity would be. This is because we talked about in class how if you turn too fast then you would make a wider turn.
 * It allows for friction to ensure that the car stays on the road. Banking the curve allows for the car if it is going to fast to stay on the road and not make to wide of a turn.
 * If the angle is bigger than the radius is smaller causing a less maximum speed.

Procedure- Start by gathering all of the materials. Hook up the usb cable to your computer and open data studio so that you are able to collect the data. After that is all set up, pit a 5 grams weight on the 40cm mark on the rotational turntable. Once that is placed there turn the voltage up on the machine up very slowly. Once the weight falls off the rotational turntable press stop on your computer so that you have recorded the period with the maximum velocity before it flew off. Repeat this 5-8 times and collect all the data.

media type="file" key="Movie on 2012-01-04 at 12.38

Methods and Materials- <span style="font-family: Tahoma,Geneva,sans-serif;">The equipment we used in this lab was a rotational turntable, photogate, metric ruler, 5 gram washer, and a power supply. We attached a tack to the rotational table so that the photogate could record everytime the tack passed through it, aka the period for each rotation. We placed the mass on our assigned radius, and increased the velocity until the washer fell off.

Class Data-

Pre-Lab Questions-
 * 1) Find an __expression__for its maximum velocity, in terms of variables you can measure in the lab.
 * 2) Vmax = 2(3.14)R/T
 * 3) Use your equation to think about your procedure, specifically, the measurements you need to make and the data you need to collect. List each variable, whether it is a constant or something to be measured, and how you think you will measure it.
 * //Variables// || //Constant or Variable// || //How to Acquire information// ||
 * Vmax || What you are finding || Use the angle and the radius to measure how fast a car can go around the bank before making a wide (out of control) turn ||
 * Radius || Variable || Measure the radius ||
 * 1) Read the notes, below. Answer the question in the 4th bullet: “//Which value do you want to use and why?//”
 * 2) You want to use the time between gates because it tells you how long it took to travel for that certain period of time.

Graphs-

Sample Calculations- Coeff. of Friction

Solving Coeff. of Friction From Line Equation

Coeff. Average Percent Error From Theoretical

Coefficient Of Friction Percent Difference from Line

Percent Difference From Class Data

Analysis- > >>
 * 1) Discuss the shape of the graph and its agreement with the theoretical relationship between R and v.
 * 2) The shape of the graph shows that it is a power fit because velocity is equal to the sum of gravity the coeff. of friction times radius times gravity. In the equation of the line we can see that the graph is a power fit because the radius, which represents the x value in this equation, is raised to the power of .4799, which is close to the theoretical value of .5.
 * 1) A “car” goes around a banked turn.
 * 2) Find an __expression__ for its maximum velocity, in terms of variables only.
 * 3) [[image:Screen_shot_2012-01-07_at_12.29.40_PM.png]]
 * 4) 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?
 * 5) If we were to do the same experiment but have it on an banked surface we could expect at least one major change. The new velocity would be slightly higher then the old one, so the graph would be altered a bit. We predict that the curve of the new graph would be slightly steeper then that of the old one because the velocity would change while the radii would remain the same.

Conclusion- Our hypothesis about the relationship between radius and velocity proved correct through experimentation. As the radius increased, we observed that the velocity increased simultaneously. In this case, radius is inversely proportional to the velocity. Our results for each trial were very close to one another, which showed that we were consistent. We also compared the coefficient of friction that we found to the coefficient of friction on the line. It seems that we only had a 6.5% error which is not high at all. We also compared our coefficient of friction to the class average and we got a .87% error which is very low. This shows that we didn't make too much error. We thought that error could have been made where we placed the weight each time. This would have caused our radius to slightly change each trial which would have caused our results to change. The speed wasn't increasing at a constant rate sometimes it would slow down or wouldn't go as fast as it did the previous trial. Also, we were under the vent which may have caused air resistance. Molly was also in-charge of stopping data studio on her computer to find the period, but due to human error she might not have been stopping it right as it flew off. We could do different things to fix each error. We could make sure that we marked where we put the weight each time to ensure that it was in the same place each trial. Also, maybe using a different machine that worked better and was more consistent could have fixed the problems that we were having with our machine. We could have moved our machine to a place that wasn't under the vent so that the air blowing out wouldn't be an issue. We could also make sure that molly stopped data studio right as the weight fell off the rotating turning table. This can be related to racecar drivers in a race. They have to go around turns trying to be the fastest that they can be so that they are able to win the race. Since they want to win it is important that they dont go over the maximum speed they can go for that radius because otherwise they would skid and then might not winning the race.