Amanda,+Elena,+Emily,+Emily

toc =Lab 3: Moving in a Horizontal Circle:=
 * Group Members:** Amanda Donaldson, Elena Solis, Emily Burke, Emily Van Malden
 * Class:** Period 2
 * Date Completed:** January 14, 2011
 * Date Due:** January 18, 2011

What is the relationship between the maximum velocity of a car rounding an unbanked turn and the radius of the turn? What is the relationship between the banking angle of a roadway and the radius of the turn?
 * __Objective:__**
 * What is the relationship between the maximum velocity of a car rounding a banked turn and the radius of the turn?**

The objective we proved in this lab is the one that is in bold above: What is the relationship between the maximum velocity of a car rounding a banked turn and the radius of the turn?

In order for a penny to remain stationary (not slide) down the banked turn, the speed and radius are of importance. If we increase the speed of the record player, then the radius at which the penny must be placed in order to stay in uniform circular motion, will decrease. Thus, the higher the speed, the smaller the radius (closer the penny needs to be to the center) to ensure it won't slide. The speed is the independent variable that the radius is dependent upon.
 * __Hypothesis:__**

For this lab, the key material is the turn table/record player. To complete this experiment, we represent a car with a penny. To verify the speed of the record player as well as to time each circle, we will need a stop watch/timer. To create a banked turn, we need the angled-triangular block. We will also need a meter stick to measure the radius.To extend the radius, we need a long piece of wood.
 * __Materials:__**

__**Lab Set Up:**__


 * __Procedure: ﻿ __**
 * 1) Verify the speed of the record player.
 * 2) Choose one of the available speeds on the record player.
 * 3) Place the penny at the close to the center and measure that radius.
 * 4) Turn on the record player and start the timer.
 * 5) Let it spin and record time for one revolution.
 * 6) If the penny fell off at that radius, record it. If not keep moving the penny farther from the center (be sure to measure the radius) until the penny falls off.
 * 7) Once the radius where the penny fall off is found, repeat three times to verify data.
 * 8) Repeat steps 3-7 using the other three speeds to find the smallest radius where the penny will fall off.

__//1. Actual Velocity//__
 * __Data:__**
 * blue=estimated values (see conclusion for explanation)
 * __Calculations//://__**

__//2. Theoretical Velocity//__

__//3. Theoretical Radius//__

__//4. Percent Error//__

Graph 1: What is the relationship between the maximum velocity of a car rounding an unbanked turn and the radius of the turn? Courtesy of: Rebecca, Niki, Alyssa
 * __Analysis - Graphs for All Objectives:__**

Graph 2: What is the relationship between the maximum velocity of a car rounding a banked turn and the radius of the turn? Courtesy of: Us (our graph)

Graph 3: What is the relationship between the banking angle of a roadway and the radius of the turn? Courtesy of: Nicole, Jillian, Spencer, Dylan

In our experiment we proved our hypothesis correct. We predicted that as the speed increases the radius will have to decrease in order to keep the penny on the wood. This is because the speed and radius inversely related. In our experiment we found what the maximum radius would be so that the penny would not fall off the wood. For the fastest speed (77 rpm) we determined that the penny falls off at .13 m which means that the maximum radius that we can have at that speed is just less than .13m. We also found for the second fastest speed (44.5 rpm) the penny fell off at .45m so to keep the penny on the radius would have to be just smaller than that. Because of our lab set up we were unable to to determine the radii that would cause the penny to fall off a the lowest speeds (33 rpm and 16.375 rpm). Even though we were able to construct a longer radius by using a piece of bolsa wood, it still was not long enough to cause the penny to fall off. When we tried to move the bolsa wood and the block farther back, it was too unstable so it would not stay up and we did not have a longer piece of wood to use. Although we do not have specific data this still supports our hypothesis. We tested smaller radii at those speeds and the penny did not move, we also tested those speeds with the largest radius we could create which was .45m and the penny did not fall. Based on this we can conclude that a larger radius would cause the penny to fall off. This supports our hypothesis because we predicted that at the slower speeds the penny would fall off with a longer radius. Since we could not build a radius long enough we can conclude that the radius at which the penny would fall off for the slowest speeds would have to be longer than the wood we have, especially since we tested smaller radii and the penny did not fall off. From this we can also predict that the radius for 33 rpm would have to be longer than .45m (the radius at 45 rpm) and the radius for 16.375 rpm would have to be longer than that. As seen in our data table we predicted what the radii would be at those speeds. We predicted at 33 rpm the radius would be .69m and at 16.375 the radius would need to be 2.81m. Therefore, the data we collected proved our hypothesis that speed and radius are inversely related correct. If we were to preform this experiment we would need to change the sizes of the equipment we used to get more accurate results. We would use a larger record player we would make the radius longer. If the record player was larger then we could also use a longer piece of would to further extend the radius if needed because it would be able to support that structure and it would not just topple over like it did in our experiment. Our percent error for this experiment was not very high at 2.34% but there were ways that we could have made it better. Human error is big in this experiment with timing and seeing if the penny slid. For timing, humans have a slower reaction time so the times we received with the stopwatch for a period were not exact. With the penny's position, it was hard to see if the penny slid at points. Even if it slid the slightest bit, we might have missed it and we needed that information. Also, our record player was not exactly level and this might have made the penny slide easier. Overall, a 2.34% error is pretty good, with almost no mistakes.
 * __Conclusion:__**

= = =Lab 2: Maximum/Minimum Tension:=
 * Group Members:** Amanda Donaldson, Elena Solis, Emily Burke, Emily Van Malden
 * Class:** Period 2
 * Date Completed:** January 6, 2011
 * Date Due:** January 10, 2011

What is the maximum/minimum tension that keeps an object attached to a string in circular motion?
 * __Objective:__**


 * __Hypothesis:__**
 * For the minimum tension experiment, we expect that as we increase the weight, the minimum velocity will stay approximately the same, assuming that the radius is constant and the minimum tension is 0.
 * For the maximum tension experiment, we expect that as we decrease the radius, the time will decrease thus decreasing the experimental velocity.
 * Rationale: We know that a piece of string has a minimum tension and speed at which an object must spin in order to complete a full circle, without falling at the top. We also know that there is a maximum tension that the mass must be less than, so that the string almost yet doesn't break when the object is spun. We set out to find these tensions in the following experiments and centripetal force equations.


 * __Materials:__**
 * For the minimum tension experiment, we used a few materials. String and a meter stick to measure the length of the string (what would be the radius of our circle). Masses were also needed. Scissors were needed to cut the string. When we were all set up, a stop watch (or two) were needed to time the trial (sometimes we would use more than one timer to ensure the timer was starting/stopping the stop watch at the correct time, with good accuracy).
 * For the maximum tension experiment, more materials were needed. Again, string and a meter stick to measure the length of it were needed. Varying masses (including heavy and light) were required to complete this portion of the lab. A mass hanger was used and the masses were placed on top. The mass hanger was connected to the force sensor (which was connected to the computer for data studio) to determine the force. A rod and clamp were used to hold the force sensor steady when conducting this experiment.

//Minimum Tension//
 * __Procedure:__**
 * 1) Gather materials: string, meter stick masses, scissors, and a stop watch.
 * 2) Decide on a starting mass and tie these masses to the string.
 * 3) Have one person hold the string, with masses, and slowly and carefully swing it around in a full circle.
 * 4) While one person is spinning, have another person (or two) ready to start and stop the stop watch. Having two people may be beneficial to ensure precise starting and stopping of the timer.
 * 5) Record the radius (length of string), mass, and time in an excel spreadsheet.
 * 6) Change the mass on the string and repeat steps 3-5.
 * 7) Repeat step 6 twice so you have three trials with different trials.

//Maximum Tension//
 * 1) Gather materials: including string, varying masses, a mass hanger, a force sensor, and the rod and clamp.
 * 2) Connect the force sensor to the USB link and plug that into a computer.
 * 3) Open data studio. Choose create experiment. Go to setup and change the force from push positive to pull positive. Be sure to change this on the graph's y-axis as well.
 * 4) Tie the string to the force sensor hook on the bottom of the force sensor.
 * 5) Tie the other end of the string to the top “hook” on the mass hanger.
 * 6) Put the force sensor on the rod and clamp the rod to the table to prevent movement.
 * 7) Begin adding weights/masses to the mass hanger. Start with a something like 100 g. Be sure to include the weight of the mass hanger to the mass of the system when recording your data.
 * 8) Click start on data studio and let the mass hang there.
 * 9) Stop the data studio recording after your desired amount of time has passed.
 * 10) Add another mass to the current hanging mass. Start data studio. Stop data recording after time.
 * 11) Repeat this addition of masses and starting and stopping of data studio. As the mass gets heavier, decrease the weight of the added mass – you do not want to add too much weight because then you won't know at weight it really broke.
 * 12) To find the velocity, choose a small mass amount and attach this to the string, then spin it in a circle. Record this data.

//Minimum Tension// //Maximum Tension// //Maximum Tension Data Studio Graph//
 * __Data:__**

__**Diagrams:**__ //Calculated Tension (Max Tension - Hanging)://
 * __Calculations:__**

//Theoretical Velocity (Max Tension - Spinning)://

//Experimental Velocity (Max Tension - Spinning)://

//Experimental Velocity (Min Tension)://

//Percent Error:// __| experimental – theoretical |__ x 100 = % error theoretical

//Experimental Max Tension vs Theoretical Max Tension:// __| 3.6554 – 3.7 |__ x 100 = 1.21 % 3.7

//Experimental Max Speed vs Theoretical Max Speed:// __| 6.8217 – 7.009 |__ x 100 = 2.67 % 7.009

//Experimental Min Speed vs Theoretical Min Speed (assuming minimum velocity is zero):// __| 2.06 – 1.4 |__ x 100 = 47.14 % 1.4

**__Conclusion:__** Prior to the lab, we hypothesized that the minimum velocity will stay the same as weight increases (there is no relationship between the two). In our experiment we kept the radius constant at 0.2 m. Our results (see tables above) supported our hypothesis as we increased the weight from .01 kg to .027 kg the velocity stayed relatively the same. The velocities were all similar ranging from 2.06-2.55 m/s.The difference between the velocities are mostly like a result of error therefore proving out hypothesis correct. Our theoretical velocity was 1.4 m/s for all of the masses which also supports our hypothesis because although the masses changed the velocity did not.

We also predicted that the maximum velocity radius is directly related to the radius so as radius decreased the velocity will decrease as well. Our results support our hypothesis for this part as well. Our results showed that for a radius of .38 m the velocity was 6.822 m/s and for a radius of .27m the velocity was 5.655m/s. This shows that as the radius decreased, the velocity decreased. Our results have a slight discrepancy because we found a velocity of 6.822 m/s for a radius of .38 m and a velocity of 7.045 m/s for a radius of .37 m. These results would nullify our hypothesis but the don't because the difference between the radii is only .01 m and the difference in velocity is only .223 m/s. We believe that this discrepancy is a result of error. Also the theoretical velocities do decrease even though the decrease is pretty small which supports our hypothesis. Both parts of our hypothesis are supported by our data.

There was much room for error in our lab, much. Human error made up a good chuck of our experiment. While spinning the mass around in a circle, our hands were never exactly in the same position every time the ball finished a rotation. One time in fact, our hands made little tiny circles of their own. This messed up our results for it would change the circumference (or the total distance the ball was covering per lap). This would mean that we were actually timing a longer revolution then we should have, for the mass was completing a much larger and longer circle. However, the circumference we used in our experimental calculation assumed that we had strong steady hands. This partly explains why our experimental velocity was so different then our theoretical and why when we tested out our excel sheet, by simply estimating and experimentally lowering the time per lap, our percent error was smaller. Another big source of error was again human – when it came to timing the laps of the mass being rotated. In some cases, when all three of us would time while the other spun, the resulting times would be as much as a second different. While we would then use the average of the times, the fact that that much difference can occur in the first place, suggest the impreciseness of hand-held timers. This too would account for our error-filled experimental velocity; perhaps we stopped the clock too late each time, after the mass had already completed its lap. This could either give us a higher experimental velocity is we stopped it too early or a lower experimental velocity if we stopped it too late.

While getting our data for minimum tension, there are a couple of errors that we could have fixed. To start we held the string in our hands so upon spinning, it sometimes caught on our fingers. Also, with timing, we weren't exact because we are only human. We have a delayed reaction to the string breaking and stop the timer shortly after. While getting our data from maximum tension there are some errors that would have made our data better if they were not present. During some trials we would add too much weight and the string would break but we weren't sure exactly at what weight the tension was too much. The use of a force meter would also have helped us come up with more accurate time per lap values. Without these simple mistakes our data would be more exact and our calculations would be closer to the theoretical.

= = =**Lab 1: Circular Motion**=
 * Group Members:** Amanda Donaldson, Elena Solis, Emily Burke, Emily Van Malden
 * Class:** Period 2
 * Date Completed:** January 3, 2011
 * Date Due:** January 7, 2011

__**Purpose**__: To examine the relationship between the speed and the force of the system.

If the speed increases, then the tension (force) of the string will also increase because if the speed increases the tension needs to be stronger so that the object is still moving in a circle.
 * __Hypothesis:__**

Although for this lab you could use a variety of materials, we chose to use a centripetal force apparatus. This included many items, however we solely used weights/masses and string. A scale was needed to measure the weight (in grams) of the masses. Additionally, we used a meter stick to measure the length of the string we used. As you can see in the picture below, four pieces of masking tape are on the floor so we can visualize the circle as we spin the masses, and one piece of tape is in the center so we can ensure the radius is remaining constant. Additionally a force sensor was needed to use with data studio to calculate the force while spinning the masses. (The string that the masses were hanging from was also attached to the bottom the force sensor to create the data studio graph) //Here is our setup//
 * __Materials__**

>
 * __Procedure__**
 * 1) Gather materials stated above.
 * 1) Cut string to preferred length (0.5 m).
 * 2) Tie a knot in the string to secure masses to the end.
 * 3) Remeasure the string (after the masses have been attached) (.255 m).
 * 4) Connect the force sensor to the string.
 * 5) Connect Force Sensor to computer and open Data Studio (create experiment).
 * 6) Under setup change the force to pull positive.
 * 7) Start data studio while spinner spins apparatus (force sensor connected to string with masses).
 * 8) After it goes around the circle the desired number of periods (4), stop data studio.
 * 9) Record the time for four periods.
 * 10) In order to find the time per one period, divide the recorded time (for 4 periods) by four.
 * 11) Repeat steps 8-11 five times so that there are multiple trials at each speed.

//Things to remember in the procedure://
 * Do not change the mass as this is a constant factor.
 * Do not change the radius, as this too is a constant factor,

Mass: 6-3/8 U weights = 34.68 grams = 0.03468 kg String: 50 cm = 0.50 m Radius: 32 cm = 0.32 m Excel Spreadsheet:
 * __Data__**


 * __Trial Graphs__**

Overall graph

0.4 Trials

0.3 Trials

0.7 Trials

0.5 Trails

1.0 Trials

__**Conclusion Graphs**__

//Our Graph: F vs. v//



//Ani, Ariel, Rachel, and Sammy's Graph: F vs. r//



//Erica, Allison, and Roshni's Graph: F vs.m//

This is what our sensor looked like with the central mass at rest. Ideally, while revolving our mall, we wanted it to look like this with the radius being the entire length of the string.
 * __Diagrams__**

Force Diagram: Since weight was never fully on the same axis as tension, we can discount it from our calculations.



//Circumference Calculation//
 * __Calculations__**

//Sample Velocity Calculation//

//Tension Calculation//

F**c** = ma**c** F**c** = (m*v**2**) / r T = (m*v**2**) / r  T = (.030438 * 2.0681**2**) / .32 T = .1302 / .32 T = .40683 N

//Sample Percent Error Calculation, Comparing Experimental Value of Tension to Theoretical Value of Tension:// __|actual - theoretical|__ x 100 = % error theoretical

__| .4 - .464 |__ x 100 = __.064__ x 100 = .1379 x 100 = 13.79 % error .464 .464

For this lab our purpose, stated above, was to examine the relationship between the speed and the force of the system. From the start we thought that if the speed increased, the tension would increase. We gathered this idea from the fact of tension needing to be stronger when speed is increased to keep the object moving in a circle. Our hypothesis was proven correct when we did our trials. For example Trial 1 had a force of 0.4N and the velocity was 2.07 m/s and Trial 4 had a force of 0.5N and the velocity was 3.35 m/s. When the speed was faster the force of tension needed to increase in order to keep the object moving in a circle. As seen in our error calculation above we had varying amounts of error for each of the speeds. Also, we were able to examine the relationships between force and mass and force and radius of the system by using our classmates' graphs. Force and radius are inversely related, as the radius increases the tension decreases, this can be seen on the graph because it has a negative slope. Force and mass are directly related; as mass increases so does the force, which can be seen in the graph above.
 * __Conclusion__**

There was a lot of room for error in this lab so the error most likely resulted from a number of different parts of the lab. One of our biggest sources of error resulted from the lab set up. We attached a string to the force sensor and then spun the object while keeping the sensor relatively still. This caused two problems. The first was that we were not always spinning the object in a perfectly horizontal circle, which means that the string was on an angle. If the string was on an angle it makes a difference in the calculations, for the radius of the circles we were creating were different each time, not constant as they should be. However, we are unable to determine what that angle was (when we were on one) so we were unable to compensate for it in our calculations. This would cause a substantial amount of error in our calculations. The other problem with our lab set up was that the string kept getting caught on the hook so the speed, within one trial, was not constant the whole time. This again would distract our results, creating a more sinusoidal graph instead of the linear one. To fix this we put tape down on the hook, to trap the the string and keep it from swaying back and forth when we revolved it, but we do not know how this may have affected the tension in the string. We were careful to not put any tape directly on the thread string, becuase we knew that would compromise our results.

If we were to do this lab again we would change the way we preformed the lab. We would tie a string to the other end of the force sensor so that the sensor would have a string attached on both sides, one with the weight on the end and the other we would hold. By spinning the string we would be moving the whole sensor in a circle so that we would not have an angle to compensate for in our calculations. Another place where error could have resulted from is the accuracy of the force sensor. We could only get one to two significant figures from the mean on our data studio. This is not the most accurate reading, if we were able to see four or five significant figures then we would have more accurate readings and less error. To fix this we could use a different and more accurate force sensor. Additionally, some of our error probably resulted from human error during the timing. We kept the time running on data studio but if we did not stop it exactly when the object finished its fourth revolution, our results would have been affected. Our error resulted from a combination of human error, our equipment, and the lab set up.