Berger,+Kaiden,+Rabin

=Lab: Moving in a Horizontal Circle= toc GROUP MEMBERS: Alyssa Berger, Niki Kaiden, Rebecca Rabin CLASS: Honors Period 4 DATE COMPLETED: January 14, 2011 DATE DUE: January 21, 2011

OBJECTIVE Part A: How does unbanking change the value of the radius at which the maximum velocity is reached? Part B: How does the presence of banking change the value of the radius at which the maximum velocity is reached? Part C: How does changing the banking angle change the value of the radius at which the maximum velocity is reached?

HYPOTHESIS Part A: decrease velocity Part B: increases velocity Part C: Larger banking angle = larger velocity, smaller banking angle = smaller velocity

PROCEDURE Materials 1. Turn Table 2. Disks 3. Penny 4. Stop watch

Set-Up and Methods 1. Confirm velocity of table turner by counting the number of revolutions while timing one minute on stopwatch. 2. Place disk on top of table turner 3. Place penny at various spots on the disk and measure the radius 4. Spin turn record player on at the constant velocity of 16 rpm and test three different radii. 5. If penny falls off the disk choose another position, if penny remains on the disk record specific position. 6. Repeat steps 3 – 5 with velocities of 33 rpm, 45 rpm, and 78 rpm and record results in excel spreadsheet.



DATA TABLE Our chart shows the data calculated using the four different RPMs provided on the juke box. The radius was acquired simply by measuring it on the juke box and seeing if it remained at the particular radius. At the end of each of the data accumulations, we calculated the velocity by multiplying the radius with the radians per second (shown below), and at the end got the average of each particular revolution to create a graph.

GRAPHS: PART A This graph shows a direct square relationship between the velocity and radius on an unbanked turn.

PART B Created by Eric, Sean, Phil and Chris.

PART C: Created by Nicole, Jillian, Spencer, and Dylan

__**Experimental calculations:**__
 * __Theoretical Calculations:__**

CONCLUSION Our initial hypothesis is proven correct in that unbanking decreases the velocity however we also discovered that the relationship between the radius and velocity during an unbanked turn have a direct square relationship, as shown on our graph by our parabolic shape. We know that our hypothesis is correct because of the specific R squared value which is close to 100%. For this lab, our percent error was very low however there were many sources of error. One could be the fact that we counted the amount of revolutions per minute wrong because with the old record machines the revolutions were very inconsistent. Also, the coefficient of friction between the turntable and penny could have been different between our turntable and penny and the penny and turntable of the group that calculated the coefficient of friction. The radius could have also changed throughout the trials. Overall, we need to be more consist with the entire procedure. We would need to find the precise revolutions per minute and keep a precise and constant radius throughout the entire lab. The more accurate results would then results in less error in our lab.

=Lab: Vertical Circle= GROUP MEMBERS: Alyssa Berger, Niki Kaiden, Rebecca Rabin CLASS: Honors Period 4 DATES COMPLETED: January 7, 2011 DATE DUE: January 12, 2011

OBJECTIVE What is the minimum velocity at the top of the loop? What is the maximum velocity at the bottom of the loop?

HYPOTHESIS and RATIONALE Minimum- Because the tension at this time is 0, altering the mass will not affect the object's ultimate velocity. Maximum- For the maximum tension experiment, as we decrease the radius, the time will decrease which will decrease the velocity in the experiment. Rationale-

PROCEDURE Materials 1. Force Sensor 2. Clamp 3. Mass Hanger 4. String 5. Masses 6. Stop watch

Set-Up and Methods 1. Cut a piece of string and measure the length of the string to obtain the radius of the circle. 2. Have a member of your group hold the string steady in the air 3. Attach a mass hanger to the string and add masses one by one onto the hanger until the string eventually breaks. 4. Once the string breaks, observe and record the amount of mass it took to break the string, which is the maximum tension. 5. With the equation, you plug in the maximum tension, for at any location in the circle, that number remains the same, the weight, the radius, and the mass, and solve for **maximum velocity.**
 * Maximum Velocity:**

1. Obtain a stop watch and use the same string that was used for the maximum velocity. 2. With a mass on the string, rotate it in a circle ten times in the air and record the time found. 3. Divide the time by ten to find the amount of time the string and mass to make **one** rotation. 4. Using the radius, find the circumference with the equation. 5. Because the circumference is equal to the distance around the circle, and you acquired the time previously, use the equation v=d/t to find the minimum velocity. media type="file" key="RABIN< KAINDE< BERGER< MOVIE OMG.mov" width="300" height="300"
 * Minimum V****elocity:**

DATA TABLES

CALCULATIONS Free Body Diagrams Minimum Tension Maximum Tension

Our first hypothesis, for the minimum velocity, stated that because the tension at this time is 0 and the radius remains the same throughout the experiment, the minimum velocity will stay constant as we alter the weight of the object. For our experiment, we decided to use a constant mass and radius, and swing the mass on a string slowly to see if we get similar results throughout the trials. As we expected, all of the experimental velocities came out to be around 3.456, which is all around the same value. Our theoretical velocity was equal to 1.98 m/s. In reality, we had many errors in this part of the lab. To be more exact to our hypothesis, we should have tested **many** different masses, rather than just the same mass and see if we get similar values. We do not doubt that our results would have ended up being very similar to our hypothesis and the different trials would have let us with values similar to each other, but we did not do that properly enough to get accurate results. For the maximum velocity, we hypothesized that decreasing the radius will decrease the time and velocity in the experiment. To test it, we first connected a piece of string to a force sensor and added masses one by one. At the point the mass broke, we were able to figure out the maximum tension of that piece of string, with which we could use those results to find the theoretical maximum velocity. As seen in our results, there was plenty of error in this lab. As always, we, as the people running the experiment, could have made a plethora of mistakes. Sometimes, we could have maybe not spun the mass in a constant rotation in the air, or slow enough or fast enough. Ultimately, this would have affected the time and the results found. WIth the minimum velocity, clearly, we did not do enough to prove our original hypothesis and could have gotten more exact results if we used our masses, not just a myriad of trials with the same mass. Measurements could have been off as well when measuring the length of the radius/ string. Also, when we were finding the maximum tension of the string and added masses on one at a time, we may have added to large of masses, and therefore, the results of the MAXIMUM tension were not as exact as they could have been. To fix these errors, we definitely should have completely thought up our procedure before we began. At some points, we definitely got a little confused, yet continued on anyway without stopping and evaluating what we should do that would have given us the most **valid and accurate** results possible. Also, we should have taken more time to measure each radius just to make sure everything seemed accurate enough and no unreasonable mistakes were made. We also could have spent more time on the minimum velocity and tried using **many** different weights, which definitely would have given us more to work with when seeing how our experimental results compared to the theoretical results.
 * CONCLUSION**

=Lab: Centripetal Force= GROUP MEMBERS: Alyssa Berger, Niki Kaiden, Rebecca Rabin CLASS: Honors Period 4 DATES COMPLETED: January 3, 4, 5, 2011 DATE DUE: January 7, 2011

OBJECTIVE Determine the relationship between the mass of an object and the tension of the attached string as it moves in a circular motion.

HYPOTHESIS and RATIONALE The larger the mass hanging at the end of the rope, the larger the tension the rope will have. The m** ore mass that is spinning will cause the rope to be pulled much harder on both sides in order to keep the mass moving in a circular motion. **

PROCEDURE Materials 1. Timer 2. Force Sensor 3. Centripetal Force Apparatus Kit 4. Masses 5. String

Set-Up and Methods 1. Attack force sensor to USB link and connect to laptop 2. Open DataStudio and Create New Experiment 3. Set y-axis to Force, pull positive ( N ); this can be done by hitting Setup and checking the appropriate box 4. Cut string approximately .5 meters and attach it to the hook on the force sensor 5. Attach a mass to opposite end of string 6. Spin mass 10 times in approximately 14.3 seconds to produce a constant velocity of 2.152 m/s 7. Repeat steps 5 & 6 using a variety of masses 8. Record data using DataStudio and Microsoft Excel

DATA Mass: 46.88 grams

Mass: 58.6 grams

Mass: 70.32 grams

Mass: 82.04 grams

DATA TABLE: The radius was found by measuring the length of the string the masses hung on. The forces were provided through the y- intercept given on data studio. We took the average of three trials to obtain the most exact result. SAMPLE CALCULATIONS Circumference: : Velocity: V= d/t V= 3.0772/1.43 V= 2.152 m/s

Created by Alyssa, Niki, & Rebecca (Honors Period 4)
 * GRAPHS **

Created by Danielle, Jae, & Jessica (Honors Period 4)

Created by Chloe, Justin, Steve and Andrew (Honors Period 2)

CONCLUSION Yes, our hypothesis was correct. As more mass was added to the apparatus, the more force was needed to keep it in motion, therefore there is a direct relationship between mass and force. As seen in our graph above, as our mass increased so did the amount of tension force being used to keep the mass in a constant speed and radius. There were many sources of error that could be found in this lab. For example, we assumed the length of the string was the radius but in reality the hanging mass did not make a perfect horizontal circle. Also, we only measured the y component of tension. To calculate the x component and total tension we would need to know the angle of the string. There was a systematic error in the lab when the amount of force kept on changing causing inaccuracy in each trial. One type of human error we calculated was when we were spinning the mass, we used our hand to do so, which could cause human error. A way to change the lab to decrease the amount of error is if we had some form of a apparatus that automatically kept both the speed and radius constant instead of depending on the speed of our hand, which is very unreliable. Most of this occurred because of the fact that this lab depended on our judgement and clearly our judgement is not as precise as an automatic machine would have been.