Hallowell,+Siegel,+Dember,+Pontillo

=Lab: Moving in a Horizontal Circle= toc By Chris Hallowell, Ross Dember, Bret Pontillo, and Scott Siegel Period 4 Due: 1/21/11

OBJECTIVES: Find the relatio﻿nships between banking angle, radius, and maximum velocity, along with how banking changes the radius and different banking angles alter the radius when maximum velocity is reached.

HYPOTHESIS: **1. The relationship between banking angle and radius is inversely related, most likely due to the equation .** 2. Without banking, the relationship between maximum velocity and radius is proportionally squared, this comes from the equation. 3. With banking, the relationship between radius and max velocity and radius will be inversely related as the presence of an angle introduces a gravitational force into consideration. MATERIALS: 1. Record Player 2. Disc 3. Velcro blocks with various angles 4. Timer/Stopwatch 5. A penny 6. Laptop

PROCEDURE: 1. Gather necessary materials 2. Have one person use a stopwatch to time the number of revolutions the record player makes per minute at constant speed. 3. Record gathered information from step 2 4. Use a protractor to calculate the angle measures for each of the velcro blocks 5. Place one of the blocks on the record player, with the penny on top of the wedge 6. Spin the record player while adjusting the radius to find the largest radius that the penny can be at without falling off of the edge of the velcro wedge 7. Run about three trials for each wedges 8. Repeat steps 5 and 6 for each of the wedges   PHOTO OF SET-UP:

DATA:
 * Trials (Radius)**
 * This data table was used to record our trials for each angle. We were recording the radius.


 * Banking Angle vs. Radius**
 * This data table was used to create our graph. We can see in this data table that as the angle is increased, the radius is decreased. We also kept the velocity and the coefficient of static friction the same. We got our coefficient of static friction from the group of Ani Papazian, Rachel Caspert, Sammy Wolfin, and Ariel Katz in Period 2.

CALCULATIONS: We first wanted to calculate the constant speed of the spinning platform. The given data as well as the calculation for the speed is shown below.

We also calculated a theoretical radius using one of the angles from our lab. First, we have a free body diagram and a force body diagram illustrating the situation.

We have our given data as well. We got our velocity from the calculation above. As stated before, we got our coefficient of friction from the group of Ani Papazian, Rachel Caspert, Sammy Wolfin, and Ariel Katz in Period 2.

We then used this information to get 2 equations for "N".

We then combined these 2 equations above in order to create one equation we could use. That is shown below. We then plugged in our given data in order to find the radius.

We then calculated the percent error for this trial. The calculation is shown below.

GRAPHS:
 * This was our group's graph. As you can see, the banking angle is inversely proportional to the radius because as the banking angle increases, the radius decreases.


 * This was the graph of Jae Li, Danielle Schimmenti, Jessica Tucker in Period 4. As you can see, the velocity and radius are proportionally squared.

Courtesy of Emily, Emily, Elena, and Amanda. This shows, for the most part, an inverse squared proportion between velocity and radius on a banked angle.

CONCLUSION:

Our hypotheses proved to be correct. For the part we did, comparing the banking angle with radius, our results showed an inverse relationship, exemplified by our graph's negative linear slope. Furthermore, for our second hypothesis, another graph proved it correct, also, as it has a parabolic shape, making it squared proportional. We were correct in hypothesizing that the equation showed that the two were squared proportional, as the values increased in a squared proportion. Our final hypothesis was mostly correct, as the graph has a negative exponent, so it is inversely proportional, only it the proportion is squared.

Our lab trying to find the relationship between the banking angle with the banking had the opportunity for major sources of error. A large source of error could be that the penny was very light and there was not a lot of friction between it (the penny) and the ramp/ bank. So it was difficult for the penny to just stay on the ramp. A way this problem could be corrected in the future would be to use a heavier object or to use something with larger static friction. The larger friction will keep the object from sliding too much and be able to stay on the banked ramp. Some error might have come from the changes in wood blocks, which could have slowed down the record player. The error in that is that it could have possibly slowed down the velocity by adding more weight to it and thus not keeping the velocity constant. Also the blocks were on velcro which seemed to be unbalanced, this combined with the low static friction between the block and the penny could have caused the penny to fall off during the rotations of turn table. Then that would have affected the point where max velocity can be reached between the bank angle and the radius.

This lab's main applications occur while driving. For example, if a NASCAR driver on a racetrack sees a banked turn ahead, he will obviously want to go at the highest velocity he can, so knowing his speed, he would want to make a tighter turn if it was steeply banked, or go out a little wider if it was more of a narrow banking angle. Furthermore, if the racetrack had no banked turns (or it was a driver doing making full-speed turns in an empty parking lot) the driver would have to take into account that the faster he drives, he will have to make a wider turn, and he should also realize the increase or decrease in the radius of his turn will be fairly drastic due to the relationship of the intervals. Finally, when approaching the banked turn, a driver who knows the angle and is familiar with physics can use this to his advantage, and alter his turn to ensure he is reaching the highest possible maximum velocity. NASCAR may be a “sport” loved in the South, yet its use of horizontal circle motion and banked turns can be appreciated by scientists from all over.

= = =Velocity of a Vertical Circle Lab=
 * By Chris Hallowell, Ross Dember, Bret Pontillo, and Scott Siegel**
 * Period 4**
 * Due 1/10/11**

HYPOTHESIS: The maximum velocity will be inversely related to the length of the radius. This comes from the fact that velocity is directly related to force, and with the equation: the radius is inversely related to force, thus velocity and radius should be inversely related. For minimum velocity, it will be squared proportional to the radius, as minimum velocity's equation is:, so as "g" remains the same, the minimum velocity will rise in a squared proportion of the radius.

OBJECTIVE: The objective of this lab was to figure out what effect certain variables had on an objects maximum and minimum velocity in a vertical circle. One of the variables that we tested was the affect of the objects mass on its maximum and minimum velocity.

MATERIALS: For this lab, you will need to gather the following materials: 1. Laptop 2. Timer/Stopwatch 3. String 4. Scissors 5. A roll of tape 6. Meter stick 7. Various small weights (10-100g)

PROCEDURE: Part 1: Finding the Maximum Tension for the String NOTE: Use the same length string as you will in the other experiments. The radius needs to be constant. 1. Tie a smaller mass to one end of the string 2. Swing the mass around in a vertical circle at a constant speed until it breaks 3. Record the number of revolutions that were required to break the string at a certain time, recorded with a stopwatch 4. Repeat steps 2 and 3 about three times for each mass 5. Repeat steps 1-3 several times with at least three different masses in order to maximize accuracy of the experiment

Part 2: Finding the Maximum Velocity at the Bottom of a Vertical Circle NOTE: Use the same length string as you will in the other experiments. The radius needs to be constant. 1. Cut a piece of string to a desired length (radius length) 2. Experimentally, measure the tension of the string 3. Tie one end of the string to a ring stand, and the other end to a hanging mass 4. Continuously add mass to the string until it breaks 5. Once the string breaks, record the mass that was required to snap the string 6. Repeat steps 3-5 several times to maximize accuracy of the experiment

Part 3: Finding the Minimum Velocity at the Top of a Vertical Circle NOTE: Use the same length string as you will in the other experiments. The radius needs to be constant. 1. Cut a piece of string at a desired length 2. Tie a certain mass to one end of the string 3. Record information from steps 1 and 2 4. Swing the chosen mass, vertically, in a circle at the slowest possible velocity with constant speed 5. Count the number of revolutions that the mass makes in a desired time (i.e. 10 seconds) 6. Repeat steps 4 and 5 several times to maximize the accuracy of your results 7. Change the mass, once steps 1-6 are complete 8. Repeat steps 1-7 several more times

PHOTO OF PART 1:

PHOTO OF PART 2:

PHOTO OF PART 3: DATA:
 * We used 4 significant figures for all of our data tables.

Part 1

Part 2

Part 3

CALCULATIONS: Part 2 For Part 2, we needed to find out the theoretical maximum velocity. Below is a force body diagram and the data known before starting the calculation. The maximum tension was found earlier in the lab.

We then used our given data to solve for the theoretical maximum velocity. We used this same method to solve for our experimental velocity.

We also wanted to know how many seconds it would take to go one full revolution. We first solved for circumference using our radius and then we solved for the time.

We also wanted to know what the percent error was between our experimental maximum velocity and our theoretical maximum velocity. The calculation is shown below.

Part 3 For Part 3, we needed to figure out the theoretical minimum velocity. Below is a force body diagram and the information that was known before starting the calculation.

We then used the information above to solve for minimum velocity. We used this same method to solve for experimental minimum velocity.

We also wanted to know how many seconds it would take to go one full revolution. We first solved for circumference using our radius and then we solved for the time.

We also wanted to know what the percent error was between our experimental minimum velocity and our theoretical minimum velocity. The calculation is shown below.

CONCLUSION: Our hypothesis did prove to be partially correct. The numbers we got through calculations were backed up through our experimental values, such that our minimum velocity did increase as our radius did, just as we stated. For Part 2, maximum velocity, we needed continually had to change the length of the radius, as the greater the length, the greater the velocity was needed, which made it difficult as a lot of force had to be applied to the spinning to make it actually snap. Thus, this experiment relied a lot on experimental values and calculations, as it was difficult to get the exact values from the experiment due to a myriad of subjective decisions such as deciding if the string was not slacking or at minimum velocity and having normal difficulties spinning a string at an extremely high velocity. There were multiple sources of error associated with this lab. One is that the rope used might not be the same each time. By that I mean, the rope could be tighter or more worn each time used. The problem with that is that the string could break at higher/ lower tension, with a different minimum or maximum velocity. The period could not be 100% correct because of human error it cannot get the precise times to which the spinning started and the rope snapped.

This lab has real life implications, especially in an integral part of society, amusement parks. If designing a roller coaster that spins in vertical circles, an engineer, just as we did, would have to see how much a centrifugal force could support at most, before deciding the maximum velocity, so that the ride does not go off the tracks. Likewise, if the designer wanted the roller coaster to just make a complete circle, he would have to find out the theoretical maximum the radius of the circle to know the smallest possible value for the minimum velocity. Below Therefore, whether the roller coaster is a force body diagram and the data known before starting the calculation. The maximum tension was found earlier in the lab. We then used our given data to solve for the theoretical maximum velocity. Part 3 CONCLUSION: going through loops at high rates of speed, or giving a dramatic effect of a slow loop, knowing the relationship between velocity, centripetal force, and radius will exponentially increase the enjoyment of a roller coaster.

= = =Centripetal Force Lab=
 * By Chris Hallowell, Ross Dember, Bret Pontillo, and Scott Siegel**
 * Period 4**
 * Due: 1/7/11**

MATERIALS: For this lab, we used a Force Sensor, rubber stopper, string, meter stick, stopwatch, tape, and several masses.

HYPOTHESIS: Mass will be directly proportional to force as keeping the both the speed and radius constant, there would need to be more force to pull the objects as they increase in mass.

PROCEDURE: 1. Gather necessary materials. 2. Shorten string to desired radius. 3. Measure length of string. 4. Attach rubber stopper to the end of the string as a mass. 5. Tape opposite end of string to the force sensor. 6. Plug force sensor into a laptop, and open Data Studio. 7. Formulate graph in Data Studio with first mass rotating at a constant speed. 8. Run 3 different trials for each mass. 9. Repeat steps 7 and 8, adding masses with intervals of 50g to the rubber stopper. 10. Keep ALL trials for each of the different masses at a constant velocity.

PICTURE OF SET-UP:

DATA TABLE:
 * Mass Changing, Radius Constant, Speed Constant[[image:Screen_shot_2011-01-06_at_10.52.47_PM.png]]**
 * Our table shows the data found when we kept the radius and speed constant, but changed the mass. The bottom part of the table shows each of the three individual trials for the five different masses. We then averaged the three trials together to get an average force for each mass. We then transferred these averages to the top part of the table. We used the mass column and the average force column for our graph. For our table, we decided to use three significant figures.

CALCULATIONS: The calculation we performed in our lab was the calculation for the speed of the mass. We were able to find out that the length of our string was .36 m. We also figured out that we could swing the mass 18 revolutions in 10 seconds relatively consistently. This was the information we started with in our calculation.

We then found out the circumference of the circle that the mass traveled as it made a revolution.

Finally, we used our circumference as well as our original information to find out the speed of the mass.

GRAPHS:
 * Our Graph


 * Graph by Tom McCullough, Tyler Samani, Richie Johnson, and Rory Vanderberg


 * Graph by Jessica Tucker, Jae Li, and Danielle Schimmenti

CONCLUSION:

Our hypothesis was correct, shown by our graph between mass and force. As mass went up, force went up at a constant rate. For further proof, Scott found the larger masses to be more difficult to spin at the constant speed, so he would have to use more force on the string. The two other variables had different relationships with force. For velocity/speed, it was directly squared proportional, shown in the graph's parabolic shape since the greater velocities led to a dramatic increase of force. In terms of radius, it was inversely proportional to force, since, keeping other variable the same, it requires less force to spin an object with a longer radius. Furthermore, all these relationships could be solved with the equation:. Mathematically, as mass increases, force will increase at a proportional rate; as velocity increases, force will increase at a squared rate, as the value for velocity is squared; finally, as radius is in the denominator, the greater its value will proportionally decrease force.

Although our lab produced great results there were multiple sources of error. The first piece of error was the trouble of keeping velocity constant. What we did to try to keep velocity constant was try to keep a consistent 18 revolutions per 10 seconds. The problem is since it is being spun by a person’s hand there was some acceleration and deceleration. Since we were trying to keep velocity and radius constant to see how the change in mass affects force, a non- constant velocity will alter our results. A way to keep velocity constant would be to use a mechanical machine that would spin at a constant rate. Another source of error is that the circle may not be horizontal along the x-axis. When the circle is not horizontal along the x- axis, we do not take into account the angle, which is created. This alters the data because it creates a Tension on the y axis along with one on the x axis. So the sensor being used is not measuring the Tension along the x-axis. Once again, a mechanical machine spinning the string from a center spot would possibly keep a constant velocity while doing its best job to keep a horizontal circle.

This lab has many uses in real-life, especially in the sport of track and field. Two of the throwing events, the discus and hammer throws, require athletes to rotate in a circle to generate power before releasing their object in a projectile. As there are different implements for different competition levels, an athlete that is moving up from the high school level to the collegiate one (thus using a discuss or hammer with greater mass) would need to apply more force on the hammer or discuss to achieve the same speed that he or she did while in high school. Likewise, the graphs also show that an athlete with longer arms can apply less force than a competitor with shorter arms, yet still generate the same speed. If two athletes were to have the same arm lengths, whoever could generate the most force would see a significant improvement in the speed he or she could generate. With this physics information, supportive genetics, and undetected performance-enhancing drugs, an athlete could be an Olympic champion.