Roshni,+Allison,+Erica

= **__Moving in a Horizontal Circle__** =

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**Group Members:** Roshni Khatiwala, Allison Irwin, Erica Levine **Class:** Honors Period 2 **Date:** January 24, 2011

OBJECTIVE What is the relationship between the radius and the maximum velocity with which a car makes a turn?

HYPOTHESIS The maximum velocity is inversely proportional to the maximum radius that can turn in a circle. Based on the equation for velocity (V=D/T), we think that the smaller the radius (D) is, the greater the maximum magnitude of velocity (V) will be.

MATERIALS Record player, penny, timer, cardboard disk, tape, piece of wood, & roll of tape



PROCEDURE 1. Verify velocity of record player by counting the number of revolutions in a minute, and making sure it matches up with the claimed velocity. 2. Place the penny at varying radii of the record player. 3. Spin the penny on the record player at a constant velocity of 16 rpm (0.335 m/s) but varying radii. 4. Make sure that the penny makes the trip around the record without moving. 5. Repeat steps 3 and 4 with speeds 33 rpm (0.69 m/s), 45 rpm, and 78 rpm. 6. Record results in excel spreadsheet.

CALCULATIONS - Theoretical CALCULATIONS - Experimental

CALCULATIONS - Percent Error

OUR RESULTS- PART A: VELOCITY V. RADIUS What is the relationship between the radius and the maximum velocity on an unbanked turn?

PART B: VELOCITY v. RADIUS (BANKED) What is the relationship between the maximum velocity of a car rounding a banked turn and the radius of the turn?



PART C: BANKING ANGLE v. RADIUS What is the relationship between the banking angle of a roadway and the radius of the turn?



CONCLUSION __ From our pre-lab calculations we derived the equation v^2= µgR. From this equation we can should have been able to see that velocity and the radius have a direct square relationship, not an inverse relationship. From our graph we can see that as our velocity increased, the square root of our velocity did too.Therefore, our hypothesis was indeed correct. However, this relationship that we guessed and confirmed, does not hold true for banked turns. As we can see from Amanda's group's graph, an radius that is banked at a certain angle, actually holds the positive relationship. For their graph, while radius increased, maximum velocity decreased. We have concluded that this is due to the nonexistent of the angle factor in our equation. In order to account for a banking angle, an entirely different equation must be used, which means that the relationship between radius and maximum velocity is more liable to change.__ __ While our graph is accurate with a R value, we did have a 27% error between our theoretical and experimental velocity. This error is most likely due to the construction of our circular motion device. First, we were using an unreliable record player. While we did check to make sure that it was moving at the correct speed, we are unsure of whether it really remained at constant speed. Second, because there were not enough wooden disks, we were forced to use a cardboard replacement. This means that the µ value we used was not 100% accurate. Next, because our record player was not big enough to fit the cardboard disk, we had to tape the disk to a thick roll of tape in order for it to be able to pass over the sides of the record player. Finally, because the disk was not long enough for use to find the maximum radius for our smallest velocity, we had to tape a thin piece of wood to the disk in order to extend the radius far enough. This has potential to not only significantly change the µ value, but it could have also affected the velocity of the record player due to the extra weight. While these are most likely not the only sources of error, it is these flaws that we think caused the most error in our lab. In order to minimize the error, we would need access to more accurate equipment and we would need to acquire the µ specific to our own disk. __ __ This lab has many real life applications. It is important for professionals such a race car drivers, road designers, and car manufacturers to know the physics behind making turns. They can use this valuable information to set speed limits, make tires, and even design roads. It is extremely important for these experts to make these calculations so that way other people don't need to worry about something like whether or not their car will skid on a turn. __

=__**Maximum and Minimum Tension of a String**__= __ **Group Members:** Roshni Khatiwala, Allison Irwin, Erica Levine __ __ **Class:** Honors Period 2 __ __ **Date:** January 6-7, 2011 __

__ OBJECTIVE __ __ What is the minimum/maximum speed that can maintain centripetal motion in a string without it breaking? __

__ HYPOTHESIS __ __We think that with more mass, the velocity will be less when it reaches maximum tension. We think this because we know that their is a direct relationship between mass and tension, and also a direct square relationship between velocity and tension. For the minimum speed, we hypothesize that no matter what mass we use, the minimum speed is constant. Our pre-lab calculations explain our rationale for this portion of the lab.__

__MATERIALS__ __Force sensor, weights, clamp, mass hanger, string__

__ PROCEDURE (to find Maximum Tension) __ __ 1. Attach force sensor to computer. __ __ 2. Attach mass hanger to string. __ __ 3. Attach string to force sensor. __ __ 4. Clamp force sensor to table to prevent movement and increase accuracy. __ __ 5. Record tension as mass is added on (until string breaks). We found the maximum tension of our sting to be 5.5N after adding 0.557 kg. __ __ 6. Spin 0.020 kg on a 0.20m string in a vertically circular path at a constant speed until the string breaks. __ __ 7. Record the time for a single revolution and the experimental velocity of the mass. __ __ 8. Repeat Steps 6 & 7 with masses of 0.022 kg, 0.024 kg, and 0.025 kg. __

__ PROCEDURE (to find Minimum Tension) __ __ 1. Attach 0.005 kg to 0.20 m string and spin in vertically circular motion at constant speed. The mass should be spun as slowly as possible while still maintaining circular motion. __ __2. Record the time for a single revolution and the experimental velocity of the mass.__ __3. Repeat steps 1 & 2 for masses of 0.010 kg, 0.015 kg, and 0.020 kg.__

__ DATA __ __ Chart to find maximum force: __

Chart to find maximum velocity based on mass:

Chart to find minimum velocity based on mass:

SAMPLE CALCULATIONS

Maximum Tension



Maximum Velocity:

Minimum Velocity:

Percent Error - Experimental vs. Theoretical Maximum Velocity

Percent Error - Experimental vs. Theoretical Minimum Velocity

CONCLUSION__ During this lab, our objective was satisfied and our experimental results validated our thesis. We hypothesized that as mass increased, the velocity at maximum tension would decrease too. First, we found maximum tension by hanging as much mass from the string until it broke. Since velocity was zero, the entire first term of the equation cancelled out and the tension in the string equalled the mass. Our string broke when we added .557 kg, indicating that the maximum tension in our string was .557 N. We then used this value of maximum tension to investigate the relationship between mass and velocity at maximum tension. Our results indicated that as mass increased, velocity at maximum speed decreased. We know our results are fairly accurate because they are very similar to our theoretical velocity. Based on the statistics in our chart above, we can conclude that our hypothesis was correct; as mass increased, velocity at maximum tension decreased. In addition, we hypothesized that varying mass would have no effect on velocity at minimum tension. When we changed the masses during our experiment for minimum velocity, the theoretical velocity stayed the same, and all of our values for experimental velocity were fairly close. This data proves our hypothesis correct. Furthermore, the nature of the equation we used to find velocity, V=sqrt(Rg) validates this conclusion. Since mass is not present in this equation, changing it will have no effect on the resulting velocity. Contrastingly, if we were to change the radius, we would see changes in velocity at minimum speed because the variable for radius is represented in the minimum velocity equation. Although our experimental results were fairly accurate in comparison to our theoretical results, there were still many sources of error in our experiment. Foremost, when measuring to find maximum tension of the string there was great diversity in our trials. For example, in one trial our string broke with .4 kg, for another it broke with .537 kg, and for another it broke at .557 kg. We chose .557 N as our maximum force because it was the trial in which we added the masses most gradually and in the smallest increments. Error in our experiment may have stemmed from this dilemma. In addition, inaccurate timing is likely to have contributed to our error. It was difficult to start timing exactly when we reached a //constant// max or min velocity, and also to record the time fast enough before the string broke. If our numbers for time were faulty, we are likely to have error in our results. Lastly, there was no way for us to tell if we were moving at exactly maximum or minimum speed during the experiment. We could only make observations and guess. If we weren't spinning at exactly the right velocity, our results would be erroneous. The experiment that we conducted about maximum velocity at maximum tension is applicable to upside-down roller coasters. When a cart is at the top of a roller coaster, the centripetal force is maximized. Engineers have to decide on a velocity for the roller coaster that will keep passengers safe. If the velocity passes a certain value, force will exceed its maximum value and the ride will fly off the tracks, resulting in many deaths and injuries.

= = =Uniform Circular Motion and Gravitational Motion Lab=
 * Group Members:** Roshni Khatiwala, Allison Irwin, Erica Levine
 * Class:** Honors Period 2
 * Date:** January 3-4, 2011

PURPOSE We are attempting to find the relationship between the mass an object and the tension of the string as it moves in circular motion.

HYPOTHESIS The greater the mass of the object moving in circular motion, the greater the tension in the string will be.

PROCEDURE 1. Attach 0.25m string to force sensor. 2. Attach 20g mass to opposite end of string. 3. Spin mass 10 times in a period of approximately 6 second, producing a constant speed of 2.616 m/s. 4. Repeat Steps 2 & 3 with 40g, 50g, 70g, 90g. 5. Record data in Microsoft Excel and make graph showing the relationship between mass (g) and tension (N).

MATERIALS We attached **masses** to one end of the **0.25m string**. We then attached this to a **force sensor**. We also used a **timer** to help us maintain constant speed.

DATA

Mass: 20g

Mass: 40g



Mass: 50g



Mass: 70g



Mass: 90g

DATA TABLE



SAMPLE CALCULATIONS

GRAPH



CONCLUSION
 * In this lab we satisfied our purpose to discover the relationship between the mass of an object and the tension of a string as it moves in constant, circular motion. Our hypothesis was correct: there is a direct relationship between mass and tension. As seen in our graph, as the mass increases, so does the tension. As the mass decreases, so does the tension. We experienced some error during this lab (as seen by the imperfection in the above graph) for many reasons. First, because we spun the mass ourselves, we had to account for that human error. It is impossible for anybody to be able to spin the mass in a perfect, level circle... especially while maintaining constant speed! This means that our radius was slightly less than the 0.25m string that we had measured out. Also, while we attempted to maintain constant speed by completing ten revolutions of the mass in approximately 6 seconds, there was most likely a minimal variance in velocity; however we were unaware of this error because, while the timer said 6 seconds, we had not accounted for our reaction time when stopping the timer. We also realized that the string was slipping back and forth on the force sensor. In order to deal with this obvious source of error, we used a small piece of tape to secure the string better. We are unable to determine how this affected our results, but it was most likely another source of error. In order to assure that the mass was moving a perfectly-level circle at constant speed, we would need to use a machine. Also, in order to get more accurate force measurements, we would use more sensitive equipment than the ones were available. We would also need to assure that the string was not moving, but without the use of an aid such as tape, etc. While the factors discussed were all minimal sources of error, we were still successful in our goal. Therefore, while these inaccuracies are undesired, thankfully they did not affect our results too significantly.