Group4_4_ch5

toc =Centripetal Motion Lab (12/14/11)=

Part A: Rob Part B: Matt Part C: Poleway Part D: Matt


 * Objective:** "What is the relationship between system mass and net Force? What is the relationship between velocity and net Force? What is the relationship between radius and net Force?"


 * Hypothesis:** System mass and net force are directly proportional. In addition, velocity and net force are also directly proportional. On the contrary, radius and net force are indirectly proportional.


 * Material:** String, gray tube, rubber stoppers, force sensor


 * Method:** The string was put through the gray tube. On one end it was tied to a rubber stopper, and on the other end it was tied to a force sensor. The side with the rubber stopper was spun in a circle while the force sensor was held down. We changed mass, velocity, and radius to get our various results.

Net Force vs. Velocity
 * Data Table:**



Net Force vs. Mass

Net Force vs. Radius




 * We took Mrs. Burns' data for Centripetal Net Force vs. Radius because we did not have enough time to get to this experiment.



In our centripetal force v. velocity graph, the x axis is velocity, while the y axis is force. As velocity increases, so does the force. This graph is like a parabola, so the the velocity is actually being squared as the force increases. We had an R^2 value of 0.99919, which is very good and it shows that our graph was very accurate. It is safe to say that as velocity increases, so does the centripetal force. By looking at the equation, we can already know that velocity is squared just by looking at the v^2.



Our centripetal force v. mass graph was also a very good graph, with an R^2 value of .99936. The x axis is mass in kilograms, while the y axis is centripetal force. As the mass increases, so does the centripetal force, and this is a linear graph, showing a steady advance. The equation shows this, as the mass is alone and single without any exponents above it. It exemplifies the fact that Centripetal force is directly proportional to V 2.

The radius has a much different affect on the centripetal force than the mass and velocity do. By looking at the equation, you can tell right away that its going to be different, since its the denominator of the equation. This tells us that as the radius increases, then the centripetal force will go down. By looking at our centripetal force v. radius graph, its obvious that the centripetal force ( y axis) decreases, as the radius ( x axis) increases. This graph (courtesy of Mrs. Burns) exemplifies this. By looking at the graph, one could see that as the radius increases, the Centripetal force decreases by a certain amount: F α 1/r (Force is directly proportional to the inverse of r). The r^2 value is very accurate, .989, which shows that the results are extremely accurate.

All of our hypotheses were correct. Our first hypothesis said that mass and net force are directly proportional. Our results proved this because force did go up as mass went up. Our second hypothesis said that velocity and net force are directly proportional. We also proved this as force went up when velocity went up. This graph was in a parabolic shape and that can be seen in its equation, F=mv^2/R. This equation also shows that they are directly proportional because one can see that force would go up if velocity did. Our final hypothesis stated that radius and net force are indirectly proportional. Our results showed this as centripetal force got smaller as radius got larger. This can also be seen by the same equation, F=mv^2/R. This shows that radius and force are inverses of each other and therefore are indirectly proportional. We had good results in this lab, but there were still some sources of error. One source is that we only took 1 measurement for each mass, velocity, or radius. We should have taken three for each and then averaged them together, but we did not have time for this. Another source of error was the fact that it is impossible for a human to keep a constant velocity throughout. This would affect the force vs. radius and the force vs. mass graphs. This could be solved by getting a machine to spin it at a constant velocity. Another source of error is human error of the timer. It is impossible to measure the exact time, so more than one person could time it and you could find the average to get a more accurate time. Another solution to this problem could be to get a machine timer.
 * Conclusion:**

=Minimum Speed Activity (12/19/11)= FBD: mass: 50g

Theoretical Calculations:

Experimental Velocity:

Data:

Class Data:

Percent Difference: Percent Error:



Conclusion: There are some sources of error that caused our percent error to be so high. It was 42% mainly because of human limitations. First, it is impossible to make the it go at the minimum velocity and still have it go in a circle. Therefore, the velocity was faster than it should have been. Another reason is that tension is lowest at the top of the circle, but we measured the whole circle. Two other sources of error are the fact that one can not make it go at a constant speed and that the circle was not completely vertical. This caused angles and slightly changed the data. All of these things combined to make our percent error very high. The only way to truly do this would be to get a machine that spins it at the perfect speed and angle.

=Moving in a Horizontal Circle= Part A: Robert Kwark Part B: Matt Ordover Part C: Michael Poleway Part D: Robert Kwark

Objectives:
 * 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: As radius increases, the maximum velocity with which a care could make a turn also increases; I have experienced this while driving my car. I can take wider turns faster than sharper turns. The presence of banking would allow a higher maximum speed to be reached than a turn with no banking with the same radius. This is because of the added component force of friction pointing toward the center of the circular motion; I have experienced this while running track at the Armory in NYC, which has banked turns. Because of this, the Armory is considered one of the "fastest" tracks in America. Finally, the higher the banking angle, the higher the maximum velocity. This is because there is a larger component of friction that enables a car to go faster without flying off the road.

Method and Materials: The materials available are a rotational turntable, a power supply, a photogate, a mass (metal ring), a banking angle, and a metric ruler. First, attach the photogate timer to the computer and open Datastudio. Set Datastudio as "Recordable Timer." Then, place the ring onto the turntable and turn on the power supply. While the turntable is rotating, record the time it takes to make one rotation using the "Time between Gate." Increase the voltage little by little, leaving time in between each increase to allow the turntable to get up to speed. When the mass finally shifts, stop recording the data and use the period before the mass slid off. Repeat this seven times and record your results on an excel spreadsheet.

media type="file" key="Movie on 2012-01-06 at 11.55.mov" width="300" height="300"

“//Which value do you want to use and why?//” We want to use the "Time Between Gates" value because as the object moves around in a circular path, the time it takes to get around would be much greater than the time it spends in the gate. Thus, it would give us a more accurate and complete value for the period.

Individual Data:

Class Data:

Average class µ value: 0.5511

Graph: Discussion: 1. Discuss the shape of the graph and its agreement with the theoretical relationship between R and v. The shape of the graph is a power graph.In the equation y=Ax^B, B means that velocity is directly proportional to the square root of the radius, which appears as the 1/2 power above the x. As the radius increases, so does the velocity. A means the square root of (mu)*g.

Percent Error of exponent: Experimental: 0.5 Actual: 0.4784

2. Derive the coefficient of friction between the mass and the surface.

3.Compare your coefficient of friction with that of all groups doing this lab. (Be sure to post a data table with the class values.
 * Radius (m) || Experimental µ ||
 * 0.1 || 0.585 ||
 * 0.15 || 0.541 ||
 * 0.2 || 0.529 ||
 * 0.25 || 0.578 ||
 * 0.3 || 0.559 ||
 * 0.35 || 0.518 ||
 * Average || 0.5512 ||

Compare your µ with the value derived from the graph (% Difference)

-Our percent difference was 13.8, which is a decent value. However, this shows that there were definitely significant sources of error.

Compare your µ with the average of all groups doing this lab (% Difference)

Our % difference was good at 4.9 %, meaning that maybe our results weren't all that bad after all. This means we were only 4.9 % off from the rest of the class.

4. A “car” goes around a banked turn. a) Find an __expression__ for its maximum velocity, in terms of variables only.

b) 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? The equation would be much like the one above, except it would have to account for the angle measures and force components. The maximum velocity would be larger, so the coefficient of A would be larger. This is because the normal force of the ground would help keep the mass in circular motion. The y values for each x value would be higher, so the graph would be steeper.

Conclusion: Our first hypothesis was indeed proven true by this lab. As the radius increased, the maximum velocity with which a car could turn also increased. The radius vs. velocity graph that we created with our data indicates this; as the radius increases, the velocity also increases. We found that the max velocity is directly proportional to the square root of the radius. In the equation y=Ax^B, the B value would signify the square root, which would be 0.5. Our value of 0.4764 was almost perfect, showing that our results were very valid. In the same equation, A signifies the square root of µ x g. Our other two hypotheses were not experimentally tested, but by deriving the equations through the discussion questions we were able to conclude that our hypothesis were indeed correct; that banking would allow a higher max velocity at the same radius, and that the higher the angle the higher the max velocity. Once we solved for the value of µ, which was .508, and compared it with our own experimental value, .578, we found that there was a percent error of 13.8%, which is absolutely awful. When we compared that value to the class's average experimental value of .551, we found that the percent different was 13.8%, which is a little better. There were several sources of error, yet although our percent error was bad, as you never want it above 10%, our percent difference was acceptable. We had a percent difference of 4.9 %, and although if it could be higher, it was still a good value. This means we weren't too far off the other groups' results, despite a somewhat bad percent error.

There are many possible sources of error. A main source of error probably came from the increasing of voltage. At first, we didn't realize that the turntable needed a few seconds to adjust to and increase in voltage, so we just cranked it up until the metal mass moved. Then we did it correctly, using small increments of increase and waiting for the turntable to catch up. But still, even then it was not perfect, as sometimes we increased the voltage a little too rapidly. Another source of error was the placement of the mass. Although we may have placed it very close to the exact radius, we did not place it exactly at the 25 cm mark and we certainly did not place it in the exact same position every time we did a trial. This would have contributed to inconsistency in trial data as well as our overall data because a change in radius would definitely cause a change in maximum velocity. A third source of error would have been human timing error. Because it takes time for neurons to travel and signal our response (reaction time), there would be a delay in the timing, which would affect our results. But even more importantly, if the mass moved just as it, then we had to use the period from almost one period before, which would certainly be slower than the actual speed the mass was moving at the time it flew off the turntable.

This activity can be applied to many other aspects in everyday life. For example, a sprinter in indoor track running around a curve moves at a slower rate than when he/she runs around a straightaway because he/she exerts some of the force that would be used to propel him/her forward so that she could make the turn without going out of his/her lane. This means that his/her speed is limited by the radius of the turn. Another scenario is while turning around a corner while driving. If the car exceeds the maximum limit for which the car can make the turn, it will go out of the lane and probably get into an accident.