Group2_4_ch5

toc Group 2 Members: Tim Hwang Ryan Luo Noah Pardes

=__**Swinging Stopper Lab (12/13/11)**__= __12/13/11__ Noah Pardes-A Ryan Luo-B Tim Hwang-C Maxx Grunfeld-D

__**Objective:**__ Our objective in this experiment is to find the relationship between the centripetal force of a system and the system's mass, radius, and speed.

__**Hypothesis:**__ We believe that mass and centripetal force are directly proportional, so when one variable increases, so does the other. Also, we believe the radius and the speed of the system are also directly proportional to the centripetal force.

__**Method and Materials:**__ To start this lab, we must first obtain a long piece of string, a rubber stopper, a black tube, and a force reader. After that, we created the contraption we are going to use for the experiment by threading the string through the black tube, tying the rubber stopper on one end, and tying the force reader on the other end. Finally, we had someone holding the force reader on the ground while another person moves the black tube in a circular motion, causing the rubber stopper to accelerate and move centripetally. The data that is recorded then goes into data studio and is recorded as data for the lab.

__**Video:**__ media type="file" key="String Lab Video.mov" width="300" height="300"

__**Table:**__ //Changing System Mass//

//Changing Velocity Data//

//Changing Radius Data (Ours)//

//Changing Radius Data (Ideal)//

__**Graph:**__ //Changing System Mass Graph//

//Changing Velocity Graph//

//Changing Radius Graph (Ours)//

//Changing Radius Graph (Ideal)//

__**Excel Spreadsheet:**__

__**Analysis:**__ Our first graph is a graph of centripetal force vs mass. The slope of this graph comes from v 2 /R since the "x" value is mass and the "y" value is centripetal force for all of the graphs. The data we collected shows that as the mass increases, the centripetal force also increases. This means that they are inversely proportional to one another. Our R2 value is .916 which is good but not the best R2 value that we could have gotten. In the second graph, we see how velocity interacts with centripetal force. In this graph, the "x" value is v 2, the "y" value is the centripetal force, and slope is equal to the m/R. This graph takes on a parabolic shape because the velocity is squared. Our R2 value is .997 meaning our data is very accurate. One can tell from that graph that as one spins the system mass faster, the greater the centripetal force will be. For out third graph, we see how the radius interacts with the centripetal force. Our data was not correct so we used that data that was given to us. The ideal graph has a hyperbolic shape to it. The"y" value is centripetal force and the "x" value is the radius. As the radius increases the centripetal force decreases. This means that they are directly proportional.

__**Conclusion:**__ In this lab, we observed the relationship between mass, velocity, radius, and centripetal force. In our hypothesis, we said that the centripetal force was directly proportional to all three other variables: the mass, velocity, and radius. In this experiment, most of our hypothesis was proved correct; however, some of our graphs were inaccurate. As the mass increases, so does the centripetal force, which is shown accurately in our first graph which is linear. For the graph of centripetal force vs. velocity, the graph we constructed had a positive exponential fit which is what it should be. This is because the net centripetal force is directly proportional to the velocity squared. Lastly, the graph of centripetal force vs. radius was inaccurate. We constructed a positive exponential graph while it should be negative. This is because the centripetal force is directly proportional to 1/radius, or inversely proportional to the radius. Therefore, we had to use the class data to show the proper results that should be obtained from the relationship between the centripetal force and the radius. Like all other labs, there are several sources of error that may be the cause of any deficiencies or inaccuracies. The circular motion of the string was difficult to maintain exactly the same each time. This is due to possible alterations of speed and radius, although unintentional. If we were to redo this lab again in the future, I would use more specialized equipment to ensure that nothing was being changed and that the radius and speed would stay the same the entire time, rather than be prone to human imperfection.

=__**Swinging Stopper Activity (12/19/11)**__=

__Theoretical:__ ∑F=ma T+W = (mv 2 )/R mg = (mv 2 )/R 9.8 = v 2 /1 v = 3.13 m/s

__Experimental:__ Sample Calculation: v = 2πR/T v = 2*1*π/1.38 v = 4.55 m/s

Trial 1: 10 Revolution = 13.76 s 1 Revolution = 1.38 s v=4.55 m/s

Trial 2: 10 Revolutions = 13.63 1 Revolution = 1.36 v=4.62 m/s

Trial 3: 10 Revolution = 13.41 s 1 Revolution = 1.34 s v=4.69 m/s

__Percent Error:__

Percent Difference: Percent Difference = ((average experimental-experimental)/average experimental)*100 ((4.88-4.62)/4.88)*100 = 5.33%

__Conclusion:__ There are several factors that could have caused such a high percent error of about 50 percent. Theoretically, the velocity would have been constant; however, since we were just approximating and trying to keep the speed constant, it's likely that it changed throughout rotations. Therefore, the results would be impacted by this error. Additionally, we assumed that the mass was moving at the slowest possible speed with the least amount of tension, thus in our calculations tension was set to equal zero. But, it's possible that it could have moved at a much slower rate, and therefore the tension we created in the activity was not in fact zero, which would have made our results incorrect as well.

=Circle Friction Lab= 1/5/12 Ryan Luo - A Timothy Hwang - B Noah Pardes - C Timothy Hwang - D

__**Objective:**__
 * 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:**__
 * 1) Max velocity and the radius is directly proportional to one another because as the radius gets larger, the car must go faster in order to match the period if the radius was smaller and there is also more room for the car to make the turn.
 * 2) Banking causes the maximum velocity to increase when compared to radii of the same length when the curve is not banked.
 * 3) With a changing banking angle, the radius gets smaller. As the angle gets steeper, the car goes faster

__**Equations:**__

__**Variables:**__ Which value do you want to use and why? A group would want to use "Time in Between Gates" because this gives the period since the time in the gate is negligible since the rod that the photo gate is detecting is so small.
 * //Variables// || //Constant or Variable// || //How to Acquire information// ||
 * Radius || measurable || Measuring with meter stick / measuring tape ||
 * Angle || measurable || Protractor ||
 * Time || measurable || Stop timer ||

__**Method and Materials:**__ The things that we need to start the lab are a metal washer (mass), a turn table, a power supply, a photo gate, and metric ruler. Each group is given a radius from 10 cm to 40 cm. Our radius was 15 cm. So we first put our mass on the turn table after measuring 15 cm from the center of the turn table. The turn table is connected to the power supply and to the computer to record the "Time in Gate" and the "Time in Between Gate". We click start and turn on the power supply and increase the voltage by about .1 each time. We wait a little before increasing again but we repeat this process until the mass falls off the turn table and we stop the trial. We record the "Time in Between Gate". We repeat this process until we have finished 8 trials.

__**Video:**__ media type="file" key="Movie on 2012-01-06 at 11.19.mov" width="300" height="300"

__**Data:**__ __**Graphs:**__
 * Yellow section represents our results

__**Link to Excel Spreadsheet**__ __**Analysis:**__ The graph is a power fit graph. 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. 1) Derive the coefficient of friction between the mass and the surface. 2) Compare your coefficient of friction with that of all groups doing this lab. (Be sure to post a data table with the class values.)
 * 1) Discuss the shape of the graph and its agreement with the theoretical relationship between R and v.
 * 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 || 0.551 ||

3) A “car” goes around a banked turn. 1) Find an __expression__ for its maximum velocity, in terms of variables only. 2) 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? In terms of the equation, it would be very similar to the one above, except you would also have to take into account the angle of the banked curve. In terms of the graph, banking decreases the value of the radius or increases the value of max velocity. This would make the value of A much bigger, and the y values of the graph (max velocity) higher for the same given radius. With this logic, it makes sense that the steeper the banking angle you can go even faster with the same radius. Also, as the equation shows, the numerator increases as denominator decreases, making a double case for a higher max velocity.

__**Conclusion:**__ We hypothesized that the radius and the maximum velocity were directly proportional; in other words, as the velocity increases, so will the radius, and vice versa. Our personal as well as the class results both support this hypothesis, but a little more precisely, for the radius is actually directly proportional to the //__**square root**__// of the velocity. This is portrayed by our graph: as the radius increases, do does the velocity at which the mass will turn. The graph's equation is y=2.241x .4761, which is a power function, following the equation y=Ax B. The "y" value represents maximum velocity, the "A" value (2.231) represents the slope, which is the square root of µ*g, the square root of the radius is the "x" value, and B represents the power of the radius. This theoretical value is 0.5, since we are trying to get the square root of g*µ*R. Our value for this, however, was slightly less.This can be due to multiple possible areas of error. Overall, our results were pretty accurate. Some of there areas of error was the turn table itself. The wheel underneath the turn table that helped it spin would take a while to spin. In the beginning, we had to set the voltage of the motor to about 7 before it actually started to move. Until we fixed it, it would start to move at about 4 volts. Also, since we did not actually measure out 15 centimeters and estimated, the mass may not have exactly been at 15 cm. Also, when the person working the motor said stop when the mass fell of the turn table, the person working the data studio may not have stopped the trial right when the other person said stop. Using a different program that has the ability to somehow stop automatically as the mass begins to move could prevent this source of error in future trials. This lab activity can be applied to everyday life in many ways, driving in particular. This is because when approaching a curve in the road, or needing to make a turn, each vehicle has a maximum velocity for which it can make this turn successfully. Therefore, the driver must not go too fast, or else he or she may spiral out of control; this is exemplified in this activity, for once the mass reached the maximum velocity, it flew off of the turntable. Also, banked turns are present when exiting a highway.