Group5_4_ch5

Group 5: Maxx Grunfeld, Gabby Leibowitz, Stephanie Wangtoc

=**__Finding Minimum Velocity Activity__** =

**__FBD__**

**__Data__** (10 cycles each) Average time for 1 cycle = 1.1548 s.
 * Trial || Time(s) ||
 * 1 || 11.73 ||
 * 2 || 11.19 ||
 * 3 || 11.18 ||
 * 4 || 11.92 ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">5 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">11.75 ||

<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">Avg. Velocity (m/s) || <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">Period 4 <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">Avg. Velocity (m/s) ||
 * || <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">Period 2
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Class Data || <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">5.16 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">4.27 ||
 * || <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">4.63 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">4.76 ||
 * || <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">5.97 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">4.62 ||
 * || <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">4.01 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">5.44 ||
 * || <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">5.61 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">6.04 ||
 * ||  || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">4.47 ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Average || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">5.08 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">4.88 ||

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**__Sample Calculations__** <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;"> <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Theoretical <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;"> <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Actual <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Percent Error

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;"> <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;"> <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Percent Difference (from Period 4) <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%; line-height: 0px; overflow-x: hidden; overflow-y: hidden;">

__**<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Video **__ media type="file" key="Movie on 2011-12-19 at 11.21.mov" width="300" height="300"

__**<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Analysis **__ <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">In this experiment, it makes sense that the actual value would be greater than the experimental value, leading to a large experimental error percentage. Firstly, its is almost unavoidable for the tension in the actual experiment to be greater than 0, which is what our entire experiment relied upon. However, for the student to apply exactly no tension onto the string and still have it move in circular motion with a constant radius and constant velocity is unrealistic. In addition, our measurements were flawed since we were looking for minimum velocity, which occurs when the object is at the top of its circular path, while we measured time for the entire circle. This resulted acceleration and a higher velocity. In addition, it proved extremely difficult to keep the circle fully vertical, and it was bound to be at an angle at points in the experiment, negatively affecting our data. It proves very difficult for a student to perform this experiment, since too many components are in their control and it is only human error that things will not be completely constant. Therefore, the only other way to determine minimum speed more accurately would be to have a mechanical device do the rotations and measuring the time from that.

=__**<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Lab: Moving in a Horizontal Circle **__=

<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">Task A: Steph Wang

<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">Task B: Gabby Leibowitz

<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">Task C: Maxx Grunfeld

<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">Task D: Gabby Leibowit

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">An objective of this lab was to determine the relationship between the radius and the maximum velocity with which a car makes a turn. In addition, this lab aimed to determine how the presence of banking changed the value of the radius at which maximum velocity was reached. Finally, this lab also ultimately determined how changing the banking angle changed the value of the radius at which maximum velocity was reached.
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Objectives: **

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**Hypothesis:** <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">We hypothesize that the larger the radius, the higher the maximum velocity. This prediction comes from the fact that since there is a larger radius, the turn will not be so sharp, and therefore, not as great of a force will be required to move the car around the circle. In addition, this hypothesis is also proven by the equation f = mv^2/R, leading us to the fact that velocity is equaled to the square root of Rf/m. This allows us to draw the conclusion that there is not an inverse relationship, and that velocity will increase with the radius. However, one can also see from the equation for velocity that the velocity and there also does //not// exist an inverse relationship between the two variables. In addition, we believe that the presence of banking changes the radius in that a smaller radius is required to reach maximum velocity since there is a force pointing the car towards the center. Ultimately, banking enables the car to travel around the circle at a greater speed with a smaller radius. Finally, we predict that changing the banking angle will also change the radius. Since there exists a normal force pointing towards the center of the circle, the turn can be more sharp when the car moves at its maximum speed. Therefore, the steeper the angle, the smaller the radius that allows the car to reach maximum velocity.


 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Prelab Questions: **
 * 1) <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**Write a hypothesis for each objective, with your reasoning.** Above
 * 2) <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**A "car" goes around an unbanked turn.**
 * 3) <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**Find an expression for its maximum velocity in terms of variables you can measure in the lab.**
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">[[image:EQUATION.png]]
 * 1) **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Use your equation to think about your procedure, specifically, the measurements you need to make and the data you need to collect. List each variable, whether it is constant or something to be measured, and how you think you will measure it. **
 * **Variables** || **Constant or Variable** || **How to Acquire Informatio**n ||
 * Radius || Measurable || Measure using a meter stick or measuring tape ||
 * Angle || Measurable || Measure using a protractor ||
 * Time || Measurable || Measure using a stop timer ||

3. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**Read the notes, below. Answer the question in the 4th bullet: “//Which value do you want to use and why?//”** <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">You should use "time between gates." This value tells you how much time it takes for the table to make 1 revolution. The "time in gate" does not provide us with information that we need, such as the revolution time. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">4. **Set up your data table on Excel, with any formulas entered and the graph created and ready to populate.** Below

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**Procedure:** <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Before actually beginning this lab, an excel spreadsheet must be set up, including radius, period 1-8, circumference, average time, max. velocity, average coefficient of friction, average acceleration, and class average. Since there are 6 groups in our particular class, we made 6 rows, since each group will have a separate set of data. Then, Data Studio is set up to use the photo gate as "recordable timer." The timer must be set to "time between gates."**The “Time In Gate” will tell you how long the gate was blocked while the “Time Between Gates” value will tell you how long it was between the time the gate was __unblocked__ to the next time it was __blocked__.** The "Time Between Gates" must be used here because it gives one the value of the period, or how many seconds per cycle. The experiment then begins when a mass is placed on a turntable, attached to a power source at a given radius. The voltage is flipped on and is slowly increased, by .1. With this, the turn table is turned with an increasing velocity. This data is measured by use of the photo gate. The velocity continues to be slowly increased until the mass reaches its maximum velocity, causing the mass to fall off the turn table. We repeat this trial multiple times. Once this data is collected, the average maximum velocity can be found.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**Data:**



Class Data:


 * Radius (m) || Experimental µ ||
 * 0.1 || 0.585 ||
 * 0.15 || 0.541 ||
 * 0.2 || 0.529 ||
 * 0.25 || 0.578 ||
 * 0.3 || 0.568 ||
 * 0.35 || 0.518 ||
 * Average || 0.5512 ||



Link to data table and graph: [|5 .xlsx]

media type="file" key="Movie_on_2012-01-06_at_12.05.mov" width="300" height="300" <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Video of the lab

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">The mass is placed on a rotational turntable with a photo gate attached. This will measure the period of the mass traveling around the rotational turntable. Then, the power supply is used to power the spinning turntable and allows it to move in order for the experiment to be performed. The banking angle can be measured by use of a metric ruler.
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Materials: **

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**Analysis:**

The percent difference from our class average was only 2.71%, meaning our results were fairly accurate.
 * 1) **Discuss the shape of the graph and its agreement with the theoretical relationship between R and v.** The shape of the graph radius vs. maximum velocity is a power fit. This is apparent due to the positive upward curve. Additionally, in this situation, friction is the only centripetal force and it is equal to (Mu)(mg), so we derive at the equation (Mu)(mg) = (mv^2)/(R). The masses cancel out on both sides, and eventually the resulting equation for velocity equals the square root of (Mu)(g)(R). With some shifting around, you see that the equation resembles y = Ax^B format, and when B = 0.5, the graph is a power fit
 * 2) **Derive the coefficient of friction between the mass and the surface**
 * 1) **Compare your coefficient of friction with that of all groups doing this lab. (Be sure to post a data table with the class values.)** (Class data below)

RESUBMIT STUFF




 * 1) **A “car” goes around a banked turn.**
 * 2) **Find an __expression__ for its maximum velocity, in terms of variables only.**
 * 3) [[image:Screen_shot_2012-01-05_at_1.31.32_AM.png width="97" height="324"]](On a level surface)
 * 4) **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?**
 * 5) [[image:Screen_Shot_2012-01-12_at_9.11.52_PM.png]]
 * 6) [[image:Screen_Shot_2012-01-12_at_9.16.09_PM.png]]
 * 7) [[image:Screen_Shot_2012-01-12_at_9.16.15_PM.png]]
 * 8) **[[image:Screen_Shot_2012-01-12_at_9.16.22_PM.png]] (On an angled surface) **

It is concluded that when banking is involved in a situation, there can be a higher velocity at a lower radius.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">This experiment proved that our hypotheses were all accurate. Our group first hypothesized that the larger the radius, the higher the maximum velocity. This first hypothesis is accurate, which was proven by completing the various trials and then comparing our results to the results of the class', those of who all had different radii. Our next two hypotheses were that the presence of banking changes the radius in that a smaller radius is required to reach maximum velocity AND that the steeper the angle, the small the radius that allows the car to reach maximum velocity. By observing our collected data, our group concluded that these two predictions were also accurate. During this experiment, we observed that as the velocity increased, there was an increasing chance that the mass would fly off the rotational turntable, until it reached its maximum velocity, and it finally did fly off. This enabled us to draw the conclusion that banking would allow a car to make a turn at a higher velocity. Therefore, it is only logical that the steeper the angle, the smaller the radius will be. Our group achieved pretty accurate results with pretty consistent trials. Our percent error was 1.22% and our percent different was 2.71%, leading us to the conclusion that we were fairly accurate in performing this experiment. However, there are various sources of error that can explain these values. Like in all experiments, the element of human error could have gotten in the way of achieving perfect results. First, it was difficult to achieve constant results since it was left up to a group member to be in charge of increasing the voltage at a slow enough rate, by .1 each time. There were times in which it would increase by .2 instead and therefore, it was difficult to know the exact point the voltage was turned to each time. In addition, it was left up to a different group member to have an accurate enough reaction time to stop his/her computer at the exact time the mass flew off the turntable. Since it is highly unlikely that both these group members would be perfect in their performance, that source of human error, without avoidance, tampered the results to some extent. Since this is an experiment designed to be performed in a physics classroom, there was no avoidance of these small sources of human error. However, if we were to alter this experiment to decrease almost all sources of error, there would have to be some type of mechanical device that automatically measures the velocity and senses when the mass falls off, automatically stopping the turntable at that exact time. This would limit the source of error associated with a slightly off reaction time. In addition, the rotational turn table would have increase voltage automatically as well, at a constant rate by .1 each time, in order to get more accurate results without flaw. However, since these materials are not available, an additional way to aid this experiment is to either perform more trials, or have more group members to observe the experiment, ultimately limiting to some extent the error that can occur. This experiment can be applied to real-life situations, for instance, driving. Driving is one of the main concepts associated with banking. Since almost all of the physics students are either getting their licenses or have been driving, it is a perfect way to compare this experiment to our life now. Therefore, we know that when completing a turn, the driver must be aware of its maximum velocity. If he/she is not, and they attempt to travel at too high of a velocity, an accidental will occur. This is comparable to the fact that at a certain maximum velocity, the mass flew off the turntable, just as a car would crash.
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Conclusion: **