Group3_2_ch5

= = =Centripetal Force Lab= toc Task A: George Souflis Task B: Ben Weiss Task C: Kaila Solomon Task D: Caroline Braunstein

__**Objectives**__ In this lab, the following objectives had to be met:
 * Determine the relationship between net centripetal force and system mass
 * Determine the relationship between net centripetal force and velocity of the system
 * Determine the relationship between net centripetal force and radius of the system's movement

__**Hypotheses and Rationales**__ Before this lab could begin, several hypotheses had to be made that offered predictions of how the objectives would be solved.
 * If the relationship is found between net centripetal force and system mass is found, then it will be found to be a linear relationship.
 * This hypothesis was reached based on preexisting knowledge of Newton's Second Law: net force=ma. Based on this equation, one can infer that net centripetal force and system mass will be proportional.
 * If the relationship is found between net centripetal force and velocity of the system is found, then it will be found to be a polynomial relationship.
 * This hypothesis is based on the equation: net centripetal force= mv^2/R. This equation demonstrates that net centripetal force will be proportional to v^2.
 * If the relationship is found between net centripetal force and radius of the system's movement is found, then it will be found to be a inversely polynomial relationship.
 * This conclusion was reached based on the equation from the second hypothesis . This equation also shows that net centripetal force will be inversely proportional to the radius.

__**Methods and Materials**__ To determine the relationship between net centripetal force, system mass, velocity, and radius of movement, the class performed an experiment in which a rubber stopper was spun in a horizontal circle. A string, run through a tube, was attached to the rubber stopper at one end, while the other end was tied onto a force meter that would calculate the tension of the string on Data Studio. The tension had to be found because this force was the only component of net centripetal force (it was the only force on the stopper pointing into the center of the circle).

When all the materials are set up, they are supposed to look like this:

Once the materials were properly set up, the class began to spin the rubber stopper, with different sets of trials that involved changing different qualities one at a time. These were: system mass, velocity, and radius of the system's movement. To change the system mass, additional rubber stoppers were tied onto the original one. To change velocity, the stopper(s) was simply spun slower/faster. To change the radius, the length of the string from the stopper(s) to the tube was increased/decreased. After recording these different variables and finding the mean tension on Data Studio, graphs of the three relationships were made on Excel. From here, one could determine the relationship between net centripetal force, system mass, velocity, and radius.

During this experiment, the stopper was spun in the manner below: media type="file" key="Movie on 2011-12-14 at 08.23.mov" width="300" height="300"


 * __Calculations, Data, and Analysis__**

Data Table:

Attachment to actual Spreadsheet:

Graphs:

Centripetal Force is directly proportional to System Mass. This means that as the system mass increases, so does the centripetal force.

Centripetal Force is directly proportional to Velocity squared. This means that centripetal force increases polynomially as velocity increases.

Centripetal force is inversely proportional to radius. This means that centripetal force is decreasing exponentially as radius increases.

__**Conclusion**__ We successfully fulfilled all of our objectives with this lab. We determined the relationship between the net centripetal force and system mass, velocity of the system, and radius of the system's movement. We hypothesized that the relationship between centripetal force and system mass would be linear because mass and net force are proportional, as proved by Newton's second law. The relationship between centripetal force and velocity would be polynomial, and the relationship between centripetal force and radius of the system would be inversely polynomial. All of our hypotheses were proved correct through the lab. Our data was extremely accurate, much more so than the rest of the class's. All of our data proved our hypotheses and all of r^2 values were of one, meaning they were 100% accurate. Many other groups did not get the correct data due to error in the lab process, which was difficult to do. Our group avoided one potential source of error by using a force sensor resting on the ground so that we would have a much more accurate measurement of net force on the system. Another potential source of error could have been measuring the radius of the system because we pretty much had to eye ball it. If we redid this lab, we could have used some sort of device that hooks up to the computer and uses imaging to measure the radius more accurately.

=Finding Minimum Velocity Activity=

__Objective:__ To determine the minimum velocity of a ball at the top of its circular motion (the circle has a radius of 1 m).







__Class Data (m/s):__ 5.16 4.63 5.97 4.01 5.61

average: 5.076 m/s

__Percent Difference:__

__Conclusion__ . the slowest one can go is almost too slow; there is too little tension . hard to get exactly a 1 m radius

As shown in the results, there was significant percent error and difference. As shown above, percent error was calculated as being 29.33%, while percent difference between this group's results and the average of all the group's results was 21%. This can be attributed to several sources of error. For example, it was difficult to measure and maintain an exactly 1 m radius. 1 m was marked on a string with a pink marker and 1 m had to be maintained for every test. These tasks were difficult because marking down 1 m was somewhat imprecise due to the width of the point and the length of the string being spun shifted after each trial. At the same time, the slowest velocity possible was almost too slow for the purposes of the lab. When the group attempted to rotate it at this speed, there was too little tension and it was difficult to maintain circular motion. To decrease the error in this activity, one might use a sharper point pen to mark 1 m and constantly check the length of the string being spun after each trial, as well as use a device that would spin the system at a speed that is slow enough to be close to the minimum velocity, yet maintain enough tension to have completely circular motion.

=Conical Pendulum Lab=

__Objective:__ What is the relationship between the period of a conical pendulum and its radius?

__Hypothesis:__ As the radius of a conical pendulum increases, its period will decrease.

__Methods and Materials:__ Set up a conical pendulum and label the length of the string, the mass of the pendulum bob, the radius of the circle, and the angle between the x-axis and the pendulum string. Measure the length of the string and the pendulum bob. Beginning with a radius of .2m, push the pendulum and create a fairly consistent radii all around. Use a stop watch to measure the amount of time it takes for the pendulum bob to complete circle. Repeat for 3 trials of the same radius, and then repeat for radius values of .5m, .75m, and 1m. Record all values and find an average for each trial. Calculate the theoretical value for each period and compare to experimental value to find the percent error.

__Data:__ Data for Pendulum Lab (and Percent Error)

This data table shows each student's recorded time period for each radius. All the recorded times for each trial were averaged to give an average experimental time period (T).

__Sample Calculation and FBD:__ calculation for period:

sample % error:



Below is a free body diagram for the weight swinging on the pendulum.



__Analysis:__ There are no forces on the tangential axis because it is the direction of motion. It would not affect the results because mass only affects velocity if we’re on another planet. As the radius increased, the period decreased. It is not linear relationship because radius appears when finding theta, velocity, and tension on the centripetal axis. Reaction time, its hard to make it go in an exact circle rather than an ellipse, rounding for measurements, timers can only so much time.
 * 1) Calculate the theoretical period.
 * 2) Calculate the average experimental period for each radius.
 * 3) Discuss the accuracy and precision of your data.
 * 4) Why didn’t we use the tangential axis at all in this lab?
 * 1) What effect would changing the mass have on the results?
 * 1) How did period change as the radius increased? Is it a linear relationship? Why or why not?
 * 1) What are some sources of experimental error?

=Circular Friction Lab= Task A- George Souflis Task B- Caroline Braunstein Task C- Kaila Solomon Task D- Ben Weiss class period- 2 date completed- January 4, 2012


 * __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?

1. What is the relationship between the radius and the maximum velocity with which a car make a turn? The smaller the radius, the slower the maximum velocity is because in my experience driving, I can take wider turns faster than sharp turns
 * Hypotheses and rationales:**

2. How does the presence of banking change the value of the radius at which maximum velocity is reached? In the presence of banking the car can have a higher maximum velocity at a lower radius. This is because banking makes it so that friction holds the car towards the center of the circle.

3. How does changing the banking angle change the value of the radius at which maximum velocity is reached? The higher the angle, the higher the maximum velocity. Based on the second hypothesis, one can assume that a greater angle will have a greater effect on the object.

Place a washer on the rotational turntable to mark the radius of the circle. Then turn on the turntable via the power supply (voltage must be increased at a constant rate); to measure the period of the table use a photogate timer. Record the periods using Data Studio. From here, use the data collected (radius, period) to calculate velocity and then calculate µ.
 * Methods and Materials:**

Photo showing the turntable, the power supply, and the cord connecting to the computer via USB for DataStudio.

media type="file" key="Movie on 2012-01-04 at 08.20.mov" width="300" height="300" Video showing the procedure of increasing the voltage until the washer slides off the turntable.


 * DATA:**

Our Data: This Spreadsheet shows the recorded radius, period (time between gates), and velocity.

Class Data:



µ class: Graph:

__To find velocity:__ __% error between our exponent value of graph and theoretical one:__ As shown, the value of the exponent should be .5, while the value we got is only .3837.
 * SAMPLE CALC****ULATIONS:**

**ANALYSIS:** The graph is a power function with an equation of Y = Ax B. Y = velocity and x = R. A in this equation is equal to the square root of (mu)(g). Also, the B value should theoretically be .5. As is shown from this equation, as the radius increases, the maximum velocity increases as well. Since the graph is a power function, not linear, as the radius increases to a certain point, the maximum velocity begins to increase in smaller amounts.
 * 1) Discuss the shape of the graph and its agreement with the theoretical relationship between R and v.

2. Derive the coefficient of friction between the mass and the surface to find the coefficient of friction:

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.)

__% difference of our data compared to class value:__

__% difference of our data compared to graph value:__

5. 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 for max velocity is as follows: It was hypothesized that a turn with a smaller radius will have a smaller maximum velocity than a turn with a larger radius. With the data collected by this group (as well as the others), this hypothesis was proven to be true. A radius vs. velocity graph (which ended up with the formula Ax^B, with A being the sqrt of µ*g and B being the power of the radius) that was made from the data shows that as radius increases, velocity does as well. While there were no tests to prove the second and third hypotheses true in this experiment, one can assume (based on previous work in class) that the presence of a banking angle will decrease the radius needed to make maximum velocity and that the greater the banking angle, the greater the maximum velocity will be. This would make sense because a banking angle would cause the spinning object to slide towards the center at a velocity that would normally cause it to fly off the wheel. Therefore, the object would need a greater velocity to make it fly off.
 * Conclusion:**

The percent error between the co-efficient of the graph and its theoretical value was 23.26%. The percent difference between the calculated co-efficient of friction and the class average was 5.96 %. The percent difference between the calculated co-efficient and the co-efficient derived from the graph was 47.47%.The possible percent error and difference might have been from the potential lapse in time between the object flying off the wheel and the stop watch being stopped. It is possible that the stop watch was actually stopped a few milliseconds after the object flew off; a small difference in time could potentially have a big effect on percent error and difference. Another could have been the rate at which voltage was turned up. In several tests (that were taken out of the results), turning the voltage up at a quicker rate than it should have been provided maximum velocities that were outliers from the rest of the results. Turning up the voltage too slowly had a similar effect. While all the results that are included in this lab are similar, perhaps if there was a uniform rate of increase of voltage, the percent error and difference could have been less. To fix these errors, one might use a stop watch that would stop at the exact moment the object flew off the wheel and have a wheel that would increase its own voltage at a uniform rate.

The results of this lab can easily be applied to real life. There are many objects that make turns (including cars). Using a similar procedure to this lab could allow a person to figure out, for example, the maximum velocity a car must go at before it skids a road.