Group4_6_ch5

** Ben Sherman, Brianna Behrens, & Lerna Girgin Period 6 Chapter 5
 * Group 4 toc

=Swinging Stopper Lab= December 12, 2011 Part A: Ben Sherman Part B: Brianna Behrens Part C: Lerna Girgin Part D: Conclusion

__Objectives:__ What is the relationship between net force and system mass? What is the relationship between net force and speed? What is the relationship between net force and radius?

__Hypothesis:__ Net force and system mass share a directly proportional relationship, where net force increases as system mass increases. This graph will depict a line with a positive slope. Net force and speed are inversely proportional, and the graph for these factors will have a negative slope. Net force and radius are directly related because as the radius length increases, a greater net force is needed to continue the circular motion. This graph will have a positive slope as well.

__Methods and Materials:__ media type="file" key="Swinging Stopper Lab.mov" width="300" height="300" Acquire all available and necessary materials. Approximate and cut appropriate length of string. Mass, using a balance, and tie the system mass to one end of the string. Slide string through a glass tube and attach the other end to a force meter. Attach force meter to a USB link, and insert the link into a computer to access Data Studio. Swing system mass in a horizontally circular motion as the force meter is held on the ground. Use the stopwatch to measure the time of a designated number of revolutions and multiple trials. Alter the system mass and continue timing multiple trials of revolutions. Use a meter stick to measure the radius and string length above the glass tube.

__Data & Graphs:__

//USED DATA://

//UNUSED DATA://

__Sample Calculations:__ __Conclusion:__ After analyzing the lab data from Ms. Burns' previous class, as well as the graphs that reflect the designated relationships, the hypothesis was incorrect. The net force is directly proportional to the velocity, where ∑F = v 2. In addition, the net force is inversely related to the radius because ∑F = 1 / R. As a result of difficulty in finding a completely successful lab procedure, it was necessary to substitute Ms. Burns' data in order to attain consistent and accurate calculations and graphs. During the procedure, all collected data was unable to be used, as the graph reached negative points, which is not possible. The error in this lab can be attributed to many factors, including misuse of the force meter and inaccurate reading of the meter stick. The most practical way to measure the radius was holding the meter stick up while the swinging stopper was in motion. However, the limited instant of time to determine the length provides a larger extent of error, and inevitably, in calculations. To eliminate the error in this experiment and gather original data, the method and procedure would need to be perfected, in that the results would show positive graphs and consistent numerical values. In order to address the numerous sources of error within the lab, several things would have to be changed. First, one of these errors originated from the problem with keeping the radius constant as the system was changing velocity in a circular motion with the string. By using the force sensor and tying the end of the string to the hook, it was easier than using a hanging mass at the other end of the string. However, as the velocity continued to change, the radius did as well. In order to attend to this problem, a piece of tape could have been useful in keeping the string at the same length against the tube, providing more accurate data. In addition, another source of error came from measuring time for five revolutions of the system at a high velocity. It was difficult to capture the exact moment to hit the start button on the timer and the exact moment to stop it. Because this is a problem that cannot be entirely fixed, one reasonable solution would be to have two people time the revolutions and compare results. The force sensor would then need to be secured to the ground. A real life application for this lab can be found in the designers of race car tracks. In order to figure out the safest distance away from the center of the circle, the designer would have to find the perfect radius. This is important so that the cars don't make dangerously sharp turns at every corner.

=Lab: Conical Pendulum= Ben Sherman, Brianna Behrens, Lerna Girgin

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

Hypothesis : The relationship between the period and the radius of a conical pendulum is inversely proportional. This is seen in objects moving in a circular motion on the horizontal axis. As the radius of the circle gets bigger, the period (T) becomes smaller. We think this because of the equation for tangential velocity is  v = (2*pi*r)/t. If velocity were to remain constant and the period and radius were to change, if the radius were to increase, the period would have to decrease and vice versa.

Data:  

Free Body Diagram:

Sample Calculations: Analysis: The accuracy of this data is pretty high and close to the theoretical period that was calculated. Many of the average experimental periods were off, within a range of two to four decimal places. The only value that lacked accuracy was the rev/s obtained for a 1 m radius. The theoretical rev/s for that measurement was .318; however, the obtained rev/s was .326. Furthermore, the precision was also relatively high, as the quantities in the average experimental column are very close in value, for example, 0.304 and 0.305 as well as 0.314 and 0.326.
 * 1) Calculate the theoretical period.
 * 2) .2m Radius - .306 rev/s
 * 3) .5m Radius - .309 rev/s
 * 4) .7m Radius - .312 rev/s
 * 5) 1m Radius - .318 rev/s
 * 6) Calculate the average experimental period for each radius.
 * 7) .2m Radius - .304 rev/s
 * 8) .5m Radius - .305 rev/s
 * 9) <span style="color: #000080; font-family: Arial,Helvetica,sans-serif;">.7m Radius - .314 rev/s
 * 10) <span style="color: #000080; font-family: Arial,Helvetica,sans-serif;">1m Radius - .326 rev/s
 * 11) <span style="font-family: 'Times New Roman',Times,serif;">Discuss the accuracy and precision of your data.

<span style="font-family: 'Times New Roman',Times,serif;">4. Why didn’t we use the tangential axis at all in this lab? <span style="color: #000080; font-family: 'Times New Roman',Times,serif;">Because of the horizontal path as seen in the procedure, the tangental axis would not have been relevant in calculating the necessary information. The tangental axis cannot be seen from the perspective of a free body diagram, which focuses on the x and y axes.

<span style="font-family: 'Times New Roman',Times,serif;">5. What effect would changing the mass have on the results? <span style="color: #000080; font-family: 'Times New Roman',Times,serif;">A change in mass would have multiple effects on the results of this lab. For example, if the mass was increased, the period of one revolution would be increased, too, because of the slower velocity. However, if the mass was decreased, the period would be shorter because of the greater velocity. Also, the tension on the cord would be affected as well, depending on the change in mass. The period for each radius would be subjected to the greatest change.

<span style="font-family: 'Times New Roman',Times,serif;">6. How did period change as the radius increased? Is it a linear relationship? Why or why not? <span style="color: #000080; font-family: 'Times New Roman',Times,serif;">The hypothesis for this lab was incorrect, as analysis of the data shows a directly proportional relationship between period and radius. As the radius was increased upon each trial, the period also increased. The relationship between these two factors is not linear because the resulting equation is more complex than that of a linear relationship.

<span style="font-family: 'Times New Roman',Times,serif;">7. What are some sources of experimental error? <span style="color: #000080; font-family: 'Times New Roman',Times,serif;">One of the greatest sources of error in this lab is the mis-measurement of the radius. Because it is hardly possible to accurately measure the radius for each trial, the closest method of doing so was to continuously practice in order to gain enough control over the mass. Also, during the lab, the mass' cord fell from the hook and required rehanging to continue data collection. Though only by a small amount, the string may not have been the exact length as before it fell, which may have caused error also.

=<span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 120%;">Lab: Horizontal Circles with Friction =

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">January 3, 2012

<span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">Part A: Lerna Girgin <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">Part B: Brianna Behrens <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">Part C: Ben Sherman

__<span style="color: #000000; font-family: 'Times New Roman',Times,serif;">Objectives: __ <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">1. What is the relationship between the radius and the maximum velocity with which a car makes a turn? <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">2. How does the presence of banking change the value of the radius at which maximum velocity is reached? <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 110%;">3. How does changing the banking angle change the value of the radius at which maximum velocity is reached?

__<span style="color: #000000; font-family: 'Times New Roman',Times,serif;">Hypotheses: __ <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">1. As the radius of a circle increases, the maximum velocity with which the car can make the turn decreases. <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">2. The presence of banking makes the radius smaller for the max velocity to stay the same. <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">3. As the angle is increased, the length of the radius is decreased.

__<span style="font-family: 'Times New Roman',Times,serif;">Materials and Procedure: __ <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Before beginning the experiment, we acquired all necessary and available materials. First, we attached the USB link to a laptop and opened Data Studio. We set up a photogate in order to measure the time of rotations. A five gram mass was placed on a rotational turn table at the designated radius of 0.3m. We adjusted the power supply slowly to increase the turntable speed. The speed was gradually increased until the mass slid from the surface. This procedure was continued for multiple trials.

__<span style="font-family: 'Times New Roman',Times,serif;">Data: __

__<span style="font-family: 'Times New Roman',Times,serif;">Graph: __ __<span style="font-family: 'Times New Roman',Times,serif;">Sample Calculations: __

__<span style="font-family: 'Times New Roman',Times,serif;">Video and picture: __ media type="file" key="Movie on 2012-01-03 at 13.56.mov" width="364" height="348"



__<span style="font-family: 'Times New Roman',Times,serif;">Analysis: __

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Free Body Diagram: <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;"> >
 * 1) <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;"> The shape of the trend line is slightly curved, indicating a circular path, as does the exponent of 0.4799; a straight path would result in an exponent of 1, whereas the theoretical exponent for this lab is 0.5.
 * 2) <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">The derivation:
 * 3) <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">[[image:derivationp1.png]]
 * 1) [[image:classavgmuped.png width="516" height="498"]]
 * 1) [[image:classavgmuped.png width="516" height="498"]]

__<span style="font-family: 'Times New Roman',Times,serif;">Conclusion: __ <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">After completing this lab and analyzing the results, the hypothesis was incorrect. As displayed in the data table, the max velocity increases with the length of the radius; the values are directly proportional.When the radius was .1m the max velocity is .748 m/s and when the radius was .3 m the max velocity is 1.237 m/s which shows the increase in both the x and y values.

<span style="font-family: 'Times New Roman',Times,serif;">There were specific errors found in this lab that prevented the results from being most accurate. The percent error calculated when comparing the theoretical and experimental values of the exponent in the equation y=Ax <span style="font-family: 'Times New Roman',Times,serif; vertical-align: super;">B was 4.02%. The percent difference of this lab for the value of the coefficient of friction was 8.36%. The sources of error can be attributed to the reaction time and the placement of the mass on the rotational turntable. Everytime the mass slid from the point of radius, it was not consistently replaced on the same side. Due to the curved edges and engraved writing on the top of the mass, each side may have provided a different coefficient of friction. Also, the reaction time between the exact point of the mass sliding from the turntable and the stop of the Data Studio collection could have increased the error in correct results. In addition, another source of error came from the inconsistency of the time recordings. The range in time for each trial was larger than expected and required more data. In order to address these errors, the group could consistently use the same side for every trial. Also, the group could have two people record the time so they could compare results.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%; vertical-align: super;">A real life application of this lab could be seen in toy train sets. If the track is arranged into a circular path, the radius would change the maximum velocity at which the trains could realistically travel. .

=<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%; vertical-align: super;">Activity: Minimum Speed at the Top of a Circle = <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%; vertical-align: super;">December 14, 2011 <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%; vertical-align: super;">Ben Sherman, Lerna Girgin, Brianna Behrens

__<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%; vertical-align: super;">Data: __

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%; vertical-align: super;">

__Sample Calculations__:



__<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%; vertical-align: super;">Conclusion: __ <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%; vertical-align: super;">The completion of this activity yielded a percent error of 66.05%, an extremely large value. Ideally, the minimum speed at the top of a circle would lack tension in the string; however, in a realistic lab experiment such as this procedure, the presence of tension is nearly impossible to avoid, thus altering the accuracy of the results and calculations. In addition, the use of a stopwatch in order to measure the time could have affected the activity. Another issue was the length of the string. Because of the minute length subtractions of the knots and the adjustments, the string was not exactly 0.75 m, the required measurement. The sum of these errors are accountable for the aforementioned percentage. Although it would prove extremely difficult to proceed with a lack of string tension in a classroom lab setting, the method can be adjusted to expel multiple other sources of error. If possible, the person holding the string might also use the stopwatch, as the coordination of starting and stopping the time would be greater than that of another lab partner. Also, meticulously measuring the string to ensure the proper length would rid the procedure of radius length mistakes.