Group1_6_ch5

Group 1: Andrea Aronsky, Maddi Steele, Sarah Gordon toc

=Centripetal Motion Lab =

Task A: Maddi Steele Task B: Andrea Aronsky Task C: Sarah Gordon Conclusion: together

**Objectives**:
 * What is the relationship between system mass and net force?
 * What is the relationship between speed and net force?
 * What is the relationship between radius and net force?

**Hypothesis:**   
 * Mass and net force are directly proportional, thus there will be a linear graph.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Speed and net force are directly proportional, thus there will be a linear graph.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Radius and net force are inversely proportional, thus this graph will appear as:

<span style="font-family: Tahoma,Geneva,sans-serif;">**Materials and Methods:** <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">media type="file" key="Movie on 2011-12-13 at 13.23.mov" width="300" height="300"
 * <span style="font-family: Tahoma,Geneva,sans-serif;">The materials necessary for this lab include string, a meter stick, stopwatch, several masses, paperclip, a rubber stopper, and a hollow plastic tube. The string will go through the hollow tube and be attached to a paper clip with many masses on one side and rubber stopper on the other. After ensuring that the radius of the circle does not change through experimentation, use the meter stick to measure the length of the radius. The stopwatch is used to measure the amount of time it takes for the stopper to make a full revolution. Throughout the experiment, more masses will be added on to the paperclip to shorten the radius and more stoppers to increase the system mass to see how different variables effect the relationship between net force and radius, speed, and mass.

<span style="font-family: Tahoma,Geneva,sans-serif;">**Procedure:** <span style="font-family: Tahoma,Geneva,sans-serif;">Attach a rubber stopper to the end of the string then feed the string through the hollow tube. On the other end of the string, attach a paperclip. Hold onto the tube so that the paperclip end is below the first. Swing the rubber stopper around and try to get the paperclip at the end to not move. Then change the variable one at a time by either adding more mass, increasing speed, or changing the length of the string being swung.

<span style="font-family: Tahoma,Geneva,sans-serif;">**Sample Calculations/Data:** <span style="font-family: Tahoma,Geneva,sans-serif;">** __//2010 DATA AND GRAPHS//:__ ** <span style="font-family: Tahoma,Geneva,sans-serif;">

<span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">** __//OUR DATA//:__ ** <span style="color: #0000ff; font-family: Tahoma,Geneva,sans-serif;">

<span style="font-family: Tahoma,Geneva,sans-serif;">**Sample Calculations:** <span style="font-family: Tahoma,Geneva,sans-serif;">

<span style="font-family: Tahoma,Geneva,sans-serif;">**Analysis:** <span style="font-family: Tahoma,Geneva,sans-serif;">Mass vs net force: for this test, the mass was changed, while the radius and velocity were kept constant. This graph shows a diagonal line because the force and mass are directly proportional, as shown in the equation F=ma.

<span style="font-family: Tahoma,Geneva,sans-serif;">Velocity vs net force: for this test the velocity was changed, while radius and mass were kept constant. This graph shows a diagonal line as well because force equals velocity squared. Therefore, the velocity and net force are directly proportional.

<span style="font-family: Tahoma,Geneva,sans-serif;">Radius vs net force: for this test the radius was changed while the mass and velocity remained constant. This graph, unlike all the other graphs, shows an inverse relationship between radius and force. This is because the net force is equal to 1/R.

<span style="font-family: Tahoma,Geneva,sans-serif;">**Conclusion:** <span style="font-family: Tahoma,Geneva,sans-serif;">Looking at the lab data from last years class and their corresponding graphs, we can see that our hypothesis was correct. As expected the velocity is directly proportional to the net force. This is because net force equals velocity squared. As can be seen from the radius vs net force graph, they have an inverse relationship, which we hypothesized. This is because the net force equals 1/ R. In addition, the mass vs net force graph was a diagonal line because the net force equals mass times acceleration. Thus, this graph makes sense because mass and net force are directly proportional.

<span style="font-family: Tahoma,Geneva,sans-serif;">Our results for this lab were unfortunately unusable, so we had to use Ms. Burn’s data. The sources of error in our own experiment as well as her last years class could have come from many different sources. One source of error could have come from measuring the radius incorrectly. Because we had to do this while the system mass was still in motion, it was very difficult to know exactly where this hit the ruler. To eliminate this source of error, we could have put marking paper (used in shoot your grade lab to mark where the projectile landed) on the ruler and then seen at what point the system mass hit the ruler. In order for this to work however the individual spinning the system mass would have to make it as horizontal as possible. Although this would not eliminate the error completely, it would make a considerable difference. In addition, it was very hard to time everything (especially as velocity increased). To minimize error for this, we could have had multiple people timing. Also, had we been able to do three separate trials for each test it would have helped to minimize error.

<span style="font-family: Tahoma,Geneva,sans-serif;">The information learned in this lab could be used in real life, as well. One example of this is used in many biology experiments for researchers. Many researchers use a centrifuge to separate particles form within a liquid. When the tube begins spinning, centripetal force pulls the material in the vials toward the center. Materials that are denser have greater inertia and thus are less responsive to the centripetal force. Therefore, less dense matter is pulled inward, which creates the separation of materials.

=<span style="font-family: Tahoma,Geneva,sans-serif;">Minimum Velocity Activity =

<span style="font-family: Tahoma,Geneva,sans-serif; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">**Methods and Materials:** <span style="font-family: Tahoma,Geneva,sans-serif; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">First, we tied a 6 gram weight to the end of a 0.75 meter string. Then, we swung the weight in a vertical circle using JUST enough tension for it to complete many cycles. Next we recorded the time it took for the weight to complete 10 cycles. We divided this time by 10 to get the time per 1 cycle.

<span style="font-family: Tahoma,Geneva,sans-serif;">**Individual Data** <span style="font-family: Tahoma,Geneva,sans-serif;">

<span style="font-family: Tahoma,Geneva,sans-serif;">**Class Data** <span style="font-family: Tahoma,Geneva,sans-serif;">

<span style="font-family: arial,helvetica,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">

**Error Analysis:** One source of error resulted from the radius being shorter than 0.75 m long. We did our calculations assuming that the radius was 0.75 m long. In reality, the radius was shorter because of our fingers holding the string. A shorter radius would have resulted in a faster velocity per cycle. Another source of error resulted from assuming that there was 0 tension in our theoretical minimum velocity calculation. In reality, the weight would not be able to make a cycle if there was zero tension in the string. Because we assumed that there was 0 tension at max height in our theoretical calculation, our percent error was not totally accurate.

=<span style="font-family: Tahoma,Geneva,sans-serif;">Conical Pendulum Lab = 12/20/11 Task B: Sarah Task C: Andrea


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


 * Hypothesis **
 * We hypothesize that the radius increases when the period becomes smaller. We predicted this because in the previous lab, when the radius increased the slower the object moved.


 * Procedure **
 * First, cut long string and tie top end to the ceiling and bottom end to the hanging weight. Tape down three measuring sticks to the ground to show the length of the radius as the weight travels in a circular path. These measuring sticks also help the timers keep track of where the cycle started. For each chosen radius, record the time for one cycle three times due to human error in timing. Then, find the average time it took per revolution for each different radius tested.


 * Data **




 * Sample Calculations:**




 * <span style="font-family: Tahoma,Geneva,sans-serif;">Analysis: **
 * 1) Calculate the theoretical period.
 * 2) Radius: 0.2 m - T: 3.26 s
 * 3) Radius: 0.5 m - T: 3.24 s
 * 4) Radius: 0.7 m - T: 3.21 s
 * 5) Radius: 1.0 m - T: 3.14 s
 * 6) Calculate the average experimental period for each radius.
 * 7) Radius: 0.2 m - T: 3.29 s
 * 8) Radius: 0.5 m - T: 3.28 s
 * 9) Radius: 0.7 m - T: 3.18 s
 * 10) Radius: 1.0 m - T: 3.07 s
 * 11) Discuss the accuracy and precision of your data.
 * 12) From our percent error, it is evident that our data is very accurate. The highest percent error occurred in the experiment with the 1 meter radius, being 2.23%, which still shows good results. The theoretical value for this period was 3.14 seconds, but the experimental was 3.07 seconds. The rest of the trials were extremely close to their theoretical values. For example, for the radius of 0.2 meters, the theoretical period was 3.26 and the experimental was 3.29. Our data was also precise as the different trials for the experimental values were all very close to one another as one was 3.20 seconds and another was 3.21 in the trials for the 0.70 meter radius.
 * 13) Why didn’t we use the tangential axis at all in this lab?
 * 14) We didn't use the tangential axis for this lab because we were focusing on the horizontal circle. The height is not measured because this horizontal circle is only moving due to the influence of gravity and the tension of the string. Thus those are the two components taken into consideration when calculating the results.
 * 15) What effect would changing the mass have on the results?
 * 16) Changing the mass would have no effect on the results because it ends up canceling of the equation when calculating the period.
 * 17) How did period change as the radius increased? Is it a linear relationship? Why or why not?
 * 18) Our hypothesis was correct. We predicted that as the period got smaller, the radius would increase. This is not a linear relationship as there is no direct or indirect relationship between the period and radius. They both change but there is no set relationship.
 * 19) What are some sources of experimental error?
 * 20) The main source of error in this lab is measuring the radius. It is very difficult to measure the radius perfectly for each trial, but by having multiple trials, the average would produce the most accurate result. The experimental periods were also not completely accurate because when timing each revolution, everyone got different times as they had different views of when a full revolution was made. During our lab, the string also fell from the ceiling and putting it back up could have caused a change in length, thus affecting the calculations.

=<span style="font-family: Tahoma,Geneva,sans-serif;">__**Moving in Horizontal Circle**__ = <span style="font-family: Tahoma,Geneva,sans-serif;">Maddi: Data Collection and Calculations <span style="font-family: Tahoma,Geneva,sans-serif;">Andrea: Set-up <span style="font-family: Tahoma,Geneva,sans-serif;">Sarah: Analysis Questions

<span style="font-family: Tahoma,Geneva,sans-serif;">Date: 1/3/12

<span style="font-family: Tahoma,Geneva,sans-serif;">**Objective:** <span style="font-family: Tahoma,Geneva,sans-serif;">1. What is the relationship between the radius and the maximum velocity?

<span style="font-family: Tahoma,Geneva,sans-serif;">**Hypothesis:** <span style="font-family: Tahoma,Geneva,sans-serif;">1. The maximum velocity is directly proportional to the square root of the radius. This is because of Newton's Second Law as F=ma, a = V<span style="font-family: Tahoma,Geneva,sans-serif; vertical-align: super;">2<span style="font-family: Tahoma,Geneva,sans-serif; vertical-align: sub;">/R. We can assume that this relationship because when solving for velocity with a FBD that has friction pointing to the right, weight down, and normal up, the calculation gives <span style="font-family: Tahoma,Geneva,sans-serif; vertical-align: sub;">us that  v= (Rµg) ^1/2.

<span style="font-family: Tahoma,Geneva,sans-serif;">**Materials and Methods:** <span style="font-family: Tahoma,Geneva,sans-serif;">To find the maximum velocity of a 5 gram mass, we used a rotational turntable and a power supply (voltage machine). We used a meter stick to measure the radius at which our mass was positioned. We attached a photogate timer to the rotation al turntable, which allowed DataStudio to collect data.



<span style="font-family: Tahoma,Geneva,sans-serif;">**Procedure:** <span style="font-family: Tahoma,Geneva,sans-serif;">1. Place the 5 gram mass on varying radii of the turntable (ours being 0.25 cm). Increase the voltage to increase the rotations per second. Keep increasing until the mass slides. Then stop the time, and use the time before the weight slid off. Repeat these steps several times. Record results in excel spreadsheet. Find the velocity of the turntable by using the radius and period.

<span style="font-family: Tahoma,Geneva,sans-serif;">media type="file" key="Movie on 2012-01-04 at 12.40.mov" width="300" height="300"

<span style="font-family: Tahoma,Geneva,sans-serif;">
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Data: **


 * Sample Calculations:**


 * Error Analysis:**

<span style="font-family: Tahoma,Geneva,sans-serif;">Analysis: <span style="color: #2f1313; font-family: Tahoma,Geneva,sans-serif;">4a) <span style="color: #2f1313; font-family: Tahoma,Geneva,sans-serif;">4b) I think it would still be a power fit because the R value is still to the ½ power. However, the values for the y (velocity) would change because the radius is no longer just being multiplied by gravity and the tangent of theta.
 * 1) <span style="color: #391818; font-family: Tahoma,Geneva,sans-serif;">The graph has a power fit. This is because the velocity (y value) is equal to the coefficient of friction times gravity times the radius all to the one half power. Since there is a power on the x value (radius), it must have a power fit. We expected the power value to be ½, but in actuality it was 0.4799 which is very close to the expected value.
 * 2) Coefficient of Friction (derived using our radius and velocity)
 * [[image:honorsphysicsrocks/CIRCLE_CALC_3.png]]
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">As seen in the data table above, our coefficient of friction is 0.559, which is interestingly the second highest coefficient of friction of all the radii. The smallest radii had the highest coefficient of friction (0.571), while the 0.20 radius and the 0.30 radius had the same coefficient of friction, which was 0.520.
 * <span style="color: #2f1313; font-family: Tahoma,Geneva,sans-serif;">[[image:honorsphysicsrocks/boooop.png width="246" height="65"]]

<span style="color: #2f1313; font-family: tahoma,geneva,sans-serif;">5. The percent error of the exponent was only 4.02% which shows that the exponent on our graph (.4799) is very close to the theoretical value,which is .5. The exponent is supposed to be 1/2 because when we first calculate the velocity it comes out as V^2. Therefore, the only way to isolate the velocity is to take the square root of both sides so the R value is to the 1/2 power. The percent difference of the class coefficient of friction was 2.95% which shows that it was very similar to the other groups' coefficient of friction, which shows that the coefficient of friction didn't change much when the radius is increased/decreased. The percent difference between our actual results and our calculated value for the coefficient of friction is 9.39%, which shows that there were some sources of error, but that these sources did not impact our results drastically.

<span style="font-family: Tahoma,Geneva,sans-serif;">Our results and our class results support our hypothesis that the maximum velocity is directly proportional to the square root of the radius. As the radius increased, so did the velocity at which the mass would turn, as seen from our graph. Our graph has the equation y=2.2379x^0.4799, which is the power function defined by y=Ax^b. The shape of the graph shows that of a square root power function, which is correct. Because maximum velocity is equal to the square root of (g*Mµ*R), or (g*Mµ*R) 1/2, the equation of our graph is representative of this known equation of velocity. The y-value is equal to the the maximum velocity, the A value is the square root of (g*Mµ), the x-value is the radius, and the B-value is the power of the radius. The theoretical value of B should be 0.5 because we are trying to get the square root of (g*Mµ*R). However, our exponent from the equation of the line is 0.4799 showing that there were some sources of error that affected our results. We also solved for the coefficient of friction (using our radius and max velocity) and got a result of 0.559. The coefficient of friction from the equation of the line on our graph was 0.511. The percent difference between the two coefficient of friction values is 9.39%, which is relatively low. However, due to the percent difference, there must have been sources of error in our experiment.
 * <span style="color: #000000; font-family: Tahoma,Geneva,sans-serif;">Conclusion: **

<span style="font-family: Tahoma,Geneva,sans-serif;">The first source of error can be attributed to the rotational turntable. Because the turntable took a long time speed up, it was hard to gauge what voltage to use. Due to the lag time, the voltage could have been increased too quickly for an accurate velocity to have been recorded. To eliminate this source of error in the future, we could use a rotational turntable that speeds up immediately (as voltage is increased). Another source of error can be attributed to the voltage machine. Because the voltage machine did not increase voltage at a constant speed, we had to increase it ourselves. This task was difficult because the dials were sensitive, making it hard to keep the voltage at which the mass flew off the turntable constant. During some trials, the mass flew off the turntable at a higher velocity than it did during other trials (which skewed the data we used to solve for the period). To eliminate this source of error in the future, we could use a voltage machine that increases its voltage at a constant rate. The last error can be attributed to human reaction time. It was impossible for someone to say "stop" at the exact time at which the mass flew off the turntable. By the time someone said "stop" and the person working DataStudio ended the trial, at least 1 second must have gone by. We tried to account for the elapsed time by using the second to last period time recorded by DataStudio. However, the second to last period time may have been slightly inaccurate, depending on how much time lapsed between one person saying "stop" and the other person stopping the trial. To eliminate this source of error in the future, we would use a different device that could stop the DataStudio trial as soon as the mass shifted position or flew off the turntable.centr