Roshni,+Amanda,+Allison,+Emily

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=Lab: Inertial Mass = **Group Members:** Amanda Donaldson, Allison Irwin, Emily Burke, and Roshni Khatiwala **Class:** Period 2 **Date Completed:** November 22, 2010 **Date Due:** November 23, 2010

__**Objective:**__  Our objective, was to find the mass of an object by using its inertia.

__**Hypothesis:**__  If the mass being used is larger (heavier), then the period will be greater. This shows that the period and mass of an object are related.

__**Materials:**__  The materials available to us included a variety of masses (we used 100, 200, 250, 300, and 350), the inertial balance, a clamp (to secure the balance to the table), a stopwatch, and a Rubik's Cube.

__//Our Setup//__



__**Procedure:**__
 * 1) First, we obtained a variety of masses including 100, 100, 200, 250, 300, 350 grams as well as a clamp and inertial balance.
 * 2) We clamped the balance onto the table to secure it.
 * 3) To ensure that the gram would not slide on the tray, we placed a paper towel on the tray and then placed the mass on top of that.
 * 4) <span style="font-family: Arial,Helvetica,sans-serif;">We started with the 100 gram mass.
 * <span style="font-family: Arial,Helvetica,sans-serif;">By using larger masses, we were able to count more precisely (we discovered that smaller masses led to faster periods, which were much harder to count than the slow ones).
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">We hit the side of the balance to start its motion.
 * 2) <span style="font-family: Arial,Helvetica,sans-serif;">As the balance moved from side to side we counted the number of periods.
 * <span style="font-family: Arial,Helvetica,sans-serif;">A period is the full cycle (the side-to-side movement of the balance). It must start at one side and return to that same side to be counted as a period.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">We timed 25 periods as the balance moved back and forth.
 * 2) <span style="font-family: Arial,Helvetica,sans-serif;">After completing the five trials for the 100 gram mass, we repeated this process with the 200, 250, 300, and 350 masses.
 * 3) <span style="font-family: Arial,Helvetica,sans-serif;">Then, we placed the Rubik's cube on the platform of the balance.
 * 4) <span style="font-family: Arial,Helvetica,sans-serif;">We used the same process to with the Rubik's cube on the balance as we did when we had a mass on it.
 * <span style="font-family: Arial,Helvetica,sans-serif;">We counted and timed the number of periods.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">We put all of our data into an Excel spreadsheet as shown below.
 * 2) <span style="font-family: Arial,Helvetica,sans-serif;">With the data, we created a graph with a linear line of best-fit.
 * 3) <span style="font-family: Arial,Helvetica,sans-serif;">We calculated the mass of the Rubik's cube (shown below).

<span style="font-family: Arial,Helvetica,sans-serif;">__**Data:**__ <span style="font-family: Arial,Helvetica,sans-serif;">

<span style="font-family: Arial,Helvetica,sans-serif;">__**Graphs:**__



<span style="font-family: Arial,Helvetica,sans-serif;">**__Necessary Numbers for Calculations:__**
 * <span style="font-family: Arial,Helvetica,sans-serif;"> Our Mass of Rubik's cube: 104.30 grams
 * <span style="font-family: Arial,Helvetica,sans-serif;"> Actual Mass of Rubik's cube: 101.41 grams
 * <span style="font-family: Arial,Helvetica,sans-serif;"> Class Average Mass of Rubik's cube: 103.36 grams

<span style="font-family: Arial,Helvetica,sans-serif;">__**Rubik's Cube Mass Calculation:**__



<span style="font-family: Arial,Helvetica,sans-serif;">__**Percent Error:**__





<span style="font-family: Arial,Helvetica,sans-serif;">__**Percent Difference:**__



<span style="font-family: Arial,Helvetica,sans-serif;">__**Questions:**__
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">Did gravitation play any part in this operation? Was this measurement process completely unrelated to the "weight" of the object?
 * <span style="font-family: Arial,Helvetica,sans-serif;">No, gravitation did not play a role in this lab.
 * <span style="font-family: Arial,Helvetica,sans-serif;">No, it was not completely unrelated to the "weight" of the object. If we wanted to find the weight of the object, we would multiply the mass by gravity.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">Did an increase in mass lengthen or shorten the period of motion?
 * <span style="font-family: Arial,Helvetica,sans-serif;">As we increased the mass, the time of the period became longer.
 * <span style="font-family: Arial,Helvetica,sans-serif;">The lighter the weight, the shorter the period.
 * <span style="font-family: Arial,Helvetica,sans-serif;">The heavier the weight, the longer the period.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">How do the accelerations of different masses compare when the platform is pulled aside and released?
 * <span style="font-family: Arial,Helvetica,sans-serif;">The acceleration of the varying masses were different.
 * <span style="font-family: Arial,Helvetica,sans-serif;">If there was a smaller mass on the platform, then the acceleration of the platform is greater.
 * <span style="font-family: Arial,Helvetica,sans-serif;">If there was a large mass on the platform, then the acceleration of the platform is lower.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">Do you imagine that the period would have been different if the side arms were stiffer? Would this change lengthen or shorten the period of the motion?
 * <span style="font-family: Arial,Helvetica,sans-serif;">Yes, if the side arms of the inertial balance were stiffer the period would be affected.
 * <span style="font-family: Arial,Helvetica,sans-serif;">The stiffer the arms, the shorter the period as it allows for less movement of the balance.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">Is there any relationship between inertial and gravitational mass of the object?
 * <span style="font-family: Arial,Helvetica,sans-serif;">Yes, if you multiply Inertial mass by gravity you have found the gravitational mass.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">Why do we almost always use gravitation instead of inertia as a means of measuring mass of an object?
 * <span style="font-family: Arial,Helvetica,sans-serif;">We almost always use gravitation instead of inertia because gravity is constant all over Earth so it is easier to calculate. Also, using a scale isn't complicated and it's more precise.
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">How would the results of this experiment be changed if you did this experiment on the moon?
 * <span style="font-family: Arial,Helvetica,sans-serif;">Gravity did not play a factor in this lab because we are trying to find the mass of the Rubik's cube, not it's weight
 * <span style="font-family: Arial,Helvetica,sans-serif;">Therefore, the results of this lab would not differ on the moon.

<span style="font-family: Arial,Helvetica,sans-serif;">__**Conclusion:**__ <span style="font-family: Arial,Helvetica,sans-serif;">The purpose, or objective, of this lab was satisfied. After experimenting with known masses, we were able to find the the inertia of an unknown mass, such as the Rubik's cube, by using only its inertia. After using the inertial balance with the known masses, we are able to conclude that our hypothesis is in fact, correct. As shown in the data tables, it takes more time for a heavier object, or mass, to complete a period on the inertial balance than it does for a lighter mass to. Therefore, our hypothesis was correct.

<span style="font-family: Arial,Helvetica,sans-serif;"> Our graph above illustrates a direct linear relationship between the mass of the object and the period time. As shown by the line of best fit, objects with shorter period times must be lighter - the opposite is true about heavier objects. The equation of the line of best fit, y = 0.0012x + 0.335, was used to estimate the unknown mass of a Rubik's Cube. The r^2 value is 0.9935, which is close to 1, only 0.0065 off. This shows that the line fits the data well, thus the data points are close to this line.

<span style="font-family: Arial,Helvetica,sans-serif;">In terms of errors, we found there to be a 2.77% error in our calculation of the Rubik's Cube's mass. We also calculated a 1.89% error in the class's average mass. Between the class's average mass and our calculated mass, there was a 0.91% difference. While these numbers are small, they still imply that there was some errors in our lab. The error occurred while we were attempting to find the time of the period lengths of the various weights. The inaccuracy was most likely due to human error while counting the periods. While we realized that using heavier weights made the periods longer, and therefore much easier to count, there was still a great possibility for this human error to occur. It was very difficult at times to count consistently with the motion of the inertial balance. However, we feel that our use of larger weights, making the periods easier to count, significantly reduced our error. Another factor that most likely affected our error was the reaction time it took for the counter and timer. The length of time it took for the counter to react and say "stop," and the length of time it took for the timer to hit the stop button both could have significantly affected our results. Overall, the amount of error in our results, were very low!

<span style="font-family: Arial,Helvetica,sans-serif;">Because most of our minimal error occurred not by a defect in our procedure or equipment, but by the fact that we are humans, there is not much we can do to rectify these errors. Perhaps we could be able to time the periods with greater ease if we used bigger weights; however, for that, we would need another, stronger balance since ours does not support extraordinarily large weights. Using a machine to time the periods eliminate the amount of human error, such as the reaction times in between the end of the period and the person pressing the button on the stopwatch. However, such a machine was not available to us. Also, if we were to change this lab, we might want to be sure of our balance's precision. Therefore, we would need to add a step in which we calibrate the balance.

<span style="font-family: Arial,Helvetica,sans-serif;">Since this lab is all about mass vs. period time, a related real life application would be a circumstance such as a car crash. We discovered that the more massive an object, the shorter its inertial period is, therefore, we can also conclude that the larger (and heavier) a car is, the more time it takes between when the driver slams on the brake, and when the vehicle actually stops. Our common sense confirms this idea, because we know that a large truck has a much slower braking time than a small convertible. It is important to know and understand this inverse relationship between mass and inertia, and to realize that more mass leads to slower time periods, while less mass leads to faster time periods.

<span style="font-family: Arial,Helvetica,sans-serif;">---
=<span style="font-family: Arial,Helvetica,sans-serif;">Lab: Newton's Second Law = <span style="font-family: Arial,Helvetica,sans-serif;">**Group Members:** Amanda Donaldson, Allison Irwin, Emily Burke, and Roshni Khatiwala <span style="font-family: Arial,Helvetica,sans-serif;">**Class:** Period 2 <span style="font-family: Arial,Helvetica,sans-serif;">**Date Completed:** November 29, 2010 <span style="font-family: Arial,Helvetica,sans-serif;">**Date Due:** December 1, 2010

<span style="font-family: Arial,Helvetica,sans-serif;">__**Objective:**__ <span style="font-family: Arial,Helvetica,sans-serif;"> Our objective was to find the relationship between system mass, acceleration, and net force.

<span style="font-family: Arial,Helvetica,sans-serif;">__**Materials:**__ <span style="font-family: Arial,Helvetica,sans-serif;"> The materials available to us included a dynamics cart with mass, dynamics cart, track, Photogate timer, Data Studio, super pully with clamp, base and support rod, string, mass hanger, mass set, mass balance, and level.

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">//__Our Setup__//



<span style="font-family: Arial,Helvetica,sans-serif;">**__Procedure:__**

<span style="font-family: Arial,Helvetica,sans-serif; text-indent: -0.25in;">1. Organize setup <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">a. Gather all materials <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">b. Set up cart on track <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">c. Tie one end of string to cart <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">d. Clamp pulley to table <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">e. Drape string over pulley <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">f. Plug photogate probe into pulley <span style="font-family: Arial,Helvetica,sans-serif; text-indent: -0.25in;">2. Open Data Studio on laptop. <span style="font-family: Arial,Helvetica,sans-serif; text-indent: -0.25in;">3. Perform Trial #1 <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">a. Make sure pulley is level and steady <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">b. Draw cart back, then let go and allow mass hanging on the end of the string to accelerate the cart forward. <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">c. At the release of the cart, click start on data studio to begin the collection of data. <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">d. Catch cart before it hits the pulley or before the hanging mass hits the ground. <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">e. When the cart stops, click stop on data studio. <span style="font-family: Arial,Helvetica,sans-serif;"> f. Repeat these steps (a-e) five times (with the same mass). <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">g. On Data Studio, there should be five different runs shown. <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">h. Make sure that the velocity-time graph is selected. <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">i. In the graph window, click the arrow next to Fit and select linear. <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">j. A linear fit box will appear on the velocity-time graph (be sure to drag it so it is not in the way of the runs). <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">k. Record the value of m (the slope). <span style="font-family: Arial,Helvetica,sans-serif; text-indent: -0.25in;">4. Repeat steps 1-3, varying the masses for the different trial groups <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">a. Trial Group 1: Hanging Mass (M1) = 25g, Mass Placed on Cart (M2) = 0g <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">b. Trial Group 2: Hanging Mass (M1) = 20g, Mass Placed on Cart (M2) = 5g <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">c. Trial Group 3: Hanging Mass (M1) = 15g, Mass Placed on Cart (M2) = 10g <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">d. Trial Group 4: Hanging Mass (M1) = 10g, Mass Placed on Cart (M2) = 15g <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">e. Trial Group 5: Hanging Mass (M1) = 8g, Mass Placed on Cart (M2) = 17g <span style="font-family: Arial,Helvetica,sans-serif;"> 5. For the second part, we kept the hanging mass consistent and varied the mass placed on the cart. We repeated steps 1-3 with the following trial groups <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">a. Trial Group 1: Hanging Mass (M1) = 20g, Mass Placed on Cart (M2) = 300g <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">b. Trial Group 2: Hanging Mass (M1) = 20g, Mass Placed on Cart (M2) = 500g <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">c. Trial Group 3: Hanging Mass (M1) = 20g, Mass Placed on Cart (M2) = 600g <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">d. Trial Group 4: Hanging Mass (M1) = 20g, Mass Placed on Cart (M2) = 840g <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">e. Trial Group 5: Hanging Mass (M1) = 20g, Mass Placed on Cart (M2) = 1000g

<span style="font-family: Arial,Helvetica,sans-serif;">**__Trials (Data Studio):__** <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">//__Hanging Mass of 25 grams and 0 grams on the cart__//

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">//__Hanging Mass of 20 grams and 5 grams on the cart__//



<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">//__Hanging Mass of 15 grams and 10 grams on the cart__//

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">__//Hanging Mass of 10 grams and 15 grams on the cart//__

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">__//Hanging Mass of 8 grams and 17 grams on the cart//__



<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">__//Hanging mass of 20 grams and 300 grams on the cart//__



<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">__//Hanging mass of 20 grams and 500 grams on the cart//__



<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">__//Hanging mass of 20 grams and 600 grams on the cart//__



<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">__//Hanging mass of 20 grams and 840 grams on the cart//__



<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">__//Hanging mass of 20 grams and 1000 grams on the cart//__



<span style="font-family: Arial,Helvetica,sans-serif;">**__Data:__** <span style="font-family: Arial,Helvetica,sans-serif;"> <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: center;">__Chart 1:__Independent Variable: ForceDependent Variables: Mass & Acceleration

<span style="display: block; font-family: Arial,Helvetica,sans-serif; font-weight: normal; text-align: center;">Chart 2:Independent Variable: Mass Dependent Variables: Force & Acceleration



<span style="font-family: Arial,Helvetica,sans-serif;">__Graphs:__





<span style="font-family: Arial,Helvetica,sans-serif;">**__Analysis Guide:__** <span style="font-family: Arial,Helvetica,sans-serif;"> 1. Explain your graphs:
 * <span style="font-family: Arial,Helvetica,sans-serif;">If linear: What is the slope of the trendline? To what actual observed value does the slope correspond? How does it compare to this actual observed value (find the percent error between the two)? Show why the slope should be equal to this quantity. What is the meaning of the y-intercept value?
 * <span style="font-family: Arial,Helvetica,sans-serif;">The following answers are based off of Chart 1 & Graph 1.


 * <span style="font-family: Arial,Helvetica,sans-serif;">The slope of our trendline was 0.4877. This number corresponds to the net mass of the system (in kg). The actual net mass of our system was 0.518 kg, representing that we had 5.85% error.


 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: left;">This value should be equal to the mass because in the equation of a line ( y = mx + b), y corresponds to the force (the weight of the hanging mass multiplied by gravity), x corresponds to the acceleration, and b (the y-intercept) corresponds to the friction. Theoretically this means that when there is no friction (b = 0), dividing force by acceleration (y/x) will result in the net mass. This calculation is the basis of Newton’s 2nd Law.


 * <span style="font-family: Arial,Helvetica,sans-serif;">If non-linear: What is the power on the x? What should it be? What is the coefficient infront of the x? To what actual observed value does the coefficient correspond? Find the percent error between the two. Show why this value should be equal to this quantity.
 * <span style="font-family: Arial,Helvetica,sans-serif;">The following answers are based off of Chart 2 & Graph 2.


 * <span style="font-family: Arial,Helvetica,sans-serif;">The power of x of our line was -1.375. This number should actually be -1, representing the fact that acceleration and mass are inversely related. Unfortunately, after repeated tests, we still had a high percent of error.


 * <span style="font-family: Arial,Helvetica,sans-serif;">The coefficient in front of the x in our line was 0.0946. This number should actually have been 0.196, representing the force (N). Again we had unfortunately had large error between the theoretical value and our measured value, despite our numerous trials.


 * <span style="font-family: Arial,Helvetica,sans-serif;">These values correspond in the following ways, again agreeing with Newton’s 2nd Law that acceleration is inversely proportional to mass....

<span style="font-family: Arial,Helvetica,sans-serif;">2. What would friction do to your acceleration? Would you need a bigger or smaller force to create the same acceleration? Was your slope too big or too small? Can friction be a source of error in this experiment?
 * <span style="font-family: Arial,Helvetica,sans-serif;">Friction would negate part of our acceleration. It would slow the cart down, by pushing it in the opposite direction. To create the same acceleration, and to minimize the effects of friction as much as possible, we would need a bigger force pulling on the cart. Our slope was exactly what it should have been, 0.5231. Friction was indeed a significant source of error in this experiment, since when we did our calculations, we did not account for its effects.

<span style="font-family: Arial,Helvetica,sans-serif;">**__Conclusion:__** <span style="font-family: Arial,Helvetica,sans-serif;"> After completing our trials we have obtained our objective—to find the relationship between mass, acceleration, and force. We all knew the equation F=ma, but with this lab, we needed to learn how variables of the experiment could be manipulated and changed. From varying both the hanging mass and the mass on the cart, to keeping the hanging mass constant while varying the cart mass, we learned how the mass variation would change the force and acceleration. With more mass hanging than on the cart, the acceleration was faster, and with a greater force. With less mass hanging than on the cart, the acceleration was slower, encompassing less force. With the constant hanging weight of 0.02 kg and much more mass on the cart, acceleration was a constant low rate along with a small force. The graphs created from our information directly show this relationship with mass, acceleration, and force. Force and acceleration are directly proportional while acceleration and mass are inversely proportional. In terms of error, we were head on with force vs. acceleration with only a 0.98% error. Unfortunately, with acceleration vs. mass we had a huge starting error of 391.3%. With such little error on the first graph, it shows that we just had very tiny human error like stopping the cart too soon or starting our data studio too soon. With such huge error on our second graph there was definitely something wrong. We did the second graph again to try and get better numbers. This time, the power of x of our line had a 37.5% error while the coefficient of out line had a 51.73% error. Our error this time around improved because we wiped down the track and were more accurate with stopping and starting the cart and data collection. We still have a large error but it is not as much as what we started with. Thus, proving that doing it again made our data more accurate and we got a more accurate relationship between the mass, acceleration, and force.

<span style="font-family: Arial,Helvetica,sans-serif;">---
=<span style="font-family: Arial,Helvetica,sans-serif;">Lab: Atwood's Machine = <span style="font-family: Arial,Helvetica,sans-serif;">**Group Members:** Amanda Donaldson, Allison Irwin, Emily Burke, and Roshni Khatiwala <span style="font-family: Arial,Helvetica,sans-serif;">**Class:** Period 2 <span style="font-family: Arial,Helvetica,sans-serif;">**Date Completed:** December 6, 2010 <span style="font-family: Arial,Helvetica,sans-serif;">**Date Due:** December 7, 2010

<span style="font-family: Arial,Helvetica,sans-serif;">**__Objective:__** <span style="font-family: Arial,Helvetica,sans-serif;">What is the relationship between net force and acceleration?

<span style="font-family: Arial,Helvetica,sans-serif;">**__Materials:__** <span style="font-family: Arial,Helvetica,sans-serif;">Atwood's Machine, clamp, rod, stand, 2 mass hangers, masses, photogate, string

<span style="font-family: Arial,Helvetica,sans-serif;">**__Procedure:__** <span style="font-family: Arial,Helvetica,sans-serif; text-indent: -0.25in;">1. Organize setup <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">a. Gather all materials <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;"> b. Set up cart on track <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;"> c. Tie one end of string to cart <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;"> d. Clamp pulley to table <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;"> e. Drape string over pulley <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;"> f. Plug photogate probe into pulley <span style="font-family: Arial,Helvetica,sans-serif; text-indent: -0.25in;">2. Open Data Studio on laptop. <span style="font-family: Arial,Helvetica,sans-serif; text-indent: -0.25in;"> 3. Perform Trial #1 <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">a. Make sure pulley is level and steady <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;"> b. Put the lighter weight on the table and hold it down. Then, let go and allow masses to travel. <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;"> c. At the release of the mass, click start on data studio to begin the collection of data. <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;"> d. Catch heavier mass at bottom of stand (before it hits the bottom - table, or base) <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;"> e. When the mass is stopped stops, click stop on data studio. <span style="font-family: Arial,Helvetica,sans-serif;"> f. Repeat these steps (a-e) five times (with the same masses on each hanging mass). <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">g. On Data Studio, there should be five different runs shown. <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;"> h. Make sure that the velocity-time graph is selected. <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;"> i. In the graph window, click the arrow next to Fit and select linear. <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;"> j. A linear fit box will appear on the velocity-time graph (be sure to drag it so it is not in the way of the runs). <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;"> k. Record the value of m (the slope). <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">l. Find this for each run. <span style="font-family: Arial,Helvetica,sans-serif; text-indent: -0.25in;">4. Repeat steps 1-3, varying the masses for the different trial groups <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">a. Trial Group 1: Pulley 1 = 375, Pulley 2= 335 <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">b. Trial Group 2: Pulley 1 = 381, Pulley 2 = 329 <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">c. Trial Group 3: Pulley 1 = 393, Pulley 2 = 317 <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">d. Trial Group 4: Pulley 1 = 403, Pulley 2 = 307 <span style="font-family: Arial,Helvetica,sans-serif; margin-left: 1in; text-indent: -0.25in;">e. Trial Group 5: Pulley 1 = 418, Pulley 2 = 292

<span style="font-family: Arial,Helvetica,sans-serif;">**__Trials (Data Studio):__**

//__Pulley 1: 375, Pulley 2: 355__//

//__Pulley 1: 381, Pulley 2: 329__//

//__Pulley 1: 393, Pulley 3: 317__//

//__Pulley 1: 403, Pulley 2: 307__//

//__Pulley 1: 418, Pulley 2: 292__//

<span style="font-family: Arial,Helvetica,sans-serif;">**__Data:__**



<span style="font-family: Arial,Helvetica,sans-serif;">**__Graph:__**



<span style="font-family: Arial,Helvetica,sans-serif;">__**Analysis Guide:**__
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">Explain your graph(s) thoroughly!
 * <span style="font-family: Arial,Helvetica,sans-serif;">If linear: What is the slope of the trendline? To what actual observed value does the slope correspond? How does it compare to this actual observed value (find the percent error between the two)? Show why the slope should be equal to this quantity. What is the meaning of the y-intercept value?
 * <span style="font-family: Arial,Helvetica,sans-serif;">The slope of our trendline was 0.6817. This number corresponds to the net mass of the system (in kg). The actual net mass of our system was 0.710 kg, representing that we had 3.99% error.
 * This value should be equal to the mass because in the equation of a line ( y = mx + b), y corresponds to the force (the weight of the hanging mass multiplied by gravity), x corresponds to the acceleration, and b (the y-intercept) corresponds to the friction. Theoretically this means that when there is no friction (b = 0), dividing force by acceleration (y/x) will result in the net mass. This calculation is the basis of Newton’s 2nd Law.


 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">What would friction do to your acceleration? Would you need a bigger or smaller force to create the same acceleration? Was your slope too big or too small? Can friction be a source of error in this experiment? Redo the calculation of acceleration WITH friction to show its effect.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Friction would slow our acceleration down.
 * <span style="font-family: Arial,Helvetica,sans-serif;">If there was friction, there would need to be a bigger force to create the same acceleration.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Our slope was too small. We got 0.6817 for our slope; however, it should have been, 0.710.
 * <span style="font-family: Arial,Helvetica,sans-serif;">The pulley is not 100% frictionless, and therefore, yes, friction could be a source of error in this experiment because we did not account for it. If we were to include friction, there would be a minimal difference.
 * <span style="font-family: Arial,Helvetica,sans-serif;">We calculated acceleration with friction using the the y-intercept of our trendline. This number (01.043) represents friction in Newtons. The chart following chart includes our calculations as well as the theoretical acceleration and the measured acceleration without friction, for comparison.





<span style="font-family: Arial,Helvetica,sans-serif;"> 3. Discuss the precision of your data.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Overall, our data was fairly precise. Throughout our trials we reproduce the same answers/values for slope, or they were at least extremely close to each other for all five trials. The first three trials are not as precise as the last two. While some groups of trials are more precise than others (such as the last two being extremely precise), they are all good data collections. The trials/trial groups where the data is not as precise may be due to human error (including stopping time on data studio and release by hand of the masses on the hanging pulley).

<span style="font-family: Arial,Helvetica,sans-serif;"> 4. The real pulley and mass arrangement is not as simple as we assumed. In fact the pulley is not massless and frictionless means that it does require a net “torque” (a turning force) to make it rotate – this is supplied by the tension in the string. The rotational inertia of the pulley then adds an equivalent mass to the total mass being accelerated, where the equivalent mass for the pulley is approximately equal to ½ of the mass of the pulley. If the mass of each pulley is 5.6 g, could the pulley mass account for a significant potion of your error in the experiment?
 * <span style="font-family: Arial,Helvetica,sans-serif;">By adding mass to the theoretical mass value, you would bring the theoretical acceleration down because with more mass an object moves slower. If the theoretical acceleration is brought down, it would become closer to our measured acceleration. Thus, making our percent error less.

<span style="font-family: Arial,Helvetica,sans-serif;">__**Conclusion:**__

Our purpose was to verify the inverse relationship between force and acceleration. During different trials, we varied the amount of mass on the two hanging weights of the Atwood's Machine; we took away mass from Weight 1 and added that same mass to Weight 2. We were extremely careful not o change the total mass of the system. As expected, our results were indeed linear, which proves that there is indeed a very close relationship between net force and acceleration. A potential source of error in our experiment would be friction; we had not accounted for it, because it was not at all visible to us. However, although it was extremely minimal, it was still present in the lab. Therefore, it is safe to contribute most of our 3.99% error to friction.

<span style="font-family: Arial,Helvetica,sans-serif;">---
=<span style="font-family: Arial,Helvetica,sans-serif;">Lab: Coefficient of Friction = <span style="font-family: Arial,Helvetica,sans-serif;">**Group Members:** Amanda Donaldson, Allison Irwin, Emily Burke, and Roshni Khatiwala <span style="font-family: Arial,Helvetica,sans-serif;">**Class:** Period 2 <span style="font-family: Arial,Helvetica,sans-serif;">**Date Completed:** December 13, 2010 <span style="font-family: Arial,Helvetica,sans-serif;">**Date Due:** December 14, 2010

Due to the varying parts in this lab there are multiple objectives:
 * __Objective:__**
 * To measure the coefficient of static friction between surfaces
 * To measure the coefficient of kinetic friction between surfaces
 * To determine the relationship between the friction force and the normal force.


 * __Hypothesis:__**
 * The value of the static friction coefficient will be greater than that of the kinetic friction force. This is because static friction, no motion, requires more force, and therefore will have a greater value than kinetic friction, motion (when an object is sliding)
 * The coefficient is a directly proportional ratio between the wood block on the aluminum track surface.

__**Materials:**__ There were multiple materials that we needed in order to complete this lab. These items include a force meter and USB link, a wooden block, varying masses, string, an aluminum track, and clamp. The force meter and USB link are sued with DataStudio. The wooden block is what the varying masses are placed on to do the lab experiments.The block is what is pulled along the surface. The string is attached to the block pulling it horizontally along the surface. The clamp secures the aluminum track that the block slides down in the second part (measuring the coefficient of friction on an incline). A protractor is attached to the aluminum track to determine the angle of the incline of the track.

__Part A: Measuring the Coefficient of Friction on a Flat Surface__

 * __Data Tables:__**

//Mean Tension @ Constant Speed//

//Maximum Tension//

__//Force pull with Mass of 1000//__
 * __Data Studio Graphs__**

__//Force pull with Mass of 1500//__

__//Force pull with Mass of 2000//__

__//Force Pull with Mass of 2500//__

**__Part B: Measuring the Coefficient of Friction on an Incline__**

 * __Maximum Angle so that the block does not slide__**
 * Trial || Maximum Angle ||
 * 1 || 12 ||
 * 2 || 11 ||
 * 3 || 11 ||
 * 4 || 13 ||
 * 5 || 14 ||
 * 6 || 12 ||
 * 7 || 11 ||
 * 8 || 11 ||
 * Average || 11.875 ||


 * __Minimum Angle so that the block slides (with a nudge) at constant speed__**
 * Trial || Minimum Angle ||
 * 1 || 11.5 ||
 * 2 || 12 ||
 * 3 || 12 ||
 * 4 || 12.5 ||
 * 5 || 11.5 ||
 * 6 || 11 ||
 * 7 || 11.5 ||
 * 8 || 12 ||
 * Average || 11.75 ||

__**Analysis:**__ <span style="font-family: Arial,Helvetica,sans-serif; margin-top: 0in;">1. From measured data in Part A, use Microsoft Excel to plot a graph of Static Friction vs. Normal Force. Add a second line for the kinetic friction data, on the SAME graph. Set the y-intercepts to zero, and show the equations of the lines with the regression coefficient. <span style="font-family: Arial,Helvetica,sans-serif; margin-top: 0in;">2. Compare the slope of line with calculated ms average (% difference).



<span style="font-family: Arial,Helvetica,sans-serif; margin-top: 0in;"> 3. Compare your result with the class results. <span style="font-family: Arial,Helvetica,sans-serif; margin-top: 0in;">4. Compare your values of the coefficient friction<span style="font-family: Arial,Helvetica,sans-serif; margin-top: 0in;"> in Part A with those found in Part B.
 * Group || Coefficient of Static Friction || Coefficient of Kinetic Friction ||
 * Ours || 0.2409 || 0.2025 ||
 * 1 || 0.1959 || 0.1823 ||
 * 2 || 0.2111 || 0.1712 ||
 * 3 || 0.2597 || 0.2103 ||
 * 4 || 0.182 || 0.164 ||
 * 5 || 0.2137 || 0.1849 ||
 * 6 || 0.2498 || 0.2159 ||
 * Average || 0.22187 || 0.190157 ||
 * The above table shows each groups' coefficients of static and kinetic friction. The last row, is our class average for each.
 * Both of the coefficients we found tended to be on the greater side of the class average; however they are not too far off.
 * Static friction, friction on an object at rest, is bigger that kinetic friction, friction on an object in motion, because it takes more force to make an object move from rest, then to keep it moving.

__**Discussion Questions:**__ 1. Why does the slope of the line equal the coefficient of friction? Show this derivation. 2. Look up the coefficient of friction between wood and aluminum. Discuss if your measured results fall within the range of theoretical values. Be sure to cite your source! 3. What variables affected the magnitude of the force of friction? What variables affected the magnitude of the coefficient of friction? 4. How does the value of coefficient of kinetic friction compare to the value for the same material’s coefficient of static friction? 5. Did putting the track on an incline significantly change the coefficient of friction? Why or why not?
 * On the x-axis of the graph, is the Normal force, N; and on the y-axis of the graph, is the Maximum tension, T, the force on the system/object.
 * Because the equation of the slope is y/x (y over x), in this case, it would be T/N, where T is the force.
 * The equation for the coefficient of friction is: coefficient of friction = f/T, where f is the force (in this case, tension)
 * Therefore, the following derivation is true:
 * These derivations show how the slope is equal to Tension/Normal force which is the same equation as the one for the coefficient of friction when Tension is the force.
 * According to the [|Engineer's Handbook], the coefficient of static friction for wood on any metal (including aluminum) varies from 0.2 to 0.6. Our static friction coefficient was 0.2409, which falls perfectly within this range.
 * The variable that effected the magnitude of the force of friction was the mass placed on the wooden block. As the mass went up, the friction force went up also. No variables affected the magnitude of the coefficient of friction because it was the same two surfaces every time we did a trial. If one of the surfaces was changed to another surface, the coefficient of friction would change greatly.
 * The value of the coefficient of static friction is always greater than that of kinetic friction.
 * This is because more force is required to start an object in motion (static friction), than keep it moving (kinetic friction)
 * The coefficient of friction is defined as the ratio of the friction force and normal force between two surfaces. This coefficient depends on the two surfaces that we used. Because we did not switch our wooden block or our track, the coefficient of friction should theoretically be the same no matter the incline of the track.

__**Conclusion:**__ Our purpose in this lab was satisfied because we learned all about the force of friction and the coefficient of friction. By doing a series of trials we learned that the mass added friction to the system, but the coefficient of friction stays the same because the surfaces remain the same. After completing this lab, we proved our hypothesis to be correct! As clearly shown in the data tables and calculations in part B, the value we found for the friction coefficient of static friction was greater than the coefficient for kinetic friction. This is because, as explained in previous questions, more force is required to start an object in motion that was originally at rest, than the amount of force that is required to keep an object in motion. Additionally, the friction coefficient is a direct ratio between the wood block and the aluminum track. This is shown in the graph (under Analysis question 1).There is a positive slope, and positive correlation, of the points on the graph.<span style="font-family: tahoma,arial,'nimbus sans l',sans-serif; font-size: small; font-weight: normal; line-height: normal;"> In order to lessen the error in this lab we could have made sure that we used the same side of the wooden block. Even the slight difference in the coefficient friction between the two different sides and the track could have been a source of error in our lab. More importantly, in order to decrease the error, we could have a machine that would pull our block at 100% constant speed, every trial. While we tried our best (by repeating trials over and over again) we are humans, so that human error must always be accounted for. The friction coefficient has many real life applications. It is a huge consideration in tire manufacturing. Tires that have high friction coefficients with the road will give a driver more control of the car, while ones with less will enable the car to go faster. Because our coefficient of static friction was within the predicted range, we had no percent error. However, the difference between our result and the class average was about 12.07. This is most likely due to natural variation in human error that is bound to occur while performing the lab.

<span style="font-family: Arial,Helvetica,sans-serif;">---
=<span style="font-family: Arial,Helvetica,sans-serif;">Lab: Acceleration Down an Incline = <span style="font-family: Arial,Helvetica,sans-serif;">**Group Members:** Amanda Donaldson, Allison Irwin, Emily Burke <span style="font-family: Arial,Helvetica,sans-serif;">**Class:** Period 2 <span style="font-family: Arial,Helvetica,sans-serif;">**Date Completed:** December 20, 2010 <span style="font-family: Arial,Helvetica,sans-serif;">**Date Due:** December 21, 2010

The objective of this lab, was to find how the acceleration of an object down an incline depends on the angle of the incline. In the first part of this experiment, the object was accelerating down an incline. In the second part of the lab, the object was accelerating up an incline.
 * __Objective:__**

The acceleration of an object down an incline is dependent upon the incline angle. The greater the incline angle, the greater the value of acceleration. Likewise, the smaller the incline angle, the smaller the value of acceleration.
 * __Hypothesis:__**

The materials needed and given to us in this lab including the mass (the wooden block), the surface (the aluminum track), a ring stand and clamp, a meter stick, two photogate timers, a picket fence, tape, photogate stands, a pulley, string, masses, and a mass hanger.
 * __Materials:__**

__**Pre-Lab Work:**__ We used the above calculations to solve for the theoretical acceleration in our lab.

**__Part A: Acceleration Down an Incline__**
//__Our Group Data__//
 * __Data Tables:__**

__//All Honors Physics Class Data//__
 * __Data Studio:__**







**__Part B: Acceleration Up an Incline__**

 * __Pre-Calculations__**:


 * __Data Tables To Be Used:__**



**__Part C: Analysis and Conclusion__**
1. Make a graph of acceleration versus sin(theta), using Excel.
 * __Analysis:__**

2. Find the coefficient of friction between your incline and the block using the equation of your trendline.


 * To find the coefficient of friction between our incline and the block, we used the y-intercept of our trendline.

3. Calculate the percent error between the slope and g of earth. Show this calculation.


 * As shown by this calculation, we had a 2.95% error.


 * Another good thing to look at is the percent difference. This is the difference between what we found g to be and what the class average for g was. In the chart above, the class average of the slope, value found for g, is 10.443. Our value found for g was 10.089. Therefore, the following calculation was made to calculate percent difference.

4. Compare the value of the coefficient of friction between your incline and the block to that from last week's lab.


 * We compared this value of the coefficient of friction with both our results from last week (µ = 0.2409) and the class' average results from last week (µ = 0.2218).


 * __Discussion Questions:__**
 * 1) Discuss your graph. What does the slope mean? What is the meaning of the y-intercept?
 * The slope of our graph should be around 9.8 as it is the acceleration over the angle.
 * Our slope is 10.089.
 * The y-intercept is the acceleration of the system on a flat, horizontal surface - no incline. The y-intercept is f/m.
 * Our y-intercept is -2.0541.
 * 1) If the mass of the cart were doubled, how would the results be affected?
 * If the mass of the cart were doubled, the value for the acceleration of the system, would be smaller. This is because the object is heavier, therefore, it will take longer for the mass to descend down an incline. Because the time is greater (longer), the acceleration would be smaller.
 * Not only would the acceleration be smaller, it would be cut in half.
 * 1) Consider the difference between your measured value of g and the true value of 9.80 m/s^2. Could friction be the cause of the observed difference? Why or why not?
 * There is a difference between the true value of g which is 9.8 m/s^2 and what we measured g to be, which is 7.26.
 * <span style="font-family: Arial,Helvetica,sans-serif;">This difference may be due to friction.
 * The mass was going down an aluminum track and there is friction between wood and aluminum. In the equation, we did account for friction.
 * The coefficient of friction between wood and aluminum is 0.2409.
 * 1) How were your results in Part B? Why was the expectation that your results be within 2% considered to be reasonable when in other labs we allow much larger margins of error?
 * No results were found in part B.

In this lab our purpose was satisfied because we learned how the degree of an angle can effect the acceleration of an object. Our hypothesis was proven correct when we did our trials and found that the bigger the angle, the bigger the acceleration. Throughout our trials the same thing happens and our data proves our point even more so. For example, angle 12 has an acceleration of -0.272 m/s^2 while angle 17.5 has an acceleration of 0.695 m/s^2. Acceleration is definitely affected by the angle in which the track is lifted to. For part A, our percent error ended up being 2.95% (as shown in the calculation above - analysis question 3). Our value for g was 10.098 which is very close to the actual value of 9.8; however, not perfect. Part of the reason as to why we had some error in this lab was due to smooth movement of the wooden block on the aluminum track. While the block was to be moving straight down the track, on some trials, it did not follow this exact straight/direct path. A second cause for error may be due to the fact the track was not 100% clean. Just because we cleaned it, doesn't mean we rid of every single specimen of dirt, dust, et cetera. This lab could be modified so that there is less error by wiping down the track so there is absolutely no dust and by making sure the track is completely balanced so that the block doesn't slid to one side more than the other. The dust probably added more friction so the acceleration is less than it really should be. With the track not being completely balanced, the acceleration is also less because the block is not on a straight path. A relevant real life application of this lab is a car going down a hill and how the angle of the hill affects the cars acceleration. When building cars you need to take into account the acceleration of a car because it could effect the driver with safety purposes.
 * __Conclusion:__**