Li,+Degisi,+Johnson,+Bickel

= = Period 5 Completed 12/17/10 Due: 12/ 20/10
 * Acceleration Down an Incline **


 * __Purpose:__**
 * To find out if the acceleration of an object down/up an incline depends on the angle of the incline.

__**Hypothesis:**__

The acceleration of the wooden block will be dependent on the angle of the incline. As the incline angle increases, the value of acceleration of the block will also increase. We hypothesize this based on the equation. In this equation, there is a direct relationship between theta and acceleration. If g and µ remain constant and theta increases, then acceleration will increase as well.

Part A set up
 * __Procedure:__**

__**Data:**__ PART A This is an example of one of the runs that was preformed to find the acceleration of the block on the plane and different angles. The slope of the highlighted section is the value that was used as acceleration

This chart shows the trials from Part A. The first column displays the angle in degrees at which we set the incline for three trials at each angle. We converted those degrees into radians so that we would later be able to find the sin of the angle using Excel and not our calculator. To find the acceleration for each trial, we took the slope of the line created on the Data Studio velocity v. time graphs. The average accelerations of the block at each incline angle are displayed in the first row corresponding with each angle. Earlier in the experiment, we had measured the band spacing of the black band when we were supposed to measure the distance from the start of one band to the start of the next. That would have doubled our band spacing measurement, and therefore doubled our accelerations. To make up for that error, we multiplied the average accelerations by 2, as seen in the final column.

The above chart displays the information used in creating our graph. Using the radians solved for in the previous chart, we found the sin of each incline angle, our x-coordinates for each trial. The second column displays our y-coordinates, the average accelerations for each trial.

This chart shows the class data for Part A of the experiment. The slopes were averaged together to use in the percent difference equation to see the percent difference between the class average of slopes and the value of the slope of our graph (see sample calculations). Because the slope is smaller when friction is not included (y-int=0), friction may be the cause of our slope being greater than the true value of g when it is included.

PART B This data was collected from Data Studio and shows the time between the two gates for 3 of our best trials. The run # does not correspond with the trial number in the following chart because the first few runs did not move at all. The above chart shows our results in trying to move the cart exactly .5m in 1.5s. Using various values of µ (such as last weeks calculated value and the largest and smallest µ solved for using angles from Part A) and the equation in the sample calculations below, we were able to solve for the mass of b that would just begin to accelerate the cart. The smallest mass solved is shown in the sample calculation and did not move the cart. We increased the mass to the other values calculated until the cart finally moved. The best results we observed were in Trial 4 when the cart was accelerated by 84 grams and moved the .5m distance in 1.496 seconds.

__**Sample Calculations:**__ Derivation of Theoretical Accelerations:

Part A Force Diagram: Part B FBD: __Percent DIfference and Error__

Percent Error Time Part B

Percent Error Mass Part B


 * __Graph:__**

Using the equation of our trend line and the equation, -2.6813 is the value of friction between our incline and the block. By setting that equal to -µ9.8cos19.4 (friction in the equation) we were able to solve for this weeks coefficient of friction, .29. Last weeks µ value was .2397. The two should be close because although this weeks experiments were performed on an incline, the two surfaces we used (the block and the track) were the same. Because the surfaces were the same, the interaction between the surfaces should also be the same.
 * __Analysis:__**

Discussion Questions: 1. Discuss your graph. What does the slope mean? What is the meaning of the y-intercept? Using the slopes of velocity time graphs created on Data Studio, we were able to solve for the acceleration of the mass at different angles. We created a graph of the sin of the angle versus the acceleration to determine the relationship between acceleration and the angle of the incline. Our graph has a very favorable r2 value of .99. Based on the equation for acceleration down an incline,, the slope of our graph is meant to be the value of g, 9.8. Based on the same equation, the y-intercept of the graph is the value of friction.

2. If the mass of the cart were doubled, how would the results be affected? If the angles were not changed but the mass of the cart was doubled, the accelerations of the cart would have been twice as fast. This would have resulted in a steeper slope on the graph because the y-values would be increased from the original graph but the x-values would be the same.

3. Consider the difference between your measured value of g and the true value of 9.80m/s^2. Could friction be the cause of the observed difference? Why or why not? Because our measured value of g is larger than the true value of 9.8, friction can be the cause of the difference. This is because including friction makes our slope larger. We know this because when the y-intercept was set to zero, making friction 0, the slope decreases. Therefore, friction could have caused our slope, the value of g, to be larger than the true value.

4. How were your results in Part B? Why was the expectation that your results would be within 2% considered to be reasonable when in other labs we allow much larger margins of error? The results we observed for time in Part B were almost exact, having less than 1% error. However, the mass that moved our cart was not one of the masses we had calculated using the various values of µ. The percent error between the mass that moved our cart, 84 grams, and the closest mass we had calculated, 78.5 grams, is 7.0%. The results should have been within 2% error because we were using variables that we knew/had calculated. If the angle, µ, mass of a, and acceleration were all the same theoretically as the experimental values we used in the calculations, we should have also gotten the correct theoretical value for the mass of b. However, this was not the case, but we did not have time to go back and fix our error to make our results for mass within the 2% range.


 * Conclusion:**

gggggg The results of our experiment supported our hypothesis. The experiment consisted of two parts. In the first element, we allowed a designated mass to travel down an incline primarily by the force of gravity. In the second component of the experiment, we attached a weight to the mass, which used the force of gravity to accelerate the object up an incline. Our objective was to discover the correlation between acceleration and the angle of incline in the first portion of the experiment, and in the second it was to apply our knowledge to achieve a time of 1.5s for the weight to travel between two photogates. We hypothesized that acceleration would be directly proportional to the angle of incline, and the this was supported by the results of our experiment. One example of this is in part A. We calculated that at 19.4º the block only moved at an average of 0.8713 m/s/s where when the incline was increased to 22.9º the acceleration increased as well to 1.2573. gggggg One of the most significant areas of possible error from this lab was that when sliding down the ramp, we cannot guarantee that the wood block did not come in contact with the sides of the track. If this occurred, it would cause another normal force and thus friction force to act on the weight, which was not accounted for and would cause data collected to be inaccurate. Also, in the second portion of the experiment we calculated that there must have been some form of error present during the dropping of the accelerating weight, due to the fact that we did not get constant values on trials using the same values. As you can see, with a weight of 84g we received time values ranging from 1.496s to 1.576s. This is supported by our determined 7% error calculation for mass of part B of the experiment. gggggg There are no practical real world applications of this experiment, however the knowledge of knowing the relationship between an angle of incline and the resulting acceleration is very valuable. If you are not a scientist developing new technology the results of this experiment will largely go unnoticed, however it is worthwhile for everyone to understand the basics: Generally, when placed on an incline, the larger the incline the larger the acceleration of an object will be down the incline. And when being pulled up an incline, the larger the weight pulling the object, the higher the acceleration will be. If we were to preform this lab again there would be a few changes that needed to be made. First to diminish as much error as possible in part A we would try to make sure the block did not slide into the sides of our incline plane. With this precaution it would be easier to come to closer experimental values due to the fact that we know friction is only coming from one surface. Also, it would be good for us to do more trials fro part B to see if our values really did differ much, and maybe with more values we could find a more meaningful average time. This however was impossible as we did not have enough time.

__ Newton's Laws: Determine the Coefficient of Friction Lab __ __Period 5__ __Completed 12/10 /10__ __Due: 12/13/10__


 * Excel Spreadsheet **__** :[[file:CoefficientFrictionFinal.xls]] **__

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 friction force will be directly proportional with the amount of normal force acting on the system. Also the coefficient of static friction will be greater than the coefficient of kinetic friction because the static friction shows how much force needs to be acting on an object to keep it in place opposed to the kinetic friction, which shows the force that it on the system as it is already moving.__

Procedure__:__
__A)__

> > > > > > >
 * 1) Mass the wooden block.
 * 1) Clamp the surface board to the table top.
 * 1) Place the block on the surface and put 1000g on top of it.
 * 1) Tie a short (15 cm) string to the block at one end, and to the force meter on the other.
 * 1) Plug the force meter into your computer. Choose Data Studio, and “Create Experiment”. A force-time graph will automatically open.
 * 1) Go to SETUP and check ** Force – Pull Positive ** and uncheck ** Force – Push Positive ** . Then on the graph display, click the y-axis label to change the name to ** Force- Pull Positive **.
 * 1) Leaving the string slack, press the button “ZERO” on the sensor.
 * 1) Press START on Data Studio, and gently pull the block with the force sensor
 * 2) Be sure to pull with a very slow constant speed once it starts to move.
 * 3) Hold the string parallel to the board.
 * 4) After the results are recorded in Data Studio highlight the data that is in a straight line and click ** ∑ ** . Record the MEAN as the value for Tension at Constant Speed.
 * 5) Highlight the maximum point and record that value as the Maximum Tension
 * 6) Repeat step 10 twice more with the same mass.
 * 7) Next repeat steps 8-11 adding 500g each time you repeat the steps.

__ B) __


 * 1) Attach a protractor to the track, using the nut-screw assembly that slides onto the track.
 * 2) Secure a 200g mass to the block with masking tape, and place it at the raised end of the track.
 * 3) Slowly lift the of the track until the block just begins to slide down the aluminum surface. Have each member of your group conduct this step 2 times, recording each angle.
 * 4) Average the angles that were found
 * 5) Place the track on an incline by clamping it to a ring stand. Make the angle just slightly less than the angle measured in Step 3. The block should NOT slide down on its own. When you nudge the block just slightly, it should continue down the ramp at constant speed. Have each member of your group conduct this step 2 times, recording each angle measurement, then take the average.

Data:
__This chart shows the mass pulled across the track (including mass of the block) and the max tension taken off of the graph created in Data Studio during each trial, as well as the average max tensions for each mass. We multiplied the masses by 9.8 to solve for the weight, the normal force. The average max tension, which in this experiment is the static friction, was divided by the normal forces to solve for µ. The values of µ were averaged together, giving us an average coefficient of static friction of .237306. __ __Next, this chart shows the mass pulled and the average tensions taken from the graphs created during each trial. The last column displays the mean of the average tensions for each mass. The same weight, or normal force, was used to solve for µ. To solve for µ, we divided the mean tension for each mass, which in this experiment is kinetic friction, by the normal force. We averaged those values of µ together for an average coefficient of kinetic friction of .214674. __

__ This chart from Part B shows the max angles in degrees without the block sliding and for it to begin sliding at constant speed. The µ for all of these angles were solved by finding the tangent of the angle. The coefficients of friction from each trial were then averaged together. The average µ for both static and kinetic friction for the max angle without sliding is .257526. The coefficient of both frictions for the max angle for the block to slide at constant speed is .176102. The value of µ is the same for both static and kinetic friction in this experiment because there is no acceleration either time. __ __ ﻿ __

Analysis__:__
__This graph displays the relationship between normal force and friction force between aluminum and wood. The r2 value for static friction is .99 and when rounded, the kinetic friction r2 value is 1, showing our graph is very good at predicting the pattern between the two forces.__ __Using the following formulas, percent difference between the average static/kinetic frictions we solved for and the slopes of the lines was able to be solved.__

__As seen above, the percent difference between our own results as well as the class average are pretty high. However, we knew that we would get high percents due to the multiple errors present in this lab which will be later explained in the conclusion. We are confident with both our level ground calculations of the coefficient of friction because they fall within the range of the theoretical values of the coefficient, yet__ __we do know that on the incline our values were further off from the real coefficients.__

** 1. ** Why does the slope of the line equal the coefficient of friction? Show this derivation.
The slope of the line is equal to µ or the coefficient of friction due to the fact that f=µN. Because f=µN, friction and normal force are directly related. Because we are comparing these two on the graph and they are directly related we know the line should be straight or equal to y=mx+b. On our y-axis we have the Frictional force (f) and on the x-axis we have the Normal Force (N), and our y-intercept is 0, so it is easy to see that f=mN, where m=slope. This way we know that m=µ.

__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!__ __ The coefficient between wood and clean, dry metals is 0.2-0.6. Our coefficient for static friction falls within this range as our calculated µ equals 0.2397. Our coefficient for kinetic friction also falls under this range as 0.2131. [] __

__3. What variables affected the magnitude of the force of friction? What variables affected the magnitude of the coefficient of friction?__ __ The magnitude of the force of friction is affected by variables such as whether or not the surface is clean. It also is affected by the wetness of the surface and system; for our experiment both needed to be dry and wiped down. The tension from pulling the wooden block in part A also affected the force of friction, changing it from static friction to kinetic friction. The weight of the system, which is also the normal force of the system on the surface, was a variable that affected the coefficient of friction since they are directly related. The friction force calculated, which is equal to the tension on the system, also affected the coefficient of friction as they are inversely related. __

__4. How does the value of coefficient of kinetic friction compare to the value for the same material’s coefficient of static friction?__ __ The kinetic friction of the wood against aluminum is slightly lower than the static friction between the same two surfaces. This is because friction is the measure of the force that is stopping the system from moving. Because static friction is the friction that is keeping the object from moving, it is higher than the friction that is measured when the system is actually moving. __

__5. Did putting the track on an incline significantly change the coefficient of friction? Why or why not?__ __ No it did not. This is because the same materials were used as well as the same acceleration (a=0) in both situations. They were both either not moving (static friction) or moving at constant speed (kinetic friction) resulting in the acceleration always equaling 0. Due to this fact, the weight or normal force of the system was always proportional to the tension so that the acceleration remained at 0. __

Conclusion__:__
__ gggggg The results of our experiment substantially supported our hypothesis. Our objective was to measure the coefficient of friction for both static and kinetic friction, and then to determine the relationship between the friction force and normal force within a system. We had hypothesized that the coefficient of friction would be larger for static friction than for kinetic friction. Our group also expected that friction force and normal force would be directly proportional to one another and thus if the value of one rose so would the other (relative to the coefficient of friction). An examination of our data section reveals our results: µstatic= .237306, which is greater than the µkinetic= .214674, thus supporting the first part of our hypothesis. Second, our graph of “Normal Force vs. Friction Force” shows x and y values of normal and friction forces respectively. One can see that as a value increases in one direction, likewise does the other value. Therefore these results support our hypothesis.__ __ gggggg There were many areas during the process of this experiment that were prone to error. Most obviously, when recording tension data with the force meter we were required to pull the mass with constant speed, an impossible task. There was no way that we could guarantee constant speed. Also, directions stated to place the mass on a perfectly flat surface and to pull it parallel to the board. Again, not only were not able to insure levelness of the surface but it is nearly impossible for a human being to guarantee a perfectly parallel pull the entire time. Even a slight incline in either the surface or the string would yield improper results. In the next section of the experiment our team searched for the maximum incline angle at which the mass would not slide and the minimum angle at which it would slide with constant speed. We had to record angle measurements with a mundane suspended weight system which flopped around when the surface was shook and was consistently difficult to read. Also, because the reading of the angle was done by man and not machine there is no way to guarantee our accuracy.__ __ gggggg Implications of this lab are numerous. There are very few if any surfaces that are frictionless, therefore almost every scenario involving kinetic motion will include friction. In order to understand how much force will be required to overcome the field of static friction and the effect kinetic friction will have on a mass in a real world situation one would need to employ the same information that we derived from this experiment. For example, in racing there is friction between the tires of the car and the surface of the road. There is a certain amount of static friction force proportional to the normal force of the car pushing down on the road. The car driver must break this initial static friction force, and then continue to apply force from the engine of the car to cope with the force of kinetic friction.__

=** Newton's Second Law **= Period 5

__ Completed: 12/3/10 __ __ Due: 12/6/10 __

__ What is the relationship between system mass, acceleration, and net forc e? __
 * Objective: **

__ If we keep one variable constant, first mass and then force, and we graph an acceleration v. force graph and a mass v. acceleration graph, then the relationship between acceleration and force will be linear and the relationship between mass and acceleration will be inverse. __
 * Hypothesis: **

__ a )We first wiped our track down to ensure minimal friction for our cart. We placed the track on a level surface. The pulley was clamped to the table where the end of the track was. We attached a string to the cart, tied a mass to the other end of that string, and ran the string parallel to the track over the pulley. __ __ b) Materials used for this lab include the dynamics cart with mass, a track, a photogate timer, the data studio program, a super pulley with clamp, a base and support rod, string, mass hangers and a mass set, and a metal stopping block. __ __ c) __
 * Procedure: **


 * 1) We attached a mass of 5 grams to the string and placed an additional 25 grams in the cart for a total system mass of 30 grams. For these sets of trials, the system mass was kept constant in attempt to find the relationship between acceleration and force.
 * 2) We ran three trials when the masses were in this position. Using the photogate timer and data studio program, we created a velocity vs. time graph. We created a linear best fit line for each trial and found the slope, which is the acceleration of the cart. We then averaged the slopes of each trial to use as the x-coordinates for the acceleration of our acceleration v. force graph in Excel.
 * 3) Step 3 was repeated four more times, moving 5 grams from the cart onto the string for each set of trials until there were 0 grams left in the cart and all 30 grams were attached to the string.
 * 4) For the next experiment, we kept the mass attached to the string constant for every trial to find the relationship between mass and acceleration.
 * 5) 100 grams were tied to the string, and for our first set of trials, 2,000 grams were placed on the cart. For each set of trials after, we removed 500 grams from the cart, keeping the 100 grams tied to the string the same.
 * 6) Using the information collected from our two experiments, we created two graphs. The first graph shows the relationship between acceleration and force. We plotted the average accelerations as our x-coordinates and the forces (the mass tied to the string during each set of trials) as the y-coordinates.
 * 7) To create a mass v. acceleration graph, we used the constant mass tied to the string in the second experiment as the x-coordinates and the acceleration (average slope of the velocity time graphs) as the y-coordinates for each set of trials. From these graphs and the equations of these graphs we are able to determine the relationship between system mass, acceleration, and force, as seen in the data and analysis below.

__** Data: ** Force vs Acceleration: __

__ ﻿ __ __ Mass vs Acceleration: __

__ Richie did the Excel sheet.__ __** Analysis: **__ __ a. If linear: Force vs Acceleration __ __ What is the slope of the trendline? –The slope of the trendline is 0.5265 __

__ To what actual observed value does the slope correspond? –The slope corresponds to the total mass of the system we are accelerating; in this case the slope should be 0.5300 because that is the total mass of the system in kg. __

__ How does it compare to this actual observed value–The slope on our graph is .5265 and the slope of the actual value should be .5300, which means that our slope is very close to the actual value. __

__ Percent Error __



__ Show why the slope should be equal to this quantity. __ __ On a strait line y=mx+b where m=slope. On our graph we have the y-axis equaling force and the x-axis is acceleration. So, if you plug force and acceleration into the equation for a strait line, respectively, your equation becomes F=ma+b where b is 0, meaning the slope should equal the mass of the system. Because the mass is 530 g or 0.530 kg then the slope should be that or close to that value. __

__ What is the meaning of the y-intercept value?—The y-intercept value is the value of force when there is no acceleration. In our graph the y intercept is 0.0098 which is very close to 0. This is good because if the acceleration is 0 then the force should be 0 because force and acceleration are directly proportional. However in real life we know that this does not always happen, so the y-intercept can be interpretted as the friction. __

__ b. If non-linear: Mass vs Acceleration __ __ What is the power on the x? –The power is -1.16 __

__ What should it be? –The power should be -1 because mass and acceleration are inversely related. __

__ What is the coefficient in front of the x? –It is 0.8659 __

__ To what actual observed value does the coefficient correspond?—The coefficient is supposed to represent or correspond with the constant force being used the accelerate the system. The actual value should be 0.9800. __

__ Percent Error __

__ Show why this value should be equal to this quantity. __ __ In a graph like this the equation for the line is y=1/x or y=mx-1 where m=slope. In our graph the y-coordinate was the mass of the system and the x-coordinate was the acceleration of the system. So, m=Fa-1. Slope=force. __

__ 2. ** What would friction do to your acceleration? **__ __ The friction would subtract from the total force and because force and acceleration are directly related, the acceleration would then be smaller. __

__** Would you need a bigger or smaller force to create the same acceleration? **__ __ You would need a bigger force so that when friction is subtracted from the force it will be the original force you are using prior to friction being a factor. __

__** Was your slope too big or too small? **__ __ On the Force vs Acceleration graph the slope was only 0.004 too small, almost perfect. However on our Mass vs Acceleration graph the slope was a lot smaller then we expected it to be. __

__** Can friction be a source of error in this experiment? **__ __ Yes it can. Even though we wiped down our track, it was to ensure // minimal // friction no to ensure that there was no friction at all. The only way we could have less friction would be to have a track made out of ice. The friction would have made the force smaller due to the fact that the friction was in the opposite direction of the tension, so this could be why on our Mass va Acceleration graph the force is smaller then we expected it to be. __

__** Redo the calculation of acceleration WITH friction to show its effect. **__ __Where the friction is .0098N. We got this number from our y intercept, which makes sense because on a frictionless surface the y intercept should be 0 however in this case, with friction is was .0098.__ __∑Fx=m*ax__

__T-f=m*ax__

__.049N-.0098N=0.525kg*ax__

__.0392N=.525kg*ax__

__.07467=ax__

__ax=.07467m/s/s__

__∑Fx=m*ax__

__T-f=m*ax__

__1.155N-.0098N=2.5kg*ax__

__1.1452=2.5kg*ax__

__0.45808=ax__

__ax=0.45808m/s/s__

__** Conclusion: **__

__ ggggggggggg The results of our experiment supported our hypothesis. We had predicted that the results of the lab would provide evidence that force and acceleration are directly proportional to each other and that mass and acceleration are inversely proportional. Meaning that if we increase the force pulling the cart, the cart’s acceleration will also increase, and if we decrease the mass of the cart, the acceleration will increase. Our results supported both parts of our hypothesis. As you can see, we had very accurate measurements, which is evident by our r2 value.__ __ ggggggggggg A few things that might have caused error in our results include friction, for which we did not calculate, and various forms of human error. For friction, we were instructed to wipe down the track with water to remove any dirt and to create a slicker surface. However, the track was very thin and difficult to get into, and we cannot be certain that friction was completely eliminated. If friction was present, it would have caused the acceleration value to be lower than expected. In terms of human error, while releasing the cart at the start of a trial if any force was acting on the cart other than the force of tension from the string, such as the person’s hand pushing or pulling, the results would be off. Also, there is no way to know for sure that the track was perfectly level. We tested it by placing the cart on the track with no force except gravity acting upon it and it did not move, however a very slight incline may not have showed up with this mundane test and yet still have affected results. Lastly, when selecting a group of points for study from Data Studio, if we accidentally included points at the end that were not affected upon by the force of the hanging weight (tension), they would not give us accurate results, thus affecting our r2 value. __ __ ggggggggggg Specific applications of this experiment include cranes and pulley-usage in general. Say for instance at a construction site that a heavy, known mass of bricks needs to be lifted up to a team of men working on a section of a building. They decide to attach a pulley to the roof, and run a rope from the bricks over the pulley and to a truck. How much must the driver accelerate to create enough force to lift the bricks? Knowing the correlation between force, acceleration and mass is crucial for many real world events. For example, knowing the weight of an airplane, you would need to know what amount of force would be necessary to reach a certain acceleration required for takeoff. Also, when flying a kite one needs a certain amount of force from the wind to accelerate the kite to a speed necessary to lift it off the ground. __


 * Lab: Inertial Mass **

__** 11/19/10 **__ __** Excel Spreadsheet: **__

Objective __The objective is to find the mass of an object only using its inertia.__

Hypothesis __If we put a known mass of a small value and after, a mass of a larger value, in the inertial balance, and conduct trials to see how many periods occur per second, then the less massive masses will have more periods per second.__

Procedure __1. Clamp the inertial balance onto the desk.__ __2. Place a known mass, 20 g, in the balance and tape it down so it does not move and affect the trial.__ __3. Count the number of vibrations that occur in 20 seconds.__ __4. Repeat step 3 so that you have at least 3 different trials for the known mass.__ __5. Calculate the average of vibrations from the 3 trials and then divide the average by 20 to find the vibrations per second.__ __6. Repeat steps 2-5 with a 50g, 100g, and 200g mass and then create a graph with a line of best fit.__ __7. Place the Rubiks cube in the inertial balance and tape it down. Count how many vibrations occur in 20 seconds and take 3 trials.__

__ 8. Average the 3 trials and divide by 20. __ __ 9. Use the number calculated for the number of periods of the Rubiks cube and plug it in as the y value of your equation on your graph to solve for x (mass of cube). __

Materials __The materials we used for this experiment were the inertial balance, known masses, a stopwatch, a clamp, and the Rubiks cube. The picture below is the 4 known masses we used.__

Data __The first chart shows the masses we knew and the number of periods that occurred over 20 seconds in each of our 3 trials. We averaged the number of periods for each mass together and then divided that number by 20 to solve for how many periods there were per second. The second chart shows our known data and our unknown, the mass of the cube.__ __The data we collected was pretty accurate, as seen by the large r2 value. Using the equation of the trend line above, we plugged the period per second in as the y-coordinate and solved for x. Because we used the quadratic formula, we calculated two different answers. One answer was 105.9 g and one was 330.8 g. We decided to throw the 330.8 g answer out because the cube did not feel that heavy.__

Conclusion __Our hypothesis was correct because after solving for the periods per second for each mass, the smallest masses had the least inertia (least amount of periods per second).__ __One source of error was Jae's reaction time in stopping the stopwatch to measure exactly 20 seconds worth of periods. Other possible sources of error include the mass perhaps moving while the trials occurred and if the balance was bent downwards. A reason that our results are not exactly the same as the other groups results is due to the fact that we all used different balances that are not exact to each other. Each balance could also have its own problems, such as more or less flexibility of the bars, due to overuse over the years.__ __To address the sources of error, we would measure the periods for a longer amount of time so the reaction time would not have as a great an affect on the results. The class would all have to use the same balance to compute the same results as well.__

Follow-up Questions__ 1. Did gravitation play any part in this operation? Was this measurement process completely unrelated to the "weight" of the object? - Gravitation did not play any part in this experiment and the measurement was therefore completely unrelated to the weight of the object. Gravity does not affect mass, which is what we were solving for in this experiment. Gravity only affects weight, which is unrelated to what we were doing.

2. Did an increase in mass lengthen or shorten the period of motion? - An increase in mass lengthened the period of motion.

3. How do the accelerations of different masses compare when the platform is pulled aside and released? - The heavier an object was, the slower its acceleration and the lighter the object was, the faster the acceleration.

4. 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? - Yes, it would slow the tray of the balance down if the side arms were stiffer. The periods would be shortened because the arms would not bend as much as they do now.

5. Is there any relationship between inertial and gravitational mass of the object? - There is no relationship because gravity does not act on mass, only weight.

6. Why do we almost always use gravitation instead of inertia as a means of measuring mass of an object? -We use gravity because it only requires the weight of the object. On the other hand, using inertia would cause one to use an inertial balance to find inertia. Also gravity is always present while inertia can vary.

7. How would the results of this experiment be changed if you did this experiment on the moon? - The results should be the same because gravity did not affect this experiment since we were measuring mass. The mass of an object would not change if we were on the moon. Also, the balance only moves back and forth horizontally and is not being acted on by any vertical forces like gravity.