Tyler+Eric+Sean+Tom+(TEST)


 * T**yler
 * E**ric
 * S**ean
 * T**om

We test things WOOOOOOO PHYSICS! :D

__**Inertial Mass Lab**__
__Hypothesis:__ Greater weights will produce greater inertial masses which will be shown by the increase in period time as the mass increases.

__Procedure:__ 1. First we collected all of the necessary materials (various known masses, clamp, inertia measuring unit, tape, stopwatch). 2. Next we clamped the measuring unit to a desk. 3. Then we pulled the inertia-measuring model. 4. We then counted the how long it took for the model to go back and forth twenty times. 5. Lastly we calculated the period time for each given mass and through this, the mass of the Rubik's Cube.




 * Discussion Questions**


 * 1) //Did gravitation play any part in this operation? Was this measurement process completely unrelated to the “weight” of the object?//
 * 2) Yes, because the weight of the object is measured by the amount of gravity acting upon that object, which in turn affected the measure of frequency. No, it was completely related to the weight of the object because the weight was the independent variable.
 * 3) //Did an increase in mass lengthen or shorten the period of motion?//
 * 4) As the mass increased, the frequency decreased.
 * 5) //How do the accelerations of different masses compare when the platform is pulled aside and released?//
 * 6) The lighter the mass, the greater the acceleration was. The heavier the mass, the lesser the acceleration.
 * 7) //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?//
 * 8) If the side arms were stiffer, than the period would be shortened.
 * 9) //Is there any relationship between inertial and gravitational mass of the object?//
 * 10) Yes, the higher the mass of the object, the higher the inertial mass.
 * 11) //Why do we almost always use gravitation instead of inertia as a means of measuring mass of an object?//
 * 12) Because usually we want to know what the weight of the object at rest, in which only gravity is acting upon it.
 * 13) //How would the results of this experiment be changed if you did this experiment on the moon?//
 * 14) If this experiment were to be done on the moon, the period and frequency of the object would be the same. This is because gravity does not affect lateral movement.

From this lab, we can infer numerous things. For one, we can conclude that lateral movement is not related to vertical motion. We have learned, through hypothesizing and thinking about this experiment on the moon, that the mass would not change. This is proven in science and backed up by our ideas. Mass is not affected by gravity, but weight is. Therefore, the weight of an object would be lighter on the moon than on Earth, but the mass would be the same in both situations. We have quantitatively concluded that the higher the mass of an object, the higher the inertial property of said object. We have shown this through the measured times per period of different massed objects. The objects with the higher mass always took more time to complete one period. This shows that these objects took longer to accelerate, which is a major component of the law of inertia. Overall, this lab has helped us understand better, Newton's Law of Inertia, as well as gain a new perspective of mass in relation to acceleration.
 * Conclusion:**

number of periods counted, more = less effect of reaction time.

__**Newton's Law Lab**__

 * Hypothesis:** On a linear pulley, the closer to zero the ratio of mass on cart : mass on hanger, the closer the total acceleration of the two systems to 9.8 m/s^2

Procedure: 1. Set up cart on frictionless track on table 2. Set up hanging mass 3. Experiment 1: Adjust masses on cart and mass so the total mass is constant 4. Experiment 2: Adjust mass on cart so that the cart's mass will change whilst the hanging mass stays constant 5. Process the results by calculating the accelerations from the tests in experiments 1 & 2


 * Data:**
 * Experiment 1 ||  ||   ||   ||   ||
 * || Distance (cm) || Mass Cart (g) || Mass Cart w/ Mass (g) || Total Mass Hanger (g) || Acceleration (m/s^2) ||
 * Trial 1 || 49 || 505 || 525 || 10 || 0.0745 ||
 * Trial 2 || 49 || 505 || 520 || 15 || 0.165 ||
 * Trial 3 || 49 || 505 || 515 || 20 || 0.264 ||
 * Trial 4 || 49 || 505 || 510 || 25 || 0.345 ||
 * Trial 5 || 49 || 505 || 505 || 30 || 0.444 ||
 * Experiment 2 ||  ||   ||   ||   ||
 * || Distance (cm) || Mass Cart (g) || Mass Cart w/ Mass (g) || Total Mass Hanger (g) || Acceleration (m/s^2) ||
 * Trial 1 || 49 || 505 || 1505 || 30 || 0.117 ||
 * Trial 2 || 49 || 505 || 1405 || 30 || 0.140 ||
 * Trial 3 || 49 || 505 || 1305 || 30 || 0.152 ||
 * Trial 4 || 49 || 505 || 1205 || 30 || 0.171 ||
 * Trial 5 || 49 || 505 || 1105 || 30 || 0.186 ||
 * Trial 6 || 49 || 505 || 1005 || 30 || 0.195 ||
 * Trial 7 || 49 || 505 || 905 || 30 || 0.228 ||
 * Trial 8 || 49 || 505 || 805 || 30 || 0.259 ||
 * Trial 9 || 49 || 505 || 705 || 30 || 0.306 ||
 * Trial 10 || 49 || 505 || 605 || 30 || 0.344 ||
 * Trial 11 || 49 || 505 || 505 || 30 || 0.449 ||
 * Trial 11 || 49 || 505 || 505 || 30 || 0.449 ||

This graph shows our first run, where the mass on the hanger was 10g and the mass of the cart was 525g. The slope on a velocity time graph represents the object's acceleration, which in this case, was .0745m/s^2.
 * Graphs From Data (Part I):**



This graph shows the acceleration of the cart when the hanging mass was 30g and the cart's mass was 505g. This graph's acceleration is .444m/s^2. These two velocity-time graphs show that as the hanging mass increased and the mass of the cart decreased, an increase in acceleration was seen in both, demonstrating the directly proportional relationship of Newton's equation F = ma. As the mass of the hanger increased, the force pulling upon the cart increased.



This graph depicts our first run of the second part of the experiment. The total mass of the cart was 1505g and the mass of the hanger was kept constant at 30g.
 * Graphs from Data (Part II)**

This graph shows our 4th run, where the total mass of the cart was 1205g and the mass of the hanger remained consistent at 30g.

These two graphs illustrate that as the force on the cart remained the same (the mass of the hanger), and the mass of the cart decreased, acceleration increased. This clearly proves the idea that if the same force is applied to a lighter mass, the acceleration on the lighter mass will be greater than on the more massive one.

//1. Explain your graphs:// //a. 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?// //b. If non-linear: What is the power on the x? What should it be? What is the coefficient in// //front 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.//
 * Discussion:**

1 b. (Pertaining to graphs 6 & 7) These graphs are to the second power. This is what they should be, considering the relationship between acceleration and the ratio of the two masses is an inverse parabolic relationship. That means that the closer the ratio to zero, the higher the acceleration. The coefficient of the x term corresponds to the rate at which the relationship between the two progresses. Between the actual value and the observed value, the percent error is for graph 6, 3.23%. For the second graph, it is 5.21%. If the observed value between the two measured quantities is the same as the theoretical value (as it should be), then the values should be equal and there should be no percent error. The values were slightly off though, as were the coefficients, and that is why there is minimal percent error.

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? Redo the calculation of acceleration WITH friction to show its// //effect.//
 * Response:** Friction acts in the opposite direction of motion. Therefore if our cart was moving left, the friction would be acting right. Because the two forces are acting against each other, friction would reduce the cart's acceleration. In order to receive the same acceleration in a frictionless environment, and in one containing friction, the latter would have to apply a greater force (add mass to the hanger). Because we did our calculations sans friction, the slopes we received were slightly higher than if they would've been done with friction.


 * Error Analysis & Percent Error:** Throughout the lab, there was friction acting upon the pulley. Friction should decrease the acceleration of the cart on each trial. We disregarded the friction in our experiment in order to complete it within a timely manner and also because we had yet to learn how to calculate it. But friction does play a somewhat significant role in the results, despite the fact that friction was minimized due to the form of the cart wheels and that the track was wiped down before the experiment began. Because we did not include friction into the equation, our slope was slightly larger than it would have been. This essentially threw off the entire data spreadsheet.



There were several sources of error we may have encountered while performing this lab. The first and biggest source of error we could have had was friction. We did not account for friction in any of our calculations even though friction was present in the lab. The track had been wiped down with a damp paper towel in order to reduce the amount of friction between the wheels and the track, but it was nearly impossible to eliminate all the friction between the two. Also there may have been friction between the axle that the wheel was spinning on and the wheel. Another source of error in this lab is how the cart was released each time. A finger was held in front of the cart to hold it steady and then pulled away at the beginning of each run. There is a chance that the finger could have moved the cart slightly backward before allowing it to move forward thus affecting the acceleration of the cart as well as the distance it traveled. Another source of error that was not accounted for in our calculations is air resistance. The cart had a large, flat, vertical surface in the front as well as weights stacked vertically on top of it. Although minuscule, air resistance did affect the rate at which the cart accelerated. Air resistance also acted on the acceleration of the hanging mass as it moved towards the ground, slightly decreasing its acceleration. In order to minimize error if we were to conduct this lab again we would do the following: To minimize the amount of friction the surface of the track as well as the axles that the wheels are spinning on could be cleaned and then oiled. This would insure a slick and nearly frictionless surface for the cart to slide on. In order to ensure that the cart was starting form the same position each time and gate could be made that is set at a specific distance that opens up in order to let the cart begin to accelerate. To minimize air resistance, a more aerodynamic cart could be used. If the front of the cart was slanted rather than being vertical, it could cut through the air more easily avoiding the affects of air resistance. There are a lot of real world applications for this lab. One example is in construction. If a certain mass of materials needed to be lifted up to a certain spot, the workers could use a pulley to do so. They would need to calculate the amount of force needed on each end of the pulley in order to lift the materials to the desired height.
 * Conclusion:**

=__ Lab: Coefficient of Friction __=

To determine both the static and kinetic coefficients of friction between surfaces. To determine the relationship between static and kinetic friction To determine the correlation between friction forces and normal forces.
 * Objective:**

The static friction of a surface is greater than the kinetic friction of a surface when both acted upon by the same object.
 * Hypothesis:**

__Experiment 1__ > > > > > > >
 * Procedure:**
 * 1) Obtain the mass of the wooden block
 * 1) Attach the experimental surface to the table top.
 * 1) Place the block on the surface and put 2500g on top of it.
 * 1) Attach a string to the block at one end of the string, and to the force meter on the other.
 * 1) Plug the force meter into your computer. Upload Data Studio and under the options, “Create Experiment”.
 * 1) Under Data Studio, check Force Pull Positive and uncheck Force Push Positiv ** e **.
 * 1) Leave some slack on the string.
 * 2) Press the button “ZERO” on the sensor.
 * 1) Press START on Data Studio.
 * 2) Begin to pull the block with the force sensor.
 * 3) Pull with increasing force until the block moves.
 * 4) Once moving, pull with constant force.
 * 5) Observe the graphed results and record the mean (in the section where the block was being pulled at constant force) as the value for Tension at Constant Speed.
 * 6) Record the max value on the graph for Maximum Tension.
 * 7) Repeat the experiment with the same mass.
 * 8) Repeat steps 8-11, taking our 500g each time.

__ Experiment 2 __
 * 1) Attach a protractor to the side of the track.
 * 2) Place 2500g mass in the block
 * 3) Place it at the raised end of the track.
 * 4) Raise (slowly) the side of the track with the block until the block just begins to slide slowly down the aluminum surface at constant speed.
 * 5) Repeat step 4 at least 7 times.
 * 6) Calculate the average of the angles from the experiment.
 * 7) Repeat step 4-6, subtracting 500g mass each time.
 * 8) Place the track on an incline. With your calculated angles from the experiment, which should all be the same, place the incline's angle to slightly less than this calculated angle. Push the block very lightly. Observe your results. * The block should move at constant speed very slowly down the inclined plane.


 * Free Body Diagrams & Equations Derived:**



The data before the break corresponds to Experiment 1. The rows after the break correspond to Experiment 2. The bottom row of the top data set is the average of each column (except for the first column). As shown by the second data set, the coefficient of kinetic friction on an inclined plane can be determined by the following. Break up the weight vector into x and y components using the angle at which the weight begins to move. Using trigonometry, figure out the tangent of these components (y comp./ x comp.). The tangent should be equal to the coefficient of kinetic friction. __Experiment 1__
 * Data:**
 * Mass of Object (kg) || Weight (N) || Friction Static (N) || Friction (Static) || Friction Kinetic || Friction Coefficient (Kinetic) ||
 * 2.69292 || 26.390616 || 5.7 || 0.215985864 || 4.8 || 0.181882833 ||
 * 2.19292 || 21.490616 || 4.6 || 0.214046912 || 3.3 || 0.153555394 ||
 * 1.69292 || 16.590616 || 2.9 || 0.174797608 || 2.2 || 0.132605082 ||
 * 1.19292 || 11.690616 || 2.5 || 0.21384673 || 1.7 || 0.145415776 ||
 * 0.69292 || 6.790616 || 1.1 || 0.16198825 || 0.6 || 0.088357227 ||
 * 0.19292 || 1.890616 || 0.7 || 0.370249696 || 0.4 || 0.211571255 ||
 * || 14.140616 || 2.916666667 || 0.22515251 || 2.166666667 || 0.152231261 ||
 * Angle (degrees) || Mass (kg) || Weight (Total) || Weight x (N) || Weight y (N) || Friction (Kinetic) (Tangent Theta) ||
 * 10 || 2.69292 || 26.390616 || 25.98753995 || 4.594821002 || 0.176808617 ||
 * 10 || 2.19292 || 21.490616 || 21.16237991 || 3.741691127 || 0.176808617 ||
 * 10 || 1.69292 || 16.590616 || 16.33721987 || 2.888561253 || 0.176808617 ||
 * 10 || 1.19292 || 11.690616 || 11.51205983 || 2.035431379 || 0.176808617 ||
 * 10 || 0.69292 || 6.790616 || 6.686899791 || 1.182301505 || 0.176808617 ||
 * 10 || 0.19292 || 1.890616 || 1.86173975 || 0.329171631 || 0.176808617 ||
 * 10 || 0.69292 || 6.790616 || 6.686899791 || 1.182301505 || 0.176808617 ||
 * 10 || 0.19292 || 1.890616 || 1.86173975 || 0.329171631 || 0.176808617 ||
 * Graphs:**

This graph can be interpreted as such. It shows, as it hypothetically should, the fact that the static friction retains a higher value than does kinetic friction. This is shown through the sudden drop in friction once the block being pulled begins to move. That causes for the friction to turn from static to kinetic and go from a higher to a lower value. These values stay proportional, as we can see that the higher the values (caused by more weight/mass being pulled), the farther away the two lines become. If we were to analyze the equations, we would discover that the coefficients for x represent the coefficients of friction. Also, when we look at the r^2 values, which are all very close to 1, we can extrapolate that we were likely extremely close to the actual values. (On the legend, disregard the third line, as it serves no purpose) This is a picture from data studio comparing two runs. The two runs being compared are that of the .19292 kg mass (pink) and that of the 2.19292 kg mass (burgundy). It can be observed that as the mass increases, the friction increases. The maximum point on either represents static friction. Very quickly, the graph drops, representing the static friction. The points where the force is zero is where the experiment has yet to begin or has ended.

__Experiment 1__
 * Calculations:**

First calculated are the percent differences. In order to determine these, we used the appropriate equations and applied the appropriated derived and experimental values calculated from our excel spreadsheet. In terms of kinetic friction, we experienced only a 4.92% difference from the rest of the class. In terms of static friction, we experienced a mere 1.00% difference. These percent difference equations show our similarities to the class' values. This means that we have performed the experiment with precision and accuracy. The next calculation we performed were the percent error equations. By following a similar format with different equations in relation to the percent difference calculations, we came up with some fairly promising results. First, in order to accomplish any of this, we needed to derive the accepted coefficients of friction with this specific set of circumstances. These equations, formulated from corresponding free-body diagrams, gave us values of .2065 and .1527 for the static and kinetic coefficients of friction respectively. The kinetic friction was the closest for percent error, as it was a nearly negligible 1.36% error. The static friction was slightly more off, as we experienced a 16.83% error. This is still fairly close, but not as much as we would have liked. We will explore the reasons why this occurred in the Error Analysis. This means that according to what our results should be, we were extremely close. This shows the reliability of this experiment, and it also proves the legitimacy.

1. Why does the slope of the line equal the coefficient of friction? Show this derivation. The coefficient of friction, as shown through equations produced from free-body diagrams, shows the relationship between f and N ( u = f/N). These graphs also show the relationship between f and N, with f being the x-axis and N being the y-axis. Using the slope equation of m = y/x, the coefficient of friction should be produced accordingly
 * Discussion Questions: **

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. http://www.engineersedge.com/coeffients_of_friction.htm. The coefficient of friction between dry contact of wood and metal ('tis all I could find) is between .2 and .6. Our static data definitely falls within this range. Assuming that aluminum is at the lower quarter, the results should be between .2 and .3. Still, our results fit this quota. Our kinetic data falls a bit lower than this range of accepted results, as it is .1784.

3. What variables affected the magnitude of the force of friction? What variables affected the magnitude of the coefficient of friction? Mass affects the force of friction between two objects. As shown by our graphs, as the mass of an object increases, the static friction's maximum point as well as the amount of force needed to maintain a constant speed is increased.

4. How does the value of the coefficient of kinetic friction compare to the value for the same material's coefficient of static friction? Compared to the value of kinetic friction, static friction is higher. This is because static friction keeps an object in place. This means that all of the force applied upon that system, as determined by Newton's Law of Inertia, goes towards moving the object. There is no auxiliary force helping move the object within the system. When the object is moving, however, inertia causes the object to continue forwards. This, in addition to the tension or normal force applied to the already moving object, results in a lower relative friction.

5. Did putting the track on an incline significantly change the coefficient of friction? No it did not. The coefficient of friction is determined by two objects upon one another. There should be the same relative forces in a system regardless of whether or not it is on an incline. The subtraction of tension from the system was replaced by the addition of weight propelling the system downward. This is determined by the angle that the incline is set at. In conclusion, the weight force propelling object forward when friction changes from static to kinetic should be the same as the tension moving the object forward.

**Conclusion:** There are many places where error could have occurred. For experiment one, if the block was not pulled with relatively constant speed, one would not be able to receive clear or accurate data. It could case a number of discrepancies, ranging from results that don't match the others to fluctuating sliding friction results. In order to solve this problem, the one applying the force could focus harder on pulling with constant speed, or the person applying the force can be replaced with another, steadier person. Another point of error in experiment one was the track. The track could have dirt or residue that could impact that data received. The solution to this problem is simple; a member of the group should wipe down the track. As well as sources of error in experiment one, there were other sources of error in experiment two. For example, if the tool used to measure the angle is not accurate, it could throw off the angle by a single degree to a few degrees. To fix this, one would have to calibrate the tool or get a new one. Also, if the person lifted the track too fast, it could possibly yield a resulting angle higher than it actually should be. In order to correct this, multiple trials could be used or the person lifting the track could be extra careful.

This run represents a trial where the block was not pulled with equal force. Based on the fact that the force applied on the block is relatively large in comparison to the other trials, it can be assumed that we are working with heavier weights. Unlike any of our other trials, there was a significant build-up to the static friction point. With our other trials, there was no build up, but rather a large spike. Also, in our other trials, the static friction point and the mean for the sliding friction were considerably far apart. In this one, however, the sliding friction is very close to the static friction point. Lastly, during the sliding friction stage, the force fluctuated too much to be used as data. Due to these reasons, this trial was not used in our data. For the other trials, another person was used to apply the force to the block, rendering us better and more accurate results.

__** Acceleration Down an Incline Lab **__
Eric Solomon, Sean Krazit, Tyler Samani, Tom Mccullough Period 4 Due: 1/3/11

1. To find a relationship between an object's acceleration down an incline and the angle of the incline. 2. To compare the coefficient of friction found in this lab to the coefficient of friction between the same substances found in a former lab.
 * Purpose:**

Hypothesis: As the angle of the incline increases, the object's acceleration will increase.
 * Hypothesis and Rationale:**

Rationale: A mass' acceleration is affected by four main things: gravity, set mass, friction, and incline angle. During this experiment, we intend to keep three of those things constant. They will be the mass (same mass), friction (same surface), gravity (same planet). The only thing that will change will be the incline angle. This angle will change the respective x and y values for the weight of the object. With a greater incline angle, the x value will increase in respect to the y value. Since the x value will always deal with an object's effect along a certain surface (as opposed to y value dealing with the effect through it), the higher the x value (weight force along the surface) is, the faster an object will be able to accelerate. Therefore, the mass will fall down the incline at a greater rate, thus proving our hypothesis.

Necessary Materials: Aluminum Track, Wooden Block, Ring Stand, Meter stick, 2 Photogate Timers, Picket, Tape, String, Pulley, Masses
 * Procedure:**

Part A Explained: The wooden block sits on the aluminum track (wipe down with water before beginning). Place a set mass as well as the picket on the block. Set up the Photogate timer s down the incline accordingly. Set up Data Studio and record the data from the picket passing through the Photogate timers.

Picture:


 * Data:**

Class Data:

Our Gathered Data:




 * Free Body Diagrams:**




 * Calculations:**









Part A


 * Discussion:**

1. Discuss your graph. What does the slope mean? What is the meaning of the y-intercept? Our graph is an accurate representation of the data and experimental values that were obtained. Just as our hypothesis posed, the acceleration of the object increased as the angle of the incline increased. This graph, showing the relationship between the sine of the angle versus acceleration, was indicative of many things. First of all, the slope allowed us to interpret the experimental value of gravity that we conceived as a result of the data from the experiment. Second off, the value of friction was produced through the y-intercept. This showed how much the friction affected the path of the object traveling down the incline.

2. If the mass of the cart were doubled, how would the results be affected? As proven by the equation derived above, the mass of the cart does not affect the acceleration of the cart. The equation for Part A shows a= gsin(theta) - ugcos(theta). This therefore explains how the masses in the equations cancel each other out when producing the final equation. To explain this more thoroughly, on an incline, the mass is divided into two distinct portions. These are the x value and the y value. These values are derived as a result of the angle of the incline that an object sits on. These values are related though. As the x value increases, thus pushing the object down the incline, the y value will increase proportionally, thus keeping the object stable. This "equilibrium" between the forces effectively neutralizes any effects that the changing mass may have on acceleration.

3. Consider the difference between your measured value of g and the true value of 9.80 m/s2. Could friction be the cause of the observed difference? Why or why not? Because of the information that we can gather from the graph, we can clearly see that the value of friction is represented by the y-intercept. This y-intercept, not being completely accurate due to experimental faults (explained later), will naturally throw off the balance of the entire graph. As also shown from the graph, the value of gravity is represented by the slope. Since the friction is wrong, therefore causing the y-int. to be incorrect, the slope will be slightly off. This caused for our slight difference in our measured value of gravity.

4. Not applicable, as the information was not available

As with ever experiment, there are points in which error could have been made. It is possible that mistakes could have been made in the calculations. This error is simple enough to correct, for all that needs to be done is a quick revision or redo of the calculations. Human error could have possibly occurred in addition. For example, when letting go of the block, a small force could accidentally be applied to the block. Regardless of the direction the force is applied to, it will affect the data. The best way to account for this is to have the person with the steadiest hands in the group to release the block. Other than that, there is not much that can be done about human error. Lastly, there is possibly mechanical error. For example, there were times in which Data Studio did not work properly. Also, if the photogate was set up too low, the block would hit it. This would cause two things to happen: the block would slightly decelerate (enough to possibly affect the data), and the photogate would move out of the way of the block (which could severely affect the data). In order to account for that, the setup must be checked thoroughly in order to make sure that the block will not even have the slightest contact with the photogate.
 * Conclusion:**