Group4_2_ch4

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Ali, Jessica, Caroline, Sarah

=Gravity and the Laws of Motion = 11/16/11 Task A: Jessica Task B: Ali Task C: Caroline Task D: Sarah

**Objective** > **Hypothesis** We believe that the value of acceleration due to gravity is 9.8 m/s/s, without air resistance, because we have measured it in a previous free fall lab. We believe that when we increase the incline angle the acceleration will increase, as we that when the ramp goes higher and higher, it behaves more like an object in free fall. We also believe that the mass is inversely proportional to acceleration as F= ma, thus, as acceleration increases, the mass must decrease. Therefore, the heavier the object, the less chance that it will accelerate at a higher rate, and vice versa.
 * find the value of acceleration due to gravity
 * determine the relationship between acceleration and incline angle
 * determine if mass has an affect on acceleration due to incline
 * use a graph to extrapolate extreme cases that cannot be measured directly in the lab

**Methods and Materials** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">During this lab, we used the following: a ball with the mass of .535 kg which we found by using an electronic balance scale, a ramp with a distance of 1.2 meters, a stop watch to measure time, a ruler to measure height, and a protractor to measure the angle of the ramp. First we set up the ramp to be at a heigh of .15 meters and placed the ball at the top so that it could travel 1.2 meters. We then recorded the amount of time it took for the ball to travel to the bottom of the ramp. To ensure accuracy, we performed three trials. We then changed the height of the ramp to .25 meters ( and .35 and .40 meters thereafter) and placed the ball at the top so it could travel 1.2 meters. We then recorded the amount of time it took for the ball to travel to the bottom of the ramp. To ensure accuracy, we performed three trials. We then recorded the data into an excel spreadsheet and thereafter formed conclusions.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">**Procedure** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">below is a video at the height of .15 meters <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">media type="file" key="15 cm.mov" width="300" height="300"

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">below is a video at the height of .25 meters <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">media type="file" key="25 cm.mov" width="300" height="300"

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">below is a video at the height of .35 meters

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">media type="file" key="35 cm.mov" width="300" height="300" <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">below is a video at the height of .40 meters <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">media type="file" key="40 cm.mov" width="300" height="300"

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">**Sample Calculations and Data** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">This is a chart showing the individual data that we collected. We changed the height of the ramp which changed the time therefore average acceleration.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">This is a chart showing the class data. The experimental g are the different slopes that groups got based on their average accelerations.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> This graph shows average acceleration vs. sin(theta).

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">sample acceleration: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">sin theta sample: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">**Analysis** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Our slope of our acceleration vs. sin theta graph was 10.175. This is a very close numerical value to the actual acceleration due to gravity of 9.8 m/s/s. Although it is impossible for the force of acceleration to be greater than 9.8 m/s/s unless a force is pulling on an object, it appears we may have had a slight miscalculation when measuring time and distance in our experiment. Yet, as shown below, the percent error is very small, proving that our experiment was mostly successful.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">percent error: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">percent difference: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">free body diagram: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; line-height: 0px; overflow-x: hidden; overflow-y: hidden;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">The force causing the ball to roll is the x component of the weight. The y component of the weight is balanced with the normal force, on the diagram they are in one straight line, therefore they're balanced, keeping the ball in place. However, the x component of the weight pulls it down the incline.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">class acceleration values @ 15 cm <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">using newton's second law of motion, we figured out what the acceleration should be. 1.225 m/s/s is fairly close to the acceleration we calculated through the lab of 1.048 m/s/s.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">**Discussion Questions**
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Is the velocity for each ramp angle constant? How do you know?
 * 2) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">No because its accelerating as it goes down the ramp
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Is the acceleration for each ramp angle constant? How do you know?What is another way that we could have found the acceleration of the ball down the ramp?
 * 4) No because as the angle becomes higher, the acceleration becomes greater. the higher the angle, the closer the object is to being in freefall, so it accelerates faster.
 * 5) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">How was is possible for Galileo to determine g, the rate of acceleration due to gravity for a freely falling object, by rolling balls down an inclined plane?
 * 6) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">He probably did something similar to us where he rolled a ball down an inclined plane at varying heights and calculated the acceleration at each incline. He realized that the angle could not get any higher that 90 degrees, so when testing at the largest possible angle, he noticed that the acceleration never exceeded 9.8 m/s/s.
 * 7) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Does the mass of an object affect its rate of acceleration down the ramp? Should it affect the motion of an object in free fall in the same manner?
 * 8) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">The mass of the object should not affect the acceleration down the ramp. It only affects it because of friction, with no friction it would not affect the acceleration. It would not affect an object in free fall in the same way because there wouldn't be friction.
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">The mass of the object should not affect the acceleration down the ramp. It only affects it because of friction, with no friction it would not affect the acceleration. It would not affect an object in free fall in the same way because there wouldn't be friction.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">**Conclusion**

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Upon the conclusion of our lab, when we had satisfied all of the objectives, we were to surmise that our hypotheses were proven relatively correct. The only one that is actually incorrect is the one where we hypothesized that objects with a greater mass travel slower than those with a smaller mass. This is untrue - as we learned by comparing our data with the class's, mass actually has no real effect on acceleration. It only //seems// to because of friction, which we ignored in this experiment - there was minimal friction anyway, as the ball was rolling. (If we hadn't ignored it, our hypothesis would have been correct - we used the equation F = ma to demonstrate this). We also did not take any air resistance into account. Otherwise, our other two hypotheses relatively correct. We found that the slope of the line in our graph - in other words, acceleration due to gravity - was 10.1 m/s/s. Though this is technically impossible, it's still very close to the actual value (9.8 m/s/s). The error here can be attributed to some of the slight inaccuracies that could have occurred when doing this lab. (These inaccuracies can be attributed to measurement and timing, which is further explored below). Finally, we had hypothesized that an object on a steeper incline will accelerate faster than one on an incline that is less steep. The data we collected during the experiment supports this hypothesis. For example, when we had the ball roll down an incline that was .15 m off the ground (and therefore had a sinθof .125), the acceleration was 1.048 m/s/s. However, when the incline was .4 m above the ground (with a sinθ of .333), the acceleration was 3.562. As the height of the ramp increases, so does the angle of elevation. The closer the angle gets to 90º, the closer it gets to a state of free fall where the acceleration is 9.8 m/s/s.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">As with every lab, there were several sources of error that could have contributed to the discrepancies in our data. When traveling down the ramp, our ball didn’t travel in a straight line – it moved towards the sides and bounced off of them. This could have caused inaccuracies in our time – it takes longer for the ball to travel diagonally than it would if it had gone completely straight. Though this extra time is very minimal, we are working with such small numbers; this could actually have caused quite the fluctuation in our data. We also must keep in mind human reaction time when analyzing the results of this experiment. It is very unlikely that the timekeeper was able to be 100% accurate, no matter how fast they were able to press the button on the stopwatch. It would be unreasonable to expect such precision. Finally, the ramp we used had a tape measure attached to it, saying that it measured 120 cm. Under closer inspection, however, there are two small gaps that the tape measure does not cover – one at the beginning, and one at the end. These distances are very small, and, like the other issues, cause disparities in the data that are likely negotiable. Nonetheless, they are discrepancies, and should be taken into account. Looking back, we should have measured the ramp with our own tape measure, just to make sure that it was accurate. It also would perhaps have been better if the barriers on the ramp were closer to the ball, to prevent it from rolling so far from the center and taking up extra time. By completing this lab, we were able to understand an important physics concept: mass does not affect acceleration, friction does. Though objects with a greater mass usually have greater friction, there are often cases - such as the one of this lab - where such a relationship does not necessarily come into play.

=<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Newton's Second Law Lab = <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Ali- Task C <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Caroline- Task B <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Jessica- Task D <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Sarah- Task A <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">date completed: 11-30-11 <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">date due: 12-1-11

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">objective: What is the relationship between system mass, acceleration, and net force?

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">hypothesis: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">The graph of acceleration vs. net force will be a linear relationship. The mass remains constant, so as more net force is applied, acceleration will become greater.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">The graph of acceleration vs. mass will be a horizontal line because all masses should fall at the same rate.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">materials and set up: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">For this lab we attached a string to a cart and placed the cart on a track that was fixed on the table with a table clamp. Then, we placed the string over the wheel of a photogate timer which was connected to a laptop via a USB link. At the end of the string opposite the cart, we tied a loop and placed a hanging mass on the end. As the lab progressed, more masses were added to either the hanging mass or the cart.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">**Procedure:** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Trial 1: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">media type="file" key="Trail 1.MOV" width="300" height="300"

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Trial 2: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">media type="file" key="Trial 2.MOV" width="300" height="300"

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Trial 3: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">media type="file" key="Trial 3.MOV" width="300" height="300"

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Trial 4: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">media type="file" key="Trial 4.MOV" width="300" height="300"

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Trial 5: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">media type="file" key="Trial 5.MOV" width="300" height="300"

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Trial 6: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">media type="file" key="Trial 6.MOV" width="300" height="300"

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Trial 7: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">media type="file" key="Trial 7.MOV" width="300" height="300"

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">**Sample Data and Calculations** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Net Force vs. Acceleration <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Mass vs. Acceleration <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Average Acceleration Example Calculation: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Net Force Example Calculation: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Percent Error for Acceleration vs. Net Force: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Percent Error for Acceleration vs. Mass: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">**Analysis:**
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Explain your graphs:
 * <span style="font-family: Tahoma,Geneva,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: Tahoma,Geneva,sans-serif;">For us, the Acceleration vs. Net Force graph's trend line followed a linear trend. The actual value of the slope was 2.1259, which corresponds algebraically to the value of 1/total mass. Our actual observed value should have been .530. The percent error between the two is 12.66%, which still fits the "20 percent error range". Therefore, our results in this section were fairly accurate. The meaning of the y-intercept value is friction. Friction, in this case, should have a negative effect on the system, thus explaining why the y-intercept value is negative. The algebraic value for friction is -f/total mass, and is shown below through substitution of the equation of slope-intercept form.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">[[image:Screen_shot_2011-11-30_at_10.08.07_PM.png]]
 * <span style="font-family: Tahoma,Geneva,sans-serif;">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.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">The graph of Acceleration vs. Mass had a trend line with a power fit. It follows the equation y= Ax <span style="font-family: Tahoma,Geneva,sans-serif; vertical-align: super;">-B <span style="font-family: Tahoma,Geneva,sans-serif;">, where the variable A is acting as the net force (mg). The power that the trend line is raised to is - 1.699. The number should hypothetically be -1. Therefore, our value is a very small amount (.699) off from the supposed value. . This may have been due to the manipulation of the mass cart when dealing with the weights. The coefficient in the equation of this graph corresponds to the net force, which so happens to be the weight of the hanging mass. Our observed value from the graph was .162, but our actual value was .294. From this, we calculated a percent error of 44.89%, which again is fairly large, suggesting that there were multiple sources of error. The value should be equaled to the weight of our hanging mass, but again due to error seems to be somewhat altered.
 * <span style="font-family: 'Trebuchet MS',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: 'Trebuchet MS',Helvetica,sans-serif;">Friction caused our acceleration to decrease. In our system, friction is the y intercept, where friction is over the total mass. We believe that we would need a bigger force in order to create the same acceleration, as friction in this case opposes the motion of force. Friction is absolutely a source of error in this experiment. It could be found multiple times through out the entire "environment" of our experiment: on the ramp, wheels, rope, and even on the little wheel that the rope rested on. In order to essentially "cancel out" the force of friction, you would need the same numerical value added to the original force of the object. Thus, friction would no longer act as a detrimental factor when determining more precise and accurate results. If friction were involved in our experiment, the equation would be the following: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">a=(hanging weight)(1/total mass)-(friction/total mass); which corresponds to the equation of y=2.1259x-0.1511; therefore, a=(9.8)(0.010)(1/0.53)-0.1511=0.0338 m/s2. Our previous acceleration was .05, so this clearly shows how much of an affect friction plays on the system.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">**Conclusion:** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">In concluding this lab, it seems that the purpose of this lab was satisfied. The goal of this lab was to determine the relationship between system mass, acceleration and net force knowing Newton's Second law which states that Net Force= mass*acceleration. We hypothesized that the graph of acceleration vs. net force would be a linear relationship. We found this to be true because as the net force increased, so did acceleration. This makes sense because if there is more force being applied to an object, it will move faster, therefore, accelerating at a greater rate. The equation of that line was y= 2.1259x-0.1511 and the r2 value is .99641. The y intercept is negative in this case because friction is having a negative effect on the cart by slowing it down. The r2 value is very close to one, indicating that there was a strong linear fit to the data, which is what we expected. We also expected that the graph of acceleration vs. mass would be a horizontal line because all of the masses should fall evenly. Our equation was y=.162x^-1.699. Because we want the power to be close to negative one, this equation is very close to the goal equation. The r2 value is .97071 which indicates that a power function was an accurate fit to the data.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">There were many possible sources of error in this lab. One of the possible sources of error we found was that the pulley and string had to be parallel to the ramp. An incline would cause the force to be on the tension of the rope, which would screw the data. Although we tried to get this as close as we could to parallel, if we were going to redo this lab it would be best to use a tool to ensure that they are exactly parallel and that the angle was 0 degree. Another possible source of error was that frequently the pulley would turn to the side, which would also cause our data to be false because the string had a longer distance to travel than expected. If we were redoing this lab we could have found a way to ensure that the device holding the pulley didn't turn such as another clamp to hold that in place. This may explain why our percent errors of 12.66% and 44.89% were so high.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">This "drop and pull" situation can be applied to real-life situations. Construction workers often have to use a rope and pulley to transport items from one level to another. In order to insure their safety, it is potent for them to understand the tool that they are working with. Another real life application is the building of elevators. Construction workers need to take into account the amount of weight that it could hold to insure the safety of the people who will be going in and out of it daily. Workers would need to be familiar with net force, weight, and acceleration, in order to truly understand the "drop and pull" concept.

=<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Friction Coefficient Lab = <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Period 2 <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">12/5/11 <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Ali- Task A <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Jessica- Task B <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Sarah- Task C <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">split it up- Task D

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">**Objectives:**
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">To measure the coefficient of static friction between surfaces
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">To measure the coefficient of kinetic friction between surfaces
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">To determine the relationship between the friction force and the normal force.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> **Hypothesis:** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">The coefficient of static friction will be close to 1 and the coefficient for kinetic friction will be close to 0. This is because the static friction when an object is moving it is going to be greater because it is slowing down the motion. Similarly, because we are measuring the weight (normal force) vs. friction on a graph, as more weight is added the friction between the two surfaces will increase.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">In this lab, we used a Force Meter connected by a USB Link to our laptop in order to measure the information in Data Studio. On the aluminum track ramp that was clamped to the table, we had a friction "cart", which we there after placed inside of it with masses of 498 g, 250 g, and 1000 g. Attached to the cart was a massless string that we could pull in order to get our results.
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Methods and Materials: **


 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Procedure: **
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Mass the friction “cart”.
 * 2) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Place the cart on the surface and put 500-g in it.
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Tie a short (~15 cm) string to the block at one end, and to the force meter on the other.
 * 4) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Plug the force meter into your computer. Choose Data Studio, and “Create Experiment”. A force-time graph will automatically open.
 * 5) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">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//**.
 * 6) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Leaving the string slack, press the button “ZERO” on the sensor.
 * 7) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Press START on Data Studio, and gently pull the block with the force sensor. Highlight the straight line part and click **S**. Record the MEAN as the value for Tension at Constant Speed
 * 8) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Be sure to pull with a very slow constant speed once it starts to move.
 * 9) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Hold the string parallel to the board.
 * 10) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Highlight the maximum point and record that value as the Maximum Tension. An alternative method is to click the smart tool to get the exact y-coordinate.
 * 11) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Repeat twice more with the same mass.
 * 12) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Repeat Steps 8 – 12 adding more mass each time (best to make **__large__** changes).
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Repeat Steps 8 – 12 adding more mass each time (best to make **__large__** changes).

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<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">**Sample Data and Calculations:** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Free-Body Diagram

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Calculations/Analysis <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Compare the slope of line with calculated µs average (% difference). <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Finding the µ for each run (example) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">greatest percent difference: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">smallest percent difference: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Compare your results with the class results. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Static <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Kinetic

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Discussion Questions: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">**Conclusion:** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Our hypothesis was somewhat accurate. The truth that holds is how we thought that static friction would ultimately be greater than kinetic friction. However, we were inaccurate in concluding that the value of static friction would be closer to one. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Since we originally found that T=f (in this situation) we could conclude that T=µN. The reason why we believed the value of these two slopes would be so small was due to our knowledge of µ (coefficient). We previously knew that the value of µ has to be between 0 and 1, and therefore led to the forming of our hypothesis stated above. For our average static friction value, we got .1713. For our average kinetic friction average, we got .12. These values, although very small, somewhat support our hypothesis.
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Why does the slope of the line equal the coefficient of friction? Show this derivation.
 * 2) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">For this experiment, we were making a linear graph; the line for this would be y = mx+b. In this case, y would be equal to f, x would be equal to N, and b would be 0. The line now would look like f = mN, and so m must really be equal to µ, thus the line f = µN.
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Look up the coefficient of friction between your material and the aluminum track. Discuss if your measured results fall within the range of theoretical values. Be sure to cite your source!
 * 4) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> According to http://www.tribology-abc.com/abc/cof.htm, the coefficient of static friction between plastic and metal is between .25 and .4. The coefficient of static friction we obtained in our experiment was .1713, which does not quite fall into this range - it's a little bit too low (by about .0787). The coefficient for kinetic friction, according to the same website, is anywhere between .1 and .3. The value we obtained in our experiment was .12, which, while being a little low, definitely falls between the two numbers.
 * 5) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">What variables affected the magnitude of the force of friction? What variables affected the magnitude of the coefficient of friction?
 * 6) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> The weight of the cart (normal force) as well as the coefficient of friction (µ) affect the magnitude of the force of friction. The force of friction and the weight of the cart (normal force) affected the magnitude of the coefficient of friction.
 * 7) How does the value of coefficient of kinetic friction compare to the value for the same material’s coefficient of static friction?
 * 8) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">The coefficient of static friction we obtained was .1713, which was larger than the value we obtained for the coefficient of kinetic friction, .12, by .0513. According to the website referenced before, it seems as if static friction should be greater than kinetic friction; our results appear to be right in this sense.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">There could be several sources of error in our lab; most of these were due to the lack of human ability to remain perfectly straight or motionless. If we didn't pull the string //exactly// horizontally, as it was nearly impossible to do, it could have thrown of our results - we would need to find the components of weight. Human hands are not often steady, and the sensor could have picked up on this, as well - very, very slight jerks to one side or up or down could have affected our data, albeit minimally. As well as this, we may have slightly accelerated the "cart" without knowing it. All of these sources, though undoubtedly slight, could have contributed to small errors and discrepancies in our data. If we were to change anything in the lab, we would have made sure that we had a method to make sure that the tiny rope was perfectly parallel to the ramp. This would ensure that there are no components of that force, skewing our results. Also, we could have made sure that the cart was in perfect working condition, as it possibly could have been worn out.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">This can be applied to real life circumstances if the coefficient of friction is ever necessary to know. Example of this would be with a tow truck is pulling a car. It is important to know the friction that will be applied to the car in the back of the tow truck. The tension of the wire pulling the car will provide the friction. It is important to know the friction coefficient to make sure that the car's tires will not be destroyed. Another example is if a people need to move a heavy object by pulling it. The people need to know the friction coefficient to understand how many people are going to be needed to help pull the item. From this lab, our group learned to be prepared. We learned to organize our thoughts in a logical manner before even beginning the experimental process. Hopefully next time the process will be just as smooth :).