Group3_6_ch4

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=**Gravity and the Laws of Motion** =
 * Group 3: Andrea Aronsky, Ben Sherman, Maddi Steele

Part A: Ben Sherman Part B: Andrea Aronsky Part C: Maddi Steele Part D: Shared

Period: 6 Date Completed: 11/15 Date Due: 11/16

**Objective:**
 * Find the value of acceleration due to gravity
 * Determine the relationship between acceleration and incline angle
 * Use a graph to extrapolate extreme cases that cannot be measured directly in lab
 * What is the relationship between the mass of the rolling ball and its acceleration?

**Hypothesis/Rationale:**
 * <span style="font-family: Tahoma,Geneva,sans-serif;">The acceleration due to gravity is 9.8 m/s/s based on free fall objects and projectiles.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">As the angle is increased, the acceleration increases. We were able to hypothesize this because while on a steep rollercoaster the car speeds up much faster. But if on a less steep rollercoaster, the car does not travel as fast, making it a less thrilling ride.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Mass does not have an effect on acceleration because the only force acting upon the ball that is making it move is gravity. Similarly, projectiles are only affected by gravity and we know that the acceleration of any projectile is 9.8 m/s/s. Therefore, we think that a ball going down an incline with the same force acting upon it to make it move(gravity) will share the same acceleration value of 9.8 m/s/s.

<span style="font-family: Tahoma,Geneva,sans-serif;">**Methods and Materials:**
 * <span style="font-family: Tahoma,Geneva,sans-serif;">First, we recorded the weight of our ball. Next, we set up the ramp to have the initial height of .15 m and we started the ball at the top, allowing it to travel 1.2 m. We then recorded the time with a stopwatch to the bottom of the ramp. We had several trials for this angle and distance. Then we changed the distance without changing the angle. Then we changed the height, thus altering the angle and repeated the process two more times. With the information recorded, we put it into an excel spreadsheet to create a data table for our results.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">[[image:ABC.jpg]]
 * <span style="font-family: Tahoma,Geneva,sans-serif;">image of the ball down the ramp
 * <span style="font-family: Tahoma,Geneva,sans-serif;">[[image:abcd.jpg]]
 * <span style="font-family: Tahoma,Geneva,sans-serif;">picture of the ramp set up to have the height of 0.15 m

<span style="font-family: Tahoma,Geneva,sans-serif;">**Data:** <span style="font-family: Tahoma,Geneva,sans-serif;">
 * <span style="font-family: Tahoma,Geneva,sans-serif;">The data table above shows the different trials with their height, distance traveled, total time, acceleration, final velocity, and sin(theta). We changed the height of the ramp three times. The chart also shows average acceleration and average sin(theta) of trials with the same angle.

<span style="font-family: Tahoma,Geneva,sans-serif;">**Class Data:** <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">We are able to see that mass does not affect acceleration.

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

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

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

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

<span style="font-family: Tahoma,Geneva,sans-serif; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">**Analysis**:
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-weight: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">In the acceleration vs. sin(thea) graph, the x axis of our graph represents sin(theta) and it goes from 0-1 because that is where the sin function lies. The y axis represents acceleration and goes from 0-10 because 10 is the maximum acceleration due to gravity. Our equation is 10.4x - 0.3178, and the slope represents our acceleration due to gravity which is 10.4 m/s/s. This is close to the numerical value to the actual acceleration due to gravity which is 9.8 m/s/s. However, it is impossible for the acceleration is be greater than 9.8 m/s/s unless another external force was acting upon the object. This error was probably due to us measuring time and distance inaccurately during the various trials. If the y-intercept was set to 0, then we would be dealing with a frictionless surface. However as our y-intercept was not set to 0, our slope was 10.4 as friction only increases the slope.


 * <span style="font-family: Tahoma,Geneva,sans-serif;">**Percent Error:**
 * <span style="font-family: Tahoma,Geneva,sans-serif;">[[image:a_pererror.png width="345" height="252"]]
 * <span style="font-family: Tahoma,Geneva,sans-serif;">**Percent Difference:**
 * [[image:new_percent_diff.png]]
 * <span style="font-family: Tahoma,Geneva,sans-serif;">This probably happened because our class data just made no sense at all. Other groups probably made mistakes in their calculations, which affected their acceleration values at 0.15 m.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">In the data section of our lab, you can see the chart with the class data. It is clear that mass does not affect acceleration.

<span style="font-family: Tahoma,Geneva,sans-serif; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">**FBD:** <span style="font-family: Tahoma,Geneva,sans-serif;">
 * <span style="font-family: Tahoma,Geneva,sans-serif;">What force is causing the ball to roll down the ramp? Is it the whole force or just a part of it? If just a part, then which part?
 * <span style="font-family: Tahoma,Geneva,sans-serif;">The x-component of the gravitational force is causing the ball to roll down the ramp.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Use Newton’s second law to calculate acceleration of the ball down one of your ramps. How does it compare to your experimental (average) acceleration for that incline?
 * <span style="font-family: Tahoma,Geneva,sans-serif;">The acceleration of the ball down one of the ramps (at h = 0.15 m) is 1.19 m/s/s. It is higher than the average experimental acceleration (1.05 m/s/s) for that incline. This is because the other trials for that incline were done from a lower point on the ramp, meaning that they have a lower acceleration. Therefore, the trial done from the highest point on the ramp will have a higher acceleration than the average (which incorporates trials with lower accelerations).
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Using Newton's Second Law, we calculated that the average acceleration of the ball down one of our ramps was 1.225 m/s/s. It is only a little bit higher than our experimental average acceleration for this incline. This shows that our experimental results are pretty accurate.

<span style="font-family: Tahoma,Geneva,sans-serif;">**Discussion Questions:**
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">Is the velocity for each ramp angle constant? How do you know?
 * <span style="font-family: Tahoma,Geneva,sans-serif;">The velocity for each ramp angle is not constant. When we made the distance shorter for each ramp angle, the ball's velocity was lower.
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">Is the acceleration for each ramp angle constant? How do you know?
 * <span style="font-family: Tahoma,Geneva,sans-serif;">The acceleration for each ramp angle is not constant. When we made the distance shorter for each ramp angle, the ball's acceleration was lower.
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">What is another way that we could have found the acceleration of the ball down the ramp?
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Acceleration is the change in an object's velocity over the change in time. Using two photogates, we could have measured the time it took for the ball to roll down the entire ramp. Then, we could have figured out the instantaneous velocity of the ball at its start <span style="font-family: Tahoma,Geneva,sans-serif;">point and end point. Last, we could have divided the change in velocity by the change in time to find the ball's acceleration.
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">How was it 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?
 * Galileo knew that weight was the only force causing the ball to move (normal force does nothing because it if perpendicular to the ball). Weight is a vector, which means that it has two components. The x component is responsible for the ball's movement down the ramp. To solve for the x-component, Galileo derived the equation wx = w[sin(theta)]. <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 13.3333px;"> He knew that F=ma, and applied this equation to his own:
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 13.3333px;">Using his final equation g = (ad)/h, he observed that g always equaled 9.8 m/s^2.
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 13.3333px;">mg[sin(theta)] = ma --> g = a/sin(theta) --> g = a/(height/distance) --> g = (ad)/h
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">Does the mass of an object affect its rate of acceleration down the ramp? Should it affect the motion of an object of freefall in the same manner?
 * <span style="font-family: Tahoma,Geneva,sans-serif;">No, the mass of an object does not affect its rate of acceleration down the ramp. The acceleration of an object is directly proportional to force and inversely proportional to mass. Increasing force tends to increase acceleration while increasing mass tends to decrease acceleration. The greater force on more massive objects is counteracted by the inverse influence of greater mass. For this reason, the mass of an object should not affect its motion while in free fall. The acceleration of any free-falling object, regardless of its mass, is 9.8 m/s/s.

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

<span style="font-family: Tahoma,Geneva,sans-serif;">Our hypotheses proved to be partially accurate. We hypothesized that the value of the acceleration would be 9.8 m/s/s, as in previous experiments such as the freefall lab, we calculated that the acceleration was close to that value. Based on our average acceleration and average sin(theta) graph, the acceleration was found to be 10.4 m/s/s. The percent error for our acceleration was 6.122%, which is fairly close to the theoretical value but not completely accurate. This difference can be accounted for by sources of error that were in this lab. The second part of our hypothesis proved to be accurate as acceleration increased as the angle increased. As an angle increases, it becomes closer to 90 degrees or a straight vertical incline, which is seen in free-fall. As the acceleration due to gravity in free-fall is 9.8 m/s/s, the acceleration becomes closer to 9.8 m/s/s as the angle increases closer to 90 degrees. Seen from our data, when decreases the angle, our acceleration gradually became smaller. We were able to support our hypothesis of mass not affecting acceleration based off the physics theory by comparing our results with that of other groups. For example, the mass of our ball was .225 kg and at an incline of 15 degrees, the average acceleration was 1.05 m/s/s. This acceleration is comparable to other groups as one mass was 0.00898 kg and had an acceleration of 1.039 m/s/s and another mass was 0.016 kg and had the acceleration of 1.056 m/s/s. Thus there is no significant effect of mass on acceleration. Although the class data seems to show a slight correlation between mass and acceleration, this is because of friction, because the greater the mass of the ball, the more friction it causes on the ramp. This friction accounts for the difference in the acceleration of the balls with varying masses.

<span style="font-family: Tahoma,Geneva,sans-serif;">Our experimental value for acceleration was 10.4 m/s/s, and our theoretical value was 9.8m/s/s, which is acceleration due to gravity. In our experiment, we had a percent error of 6.122%, which isn’t terrible, but it also isn’t very accurate. By looking at our data chart, our trendline was very far off on our middle data point. This shows that our second data point, which had an average acceleration of .66 m/s/s and a sin theta value of .102 degrees. If this value was more consistent with the other points, the trendline would have been much more accurate, and our percent error would be smaller. To eliminate this inconsistency in the future, we would do more trials for each ramp angle to reduce the impact of any outliers. There are several reasons for our inaccurate results. One reason is that when the ball traveled down the ramp, it wouldn’t travel in a straight path. After the ball was released, it would move across the width of the ramp, which would cause it to take longer to reach the bottom of the ramp, which would throw off our values. Another issue was that when the tester released the ball, he or she could have put added force on the ball, which would result in values that would be inconsistent. This is because there was added force on the ball, it would travel faster than if it was just released, and started to move as a result of gravity. Another area of inconsistency is that when we timed the ball, our reaction time was not only delayed, but also not consistent for each trial. This means that when we released the ball, the time from when we released the ball to when we pressed the button on the timer was not zero, and also was different for each test, which would lead to strewed results. To fix these issues, we need to change the experiment. For example, a more accurate device for timing the ball is necessary. Another method of timing the ball that would be more accurate is that we could take a video of the launch, and find the time differences from the release to the end point. By using a video, we would be able to stop the frame when we would like, and would have much more accurate times, making our data more consistent. Another fix is that the ramp should be less wide or have a groove that allows the ball the roll without moving across the ramp. Lastly, to make our experiment more consistent, we would need a device to release the ball without putting any extra forces on it.

<span style="font-family: Tahoma,Geneva,sans-serif;">This concept is relevant for people who participate in Zorbing (see picture below). Zorbing is a recreational sport, which involves rolling downhill in an orb, generally made of transparent plastic. People who “Zorb” would need to understand this concept, in order to calculate how far and fast it is safe to go down a certain hill.

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=<span style="font-family: Tahoma,Geneva,sans-serif;">__ **Newton's Second Law** __ = <span style="font-family: Tahoma,Geneva,sans-serif;">Members: <span style="font-family: Tahoma,Geneva,sans-serif;">Ben Sherman (Part B) <span style="font-family: Tahoma,Geneva,sans-serif;">Andrea Aronksy (Part C) <span style="font-family: Tahoma,Geneva,sans-serif;">Maddi Steele (Part A)

<span style="font-family: Tahoma,Geneva,sans-serif;">Group: Period 6, Group 3 <span style="font-family: Tahoma,Geneva,sans-serif;">Lab Due: 11.30.11 <span style="font-family: Tahoma,Geneva,sans-serif;">Lab Completed: 11.29.11

<span style="font-family: Tahoma,Geneva,sans-serif;">**Objective**: What is the relationship between system mass, acceleration and net force?

<span style="font-family: Tahoma,Geneva,sans-serif;">**Hypothesis** : <span style="font-family: Tahoma,Geneva,sans-serif;">We hypothesize that acceleration happens when the net force is not zero, acceleration and mass are inversely proportional, and that acceleration and net force are directly proportional. We believe that acceleration will happen when the net force is not zero because Newton's second law states that an object will stay in a constant state of motion unless acted on my an unbalanced force. We think that acceleration and mass are inversely proportional because of Netwon's second law, as described in the equation ∑F=ma. That means when mass increases or decreases, acceleration must do the opposite so that the net force will be the same. Lastly, acceleration and net force are directly proportional because Netwon's second law states that ∑F=ma, so when net force increases, acceleration must increase if mass stays constant.

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

<span style="font-family: Tahoma,Geneva,sans-serif;">-First, we started to put together our lab setup. The first part of this was to take a metal track and lay it flat on a table, and then then mount the photogate/pulley combo to the table. We positioned the track so that the side with the bumper was on the same side as the photogate, to protect the sensor/pulley from being damaged during testing. Next, we placed the dynamics cart on the track, and tied string to it. The string went on the pulley, and then went at an angle downward to attach to the weights and hanging mass. After this, we checked and recorded the mass of our carts, weights and hanging mass. Once this was done, we placed the cart on the track and started to run our trials. At first, we placed the 10g and 5g weights in the cart, and added a 10g weight to the 5g hanging mass. For the next run, we took the 5g weight off the cart and placed it on the hanging mass, and did the same for the third run, but with the 5g mass. All of the data should have been recorded in data studio then placed in excel, but for this lab we had to use previous years’ data. In the case of the data we used, the method was similar, but the weights transferred between the hanging mass and cart were solely 5g, and this was done repeatedly.

<span style="font-family: Tahoma,Geneva,sans-serif;">Lab Set Up Image: <span style="font-family: Tahoma,Geneva,sans-serif;">

<span style="font-family: Tahoma,Geneva,sans-serif;">Experiment Video: <span style="font-family: Tahoma,Geneva,sans-serif;">media type="file" key="VID_20111129_130742.m4v" width="300" height="300"

<span style="font-family: Tahoma,Geneva,sans-serif;">**Data:** <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">(Link to document)

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

<span style="font-family: Tahoma,Geneva,sans-serif;">**Average Acceleration Sample Calculation:** <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">**Net Force Calculation:** <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">**Analysis:**
 * <span style="font-family: Tahoma,Geneva,sans-serif;">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;">The Acceleration vs. Net Force graph came out to be a linear graph as acceleration and force are directly proportional. The slope of our trendline is 1.8475, while our observed value is 1.87 by doing 1/m, as the reciprocal mass of our mass of 0.535 kg is 1.87. This value is extremely close to our experimental one. The slope of this linear equation is representative of the reciprocal of mass, found by the acceleration equation underneath. Also seen below is our percent error of only 1.20 %, showing that our experimental value is very accurate. The y-intercept is related to friction. This value is friction divided by the system mass, thus by multiplying the y-intercept by the system mass, you are able to find the force of friction. The equation shows the y-intercept as negative, explaining why friction has a negative effect on the system.
 * [[image:Screen_shot_2011-11-30_at_6.28.38_PM.png]]
 * [[image:USE_THIS_ONEE.png]]
 * [[image:Screen_shot_2011-11-30_at_6.48.08_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 for Mass vs. Acceleration was non-linear. The power on the x is -1.432, but the theoretical value should be equal to -1. The coefficient is 0.0361, which represents the net force which is the hanging mass X gravity. The theoretical value for the coefficient is 0.03626, obtained by multiplying the hanging force (0.0037) by gravity (9.8). As seen by our small percent error of 0.44%, the experimental value was very close to the theoretical one showing that it was accurate. The equation below shows why the coefficient is equal to the net force.
 * [[image:Screen_shot_2011-12-01_at_10.52.23_AM.png]]
 * [[image:Screen_shot_2011-12-02_at_4.55.54_PM.png]]
 * <span style="font-family: Tahoma,Geneva,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: Tahoma,Geneva,sans-serif;">Friction would cause our acceleration to decrease as it goes against the tension force of the string and the motion of the cart. A larger force would be needed to maintain the same acceleration as a result of friction moving in an opposing direction.The original force plus the equivalent value of force of friction would have to be pushing the cart forward so that the friction pulling in the opposite direction would cancel out and not affect the acceleration. Friction can be a source of error in this lab because it is not possible to eliminate it given our procedure and materials, so the friction causes the cart to have a lower acceleration. Friction can be found on the ramp, wheels, rope, and the wheel that the rope goes through. Our slope was too small, which is probably due to friction and can be seen in the percent error. When redoing the calculation with friction, as seen below, the acceleration comes out to be slower, 0.0579 m/s/s, compared to the acceleration of 0.0595 m/s/s without friction.
 * [[image:Screen_shot_2011-12-03_at_6.17.12_PM.png]]

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

<span style="font-family: Tahoma,Geneva,sans-serif;">After experimenting, we have found that our hypothesis was completely correct. First, we hypothesized that acceleration takes place when the net force acting on the system is not zero. In our experiment, we didn’t test when there was zero net force, but when there is zero net force, the object will stay at rest since there are no unbalanced forces causing it to move. For each point where net force was above zero, the cart started to move. Next, we hypothesized that acceleration and mass are inversely proportional. In our mass v. acceleration graph, this can clearly be seen as true. Whenever we would increase the mass of the cart, acceleration would decrease. Also, Netwon’s second law states that this is true. If ∑F=ma, then when acceleration increases and force stays the same, mass must decrease and vice versa. Lastly, we hypothesized that acceleration and net force are directly proportional. As seen in the net force v. acceleration graph, this is true. Whenever the net force was increased, acceleration would increase as well. This also is proved true by Netwon’s second law. If ∑F=ma, then as the net force increases and mass stays constant, acceleration must also increase and vice versa.

<span style="font-family: Tahoma,Geneva,sans-serif;">The percent error for our Acceleration vs. Net Force graph was only 1.20% which shows that our experimental data was very accurate to the theoretical. Our experimental slope was 1.8475 compared to the theoretical value of 1.87. Even better, the percent error for our Acceleration vs. Mass graph, which was only 0.44% justifying our results for this portion. We got the coefficient of 0.0361 while the expected coefficient was 0.03262. The large R2 values very close to 1 on both graphs also support the accuracy of the results.

<span style="font-family: Tahoma,Geneva,sans-serif;">To eliminate sources of error in the future, we would first make sure that Data Studio is working. We couldn't actually do the lab because Data Studio was not working properly. Had we done the lab procedure, the first source of error could have resulted from the ramp not being parallel to the table. To fix this in the future, we would make sure the ramp was completely flat on the table. The second source of error could have resulted from the photogate sensor and string being positioned higher or lower than the cart. To fix this in the future we could use a bubble level, which would allow us to gauge whether or not the string was completely level with the cart.

<span style="font-family: Tahoma,Geneva,sans-serif;">This concept is relevant to people who make elevators. They must be aware of how net force (people, gravity, and tension of cable) impacts an elevator's (hanging mass) acceleration. If too many people cram into an elevator that is going down, the net force on the hanging mass will be too great and cause the elevator materials to give out (cable snapping). To prevent this occurrence, elevator makers put "person capacity" stickers.

=<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px;">**Lab: Coefficient of Friction** =

<span style="font-family: Tahoma,Geneva,sans-serif;">By Madison Steele and Andrea Aronsky

<span style="font-family: Tahoma,Geneva,sans-serif;">**Objectives:**
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">To measure the coefficient of static friction between surfaces.
 * 2) <span style="font-family: Tahoma,Geneva,sans-serif;">To measure the coefficient of kinetic friction between surfaces.
 * 3) <span style="font-family: Tahoma,Geneva,sans-serif;">To determine the relationship between the friction force and the normal force.

<span style="font-family: Tahoma,Geneva,sans-serif;">**Hypothesis:**
 * <span style="font-family: Tahoma,Geneva,sans-serif;">To measure the coefficient of both static and kinetic friction, we must isolate µ from the equation f=(µ)(N), thus the equation we will use will be µ= f/N. The coefficient of static friction will be greater than the coefficient of kinetic friction because this friction is keeping the object from sliding. The coefficient of static friction will be closer to 1 than the coefficient of kinetic friction.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">By dividing f/N, we can figure out µ.Because µ is a constant, normal force and friction force are directly proportional.

<span style="font-family: Tahoma,Geneva,sans-serif;">**Methods and Materials:** <span style="font-family: Tahoma,Geneva,sans-serif;">First, one should measure the mass of the friction “cart” and place it on an aluminum track (flat surface). In order to measure the force, one must tie a 15 cm string to one end of the block and the force meter on the other end. The force meter will measure the friction between the friction “cart” and the flat surface. Next, holding the string parallel to the aluminum track, one would gently pull the string with a very slow constant speed once it starts to move. The friction would be recorded on Data Studio. One would repeat this experiments using 5 different blocks with varying masses.

<span style="font-family: Tahoma,Geneva,sans-serif;">media type="file" key="friction procedure.mov" width="300" height="300" <span style="font-family: Tahoma,Geneva,sans-serif; line-height: 0px; overflow-x: hidden; overflow-y: hidden;"> <span style="font-family: Tahoma,Geneva,sans-serif;">

<span style="font-family: Tahoma,Geneva,sans-serif;">**Graphs and Data:** <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">This graph shows multiple trials of pulling the cart (same weight each time). The highlighted section is the mean tension. The highest points are the max tension.

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<span style="font-family: Tahoma,Geneva,sans-serif;">**Sample Calculations:** <span style="font-family: Tahoma,Geneva,sans-serif;">- The acceleration is set to zero because the object is moving at constant sped, thus there is no acceleration. The tension and friction forces become equal to each other as a result. The tension is the average tension of the trials of a specific mass. <span style="font-family: Tahoma,Geneva,sans-serif;">- Again there is no acceleration because the object is not accelerating in an upwards or downwards direction so the acceleration is 0. The normal force and weight become equal to one another. As weight is equal to mass X g, the normal force is then found from plugging in a mass and multiplying it by g, which is 9.8

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

<span style="font-family: Tahoma,Geneva,sans-serif;">**Discussion Questions:** <span style="font-family: Tahoma,Geneva,sans-serif;">**Analysis:**
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">//Why does the slope of the line equal the coefficient of friction? Show this derivation.//
 * <span style="font-family: Tahoma,Geneva,sans-serif;">The equation of our kinetic friction line is y=(0.1108)x, 0.1108 being the only constant value. Similarly, µ is the only constant value in the theoretical equation for friction (f=µ*N). Also, just as µ is calculated in the theoretical equation by dividing friction by normal force, 0.1108 is calculated by dividing the rise of each point on the line (y) by the run (x).
 * [[image:Screen_shot_2011-12-07_at_8.28.43_PM.png]]
 * 1) <span style="font-family: Tahoma,Geneva,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!//
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Our material was smooth plastic. The theoretical value for the coefficient of static friction between plastic and metal ranges from 0.25 to 0.4. Our coefficient of static friction is 0.1562, which is kind of close to the low end of the theoretical value. The theoretical value for the coefficient of kinetic friction ranges from 0.1 to 0.3. Our coefficient of kinetic friction is 0.1108, which falls within this range. (http://www.tribology-abc.com/abc/cof.htm)
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">//What variables affected the magnitude of the force of friction? What variables affected the magnitude of the coefficient of friction?//
 * <span style="font-family: Tahoma,Geneva,sans-serif;">As the object was traveling at constant speed, the acceleration in the lab was 0. This caused the friction force to be equal to the tension force, thus the force of friction was directly affected by the magnitude of the tension force. The surface the object was rubbed against also affected the force of friction. If there was another type of surface, the magnitude of friction would have changed.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">The weight of the friction cart (normal force) and the coefficient of friction affected the magnitude of the force of friction.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">The force of friction and the weight of the cart (normal force) affected the magnitude of the coefficient of friction. Because the acceleration is 0, the normal force is equal to weight so as the weight of the object moving across the surface changes, as does the coefficient of friction because of the equation [[image:Untitled.png]].
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">//How does the value of coefficient of kinetic friction compare to the value for the same material’s coefficient of static friction?//
 * <span style="font-family: Tahoma,Geneva,sans-serif;">The coefficient of static friction is greater than that of coefficient of kinetic friction by 0.0454. This is because when an object is not in motion, the force of friction is stronger than when the object is sliding. The static friction was the maximum tension to get the object to move so it will be larger than the coefficient of kinetic friction.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Compare the slope of line with calculated µaverage (% difference).
 * [[image:Screen_shot_2011-12-07_at_1.07.02_PM.png]]
 * [[image:Screen_shot_2011-12-07_at_1.07.10_PM.png]]
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Compare your result with the class results.
 * [[image:Screen_shot_2011-12-10_at_9.51.34_AM.png]]
 * [[image:Screen_shot_2011-12-10_at_9.51.41_AM.png]]

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

<span style="font-family: Tahoma,Geneva,sans-serif;">The purpose of this lab was to determine the coefficient of friction between the aluminum track the object going across it. We were also supposed to determine the relationship between the normal and friction forces. Our hypothesis proved to be accurate. We said that the relationship between normal force and friction force is directly proportional because of the equal f = µ N. There was a linear graph for both static friction vs. normal force and kinetic friction vs. normal force, proving that there is direct relationship between these forces. Seen by our data, as the normal force increased, the friction did as well, and vice versa. Another part of our hypothesis stated that the coefficient of static friction would be greater than that of kinetic friction, which also was correct. Comparing the slopes of linear equations for static and kinetic friction, (because the slopes are representative of the coefficient of friction), we found the coefficient of static friction to be 0.1562, from the graph using maximum friction, and the coefficient of kinetic friction to be 0.1108, from the graph using average friction. Therefore, the coefficient of static friction is closer to 1 than that of kinetic friction.

<span style="font-family: Tahoma,Geneva,sans-serif;">Our percent difference were relatively small as the percent difference for the coefficient of static friction was 3.07% and the percent difference for the coefficient of kinetic friction was only 0.18%. When comparing our results to the class we also obtained only small percent differences: 0.19% for the coefficient of static friction and 3.57% for the coefficient of kinetic friction. This provides evidence that our data was very accurate and by eliminating various sources of error we would have precise results in the future.

<span style="font-family: Tahoma,Geneva,sans-serif;">One source of error could have resulted from dragging the friction "cart" at an inconsistent rate. Doing so would have resulted in a skewed mean tension value. To eliminate this problem in the future, we could somehow attach the friction sensor to a CMV as this would ensure a constant pulling rate. Another source of error could have resulted from pulling the string too quickly or sharply. Doing so would have resulted in a max tension value that was too high. In the future, this problem could also be eliminated by attaching the friction sensor to a CMV. A third source of error could have resulted from the aluminum track not having a perfectly smooth surface. There were ridges in the ramp, which would change the coefficient of friction between the ramp and the friction cart. To eliminate this problem in the future, we could use a perfectly smooth aluminum ramp without ridges.

<span style="font-family: Tahoma,Geneva,sans-serif;">This concept is useful in everyday life. It is important to understand how the interaction between different materials affects the coefficient of friction. For example, the coefficient of friction changes when tires and roads are wet, and tire makers must take this fact into account to ensure the safety of drivers in sever weather. Another example is how sweat affects the coefficient of friction between a basketball and a person's hands. When a person sweats, the coefficient of friction changes between skin and the ball. When synthetic basketballs were first made, this concept was not taken into account and the players had cuts on their hands as a result.

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

Methods and Materials: First, we tied a 6 gram weight to the end of a 0.75 meter long string. Next, we swung the weight in a vertical circle using JUST enough tension to complete each cycle. Then, we recorded the time it took for the weight to make 10 cycles. We divided this time by 10 to get the time per 1 cycle.

Data: