Group6_2_ch4

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**Make up Wiki**

**Coefficient of Friction Lab- Make up**
Part A & B: Maddie Margulies Part C & D: Matt Ordover

To Measure the coefficient of static friction between durfaces To measure the coefficient of kinetic friction between surfaces To determine the relationship between the friction force and the normal force
 * __Objectives__:**

__**Procedure**__: media type="file" key="Movie on 2011-12-09 at 11.22.mov" width="300" height="300"

__**Hypothesis**__: The coeffients of frictions should be a value ranging from zero to one. Also, coefficient of static friction will be higher than the kinetic because static friction must change state of motion and overcome inertia. The relationship between the friction force and the normal force is f = µ * N.

__**Materials/ Method:**__ First, the mass of the cart was found and then a 15 cm string was attached to one end of the cart and the other to the force meter. We then plugged the meter into the computer and used data studio to collect the data. After this was set, cart was pulled at a constant speed and the velocity was measured through the force meter. The string had to be horizontal to get the best results.

__**Data**__: Static Friction

Kinetic Friction

__**Graph**__:



__**FBD**__

__**Sample Calculations**__ Static Friction

Kinetic Friction

Normal Force

Average Max Tension

__**Discussion Questions**__ 1) Why does the slope of the line equal the coefficient of friction? Show this derivation.
 * The equation of a the line is y=mx+b. The y-intercept is 0, so b=0. This just leaves y=mx, which mirrors the equation f=µN. Thus, y equals friction, x equals normal force, and m (slope) equals the coefficient of friction.**

2) 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!
 * The coefficient of static friction between plastic and aluminum is .25 to .4. Ours was .145 which is not in the expected range of values. However, the class average was not much higher at .161, so most if not all of the class was less than the expected value. The coefficient of kinetic friction is .1 to .3. Ours was inside this range at .114.**

3) What variables affected the magnitude of the force of friction? What variables affected the magnitude of the coefficient of friction?
 * Weight affects the magnitude of the force of friction because friction is dependent on normal force times µ. If weight is larger, then the normal force will also be larger, which affects friction. Coefficient of friction is also dependent on weight as well as the magnitude of friction.**

4) What variables affected the magnitude of the coefficient of friction?
 * Our static coefficient of friction was slightly larger than our kinetic coefficient of friction. This is because static friction must overcome inertia because the object is changing state of motion, while in kinetic friction the object is already moving.**

__**Conclusion**__: Our hypothesis was correct as our values were in between 0 and 1. In addition, our coefficient of static friction was slightly larger than the coefficient of kinetic friction, which makes sense because static friction must overcome inertia. Our percent differenced were pretty good and that indicates that we had similar values to the rest of the class. Our percent difference for static friction was 9.94%, while our percent difference for kinetic friction was just .885%. While these results were consistent with the rest of the class, they could have been more accurate. One source of error was that it was impossible to tell how much force you were pulling with and this could have affected the max tension. This could never be completely solved, but it would be more accurate to start pulling slowly at first and gradually get faster. To get even more accurate results, a machine could be used to pull it at a constant speed. Another source of error is that the string was not perfectly parallel to the ramp. This could be solved by using a protractor or a laser guide to make sure the string stays parallel. This has many applications to the real world. One example is pushing a table across a wooden floor.

Newton's Second Law
Maddie Margulies Sarah Gordon

Objective: What is the relationship between system mass, acceleration and net force?

Hypothesis: A a higher net force there will be a higher acceleration and a higher mass there will be a lower acceleration.

Procedure: For the first part of the lab, a photo gate was attached to pulley and then plugged into a computer. Data studio was used to see the velocity-time graph and then the slope was used to find the acceleration. The cart had a string the went over the pulley and on the other end was a mass hanger. The car was placed on a track and the acceleration was found when the mass changed on the mass hanger.

Accel vs. Net Force:

media type="file" key="Movie on 2011-12-09 at 11.33.mov" width="300" height="300"

Accel vs. Mass media type="file" key="Movie on 2011-12-15 at 11.47.mov" width="300" height="300"


 * Data**:


 * Graphs**:




 * Sample Calculations:**

Net force:

Average acceleration:

Percent error (Net force):

Percent error (Car mass): // The acceleration vs force graph was linear due to the fact that acceleration and force are directly proportional. The y intercept shows friction divided by the system mass. This means that when multiplied by the mass of the system, it is friction. The y intercept is also negative because it negatively affects the system. The slope of the trendline was 1.81. This is very different than the theoretical value and this is shown through the percent error. In the lab we got a high percent error and then it decreased as there was more acceleration. // // The graph of acceleration vs mass was nonlinear. The power on x for our graph was -1.65. The theoretical value for this power should be .091. The coefficient in front of the x on our graph was .1243 which represents the net force (mg). The percent difference between our data and the theoretical value (which is found by multiplying the mass times gravity) is 87%. This which is large, thus showing that our coefficient is not very to the theoretical value.// // Friction should slow down the acceleration because friction opposes motion. Since more friction would act against he forward movement of the car there would need to be a bigger force to create the same acceleration. In order to eliminate friction, one would need to use the same force as the original but then also apply a force in the forward direction equal to that of the force of friction. Our slopes were _ compared to the theoretical value of slope. This might have been caused by gravity. When accounting for friction, the equation looks like this: // // a= (hanging weight)/(total mass)-( friction/ total mass) // // a= (9.8)(.03)/(.054)-(.0787/.054) // // a=3.99m/s/s //
 * Analysis**:
 * 1) Explain your graphs:
 * 2) 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?
 * 1) 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.
 * 1) 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.

Conclusion: Both our hypothesis were correct in that one correctly predicted that the acceleration vs force graph would be linear (as force increases so does acceleration) and that the acceleration vs mass graph would be inversely proportional (as mass increases acceleration decreases). Our percent error for the acceleration vs net force graph was 87% however it went down to 21%. The percent error for the acceleration vs. Cart Mass started at 82% and ended at 42%. This is because the force of friction would have a greater affect on more massive objects rather than lesser ones. When the mass increased the percent error decreased. This lab has many different sources of possible error. One was friction. This was not taken into account when the cart was let go. Another could have come from the fact that the surface might have been on an angle (the desk might have not been completely even), which could have changed the acceleration slightly. In addition, if the string was not held taunt, then it could possibly change the value for acceleration. Both these sources of error could be dealt with by making sure the surface is as flat as possible and by carefully checking that the string is taunt. Also, when the car was let go, another force could have acted upon it with out realizing such as a hand. This could have been prevented by setting the cart in a contraption that releases it without any other force acting upon it. A relevant real-life application of this concept is using pulleys to lift heavy objects, such as a car factory. The workers can't lift the massive car parts by themselves so they use pulleys to allow them to move these objects. Also, it provides them a safe way to lift these heavy objects.