Group4_2_ch5

= = =toc Centripetal Motion Lab = Task A: Amanda Task B: Ali Task C: Julia Task D: Nicole date assigned: 12/14 date due: 12/15

**Objective**
 * find what factors influence the centripetal force acting on a system
 * find the relationship between these forces and centripetal force

**Hypothesis** The factors that influence the centripetal force acting on a system include mass, velocity, and radius. These are the forces that we will be specifically testing through this lab. Through this lab, we are going to experiment and find out the direct relationship between these forces and centripetal force. We predict that the smaller the mass, the smaller the force; the smaller the velocity, the smaller the force; the smaller the radius, the larger the force. Below are our predictions of what each graph will look like. 

**Methods and Materials** In this lab we will be using a meter stick to measure the radius of our potential circle, which happens to be the length of the string to the center of the hollow tube. We will then use a timer to measure the amount of time that passes for the string to move in circular motion, 10 times. At the top of the string lies a rubber stopper connected by a knot to ensure security, along with a piece of tape at the bottom of the hollow tube. At the bottom of the string (which lies through the hallow tube) is a force meter that connects via USB to the laptop.

**Procedure** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">The first step we took was connecting a rubber stopper to the end of a string and a force meter clipby the end by tying a knot. We then placed a string through the hollow tube. We then held up the tube in the air, and let the force meter rest on the floor. We thereafter swung the rubber stopper around in a horizontal, circular motion, while checking that the force meter remained steady on the floor. In order to test different variables, we change one variable (additional mass, length of radius, and increase of speed) while keeping all other variables constant. Below are is a picture and video of our procedure. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Below is a video of our procedure <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">media type="file" key="Movie on 2011-12-14 at 09.05

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Sample Calculation/Graphs/Data** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Analysis** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">For our force vs. radius graph, we got an r squared value of .4. This is a poor value, however may be due to lack of more points, as our final data point seems to be the issue as the centripetal force increases though it should have decreased. This graph takes the shape of an inverse power function. For our force vs. mass graph, we got an r squared value of 0.94. This is not a perfect value, and it could be better, although our graph form somewhat fit to the shape that it is supposed to. It is supposed to be a linear line, but it does slightly curve. For our force vs. velocity graph, we got an r squared value of 1. The velocity graph is supposed to take the shape of a polynomial function more than a linear line, although we did get a good r squared value.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Conclusion** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> In conclusion of this lab, the results we gathered were almost perfectly correct to our hypothetical and theoretical graphs therefore the purpose was satisfied. Each of our graphs look pretty close to the way it should have been, with the exception of the radius vs. centripetal force graph, which should have been a power function. The relationship between centripetal force and mass, velocity, and radius were illustrated well in this lab. The R square value for the force vs velocity graph was 1 which means it was accurate while the force vs mass had an R square value of .94. The reason the force vs radius had the lowest R square value was most likely due to an error on our part.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">As the mass of the system mass increased, the centripetal force did as well which is displayed in the linear graph. The centripetal force and the radius are a power graph because the centripetal <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">force is inversely proportional the radius squared. The greater the radius, the smaller the force will be. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">The velocity graph too is supposed to be polynomial graph because the centripetal force is directly proportional the velocity. The greater the velocity is, the stronger the force will be.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> The lab turned out to be very successful for us, with the exception of the force vs. radius data, due to the force sensor holding the string down more straight. However, we feel that there could be some improvements. It was difficult to keep all of the variables constant which definitely was not perfect for each trial. The string was not exactly horizontal for every trial.The radius was not consistently the same but we tried our best to keep it within a small range of meters. It was hard to make everything constant and observe one variable at a time. Next time, we should try to be more consistent, patient, and careful so careless error does not happen. Also I think within our data the variable we were observing was not being changed drastically. Our data was too similar, we needed to manipulate the lab so we can see the relationship in very different quantities.

=<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Minimum Speed Activity = <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Task A: Nicole <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Task B: Amanda <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Task C: Ali <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Task D: Julia

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">//**Objective**//:
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Calculate the minimum velocity needs to complete a full vertical circle using a one meter long string, one washer, and a timer.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**//Methods//**:
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">In this activity, we attached a washer to the end of a one meter stick. We then moved the string in a circular motion. We tried to maintain the lowest possible velocity of the string without letting it slack. We were able to find an average velocity by timing how long it took for the string to complete ten revolutions.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**//Sample Calculations/Data/Graphs://**

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%; line-height: 0px; overflow: hidden;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%; line-height: 0px; overflow: hidden;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Our percent error turned out to be a whopping 47.55%. This is most likely due to a lack of being able to reach "almost slack-tension" while swinging in a horizontal, circular motion. Our theoretical value for velocity was 3.13 m/s, while our observed value was 5.967 m/s.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Conclusion: <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Through our experiment, we were trying to find the minimum speed at the max height without having any tension. We counted revolutions as 10 and took down the times that it took. We then averaged our results to find the average experimental velocity. There was a lot of error throughout the lab though, which is shown above in the calculations as 90.64%. Sources of error ranged from our inability to know the exact speed, and we probably did different speeds in different trials, for we did it manually. We also used a timer, which we were in control of, so not being able to get very exact timing could have hurt our results. The radius of the string could have either changed or become too small throughout our trials. If the radius became too small, the velocity probably increased which could account for our results of faster speeds in the class averages. It was also hard to keep the wrist still and avoid moving it so that another component was not involved. In order to fix these percent errors, we probably could have tried to use more technological tools. For example, maybe there is some kind of sensor which calculates speed to keep it the same, as well as making sure that there is no, consistent tension.

=<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Conical Pendulum Lab = <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Task A: Ali <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Task B: Julia <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Task C: Nicole <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Task D: Amanda

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Objective** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">What is the relationship between the radius of a conical pendulum and its period?

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Hypothesis** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">As the radius of the conical pendulum gets bigger, the period will become shorter, as it is getting faster.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Methods and Materials** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">We will be using a massive ball with the mass of 1.744 kg, attached to a string with the length of 2.48 meters. We will be using stop watches to time the amount of time it takes for the ball to complete a period.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Procedure** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Before beginning the lab, we prepared by creating a 2D sketch of the conical pendulum in our notebooks. We labeled parts of the sketch L (length of the string), m (mass of the pendulum bob), r (radius of the circle), and theta (for the angle between the x axis and the pendulum string). We then measured the length of the pendulum string (2.48 meters) and the mass of the pendulum bob (1.744 kg). We then chose four radius sizes, .2,.5,.75,1 m respectively, and performed three trials for each. Below is a chart of the class values. For each trial, we recorded the amount of time it took for the circle, we a radius of some size, to complete a full revolution. We then compared our results and calculated the average and percent error.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Class Data** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Above is a chart of our class data. As you can see, many of the values are consistent. The averages suggest that as the radius becomes bigger, the time period gets smaller (or faster). <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Calculations** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;"> Sample Percent Error Calculation <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">**Analysis**


 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Calculate the theoretical period.
 * 2) See above
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Calculate the average experimental period for each radius.
 * 4) See above
 * 5) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Discuss the accuracy and precision of your data.
 * 6) Our data was very close to accurate.
 * 7) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">Why didn’t we use the tangential axis at all in this lab?
 * 8) We did not use the tangential axis because there were no forces on it therefore was not needed in the lab. We were solving for the constant velocity which was at various points and used the centripetal axis not the tangential axis that is the direction of motion at one point.
 * 9) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 12px; line-height: 17px;">What effect would changing the mass have on the results?
 * 10) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">An object with a higher mass would have a smaller velocity, which would therefore lead to a larger time to complete a period. The mass slows down the object making it move slower. An object with less weight will have a shorter and smaller period because there would be a higher velocity on the object. The mass would also affect the tension and most obviously the weight.
 * 11) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">How did period change as the radius increased? Is it a linear relationship? Why or why not?
 * 12) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">As radius increased, time decreased which proved our hypothesis to be correct. Radius and time will not have straight direct proportional relationship. It is not a simple inverse. It is proportional to the square root of are. The relationship is very complex because the radius is used in many equations to find the x component of tension, finding the angle measure, as well as the velocity equation. There’s not a direct relationship between time and radius.
 * 13) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">What are some sources of experimental error?
 * 14) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 90%;">There could have a few sources of error. Human reaction is delayed so therefore the timing could be off. The length of the string changed a little bit after it fell to the ground changing the time results, which makes the angle measure different than the original. The angle measure affects the component of tension we find which will affect our results.

=<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">** Lab: Moving in a Horizontal Circle ** = <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Task A: Nicole <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Task B: Julia <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Task C: Ali <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Task D: Amanda <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">**__Objectives:__** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">__**Hypotheses:**__
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">What is the relationship between the radius and the maximum velocity with which a car make a turn?
 * 2) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">How does the presence of banking change the value of the radius at which maximum velocity is reached?
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">How does changing the banking angle change the value of the radius at which maximum velocity is reached?
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">The relationship between the radius and the maximum velocity is F=mv 2 /r. When radius is increasing, maximum velocity is going to decrease.
 * 2) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Banking will change the value of the radius at which maximum velocity is reached by making that value smaller. This is because the presence of banking will help to balance the car even when traveling at a faster speed with a smaller radius.
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Changing the banking angle will either decrease the value of the radius or increase it at which it reaches a maximum velocity. When increasing the angle, the radius will decrease while when decreasing the angle, the value of the radius should increase.
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">//Variables// || <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">//Constant or Variable// || <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">//How to Acquire information// ||
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">radius || <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">r || <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">meter stick ||
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">angle || <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">theta || <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">protractor ||

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">**__Methods and Materials:__** <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">We will be using a rotational turntable attached to a power supply in order to find the max speed of a 6 gram mass. The 6 gram mass will be placed on the rotational turntable at the 30 cm mark. We will ensure that this is truly 30 cm by measuring it with a meter stick. Attached to the rotational turntable is a photo gate, which we will use via Data Studio to collect our results.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">__**Procedure:**__ <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Below is a video of our procedure. Data was recorded through using the Recordable Timer on Data Studio to find the period. The period of the maximum speed was found as the last period before the 6 gram mass flew off the rotational turntable. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">media type="file" key="horizontal.mov" width="300" height="300"

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

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">__**Sample Calculations:**__ <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">
 * finding velocity**
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">finding the coefficient of friction **

<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;">__**Analysis:**__ <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;">finding the maximum velocity **
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">finding µ on our graph **
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Percent Error (exponent) **
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Percent Error (graph µ vs. our µ) **
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Percent Difference **

>>
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Discuss the shape of the graph and its agreement with the theoretical relationship between R and v.
 * 2) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Since velocity squared is equal to (R)(g)(µ), we can assume that the best fit shape of the graph would be a power function. On the y-axis we have maximum velocity in m/s and on the x-axis we have our radius in meters. As you can see from the graph, as the radious increases, the maximum velocity follows suit. Yet, the amount that which the maximum velocity increases becomes less steep, suggesting a slower increase with radial change. As you can see above in the sample calculation section, the coefficient we found, 2.0672, is equal to ((R)(µ)) 1/2 . By plugging in our information, we were ultimately able to calculate the value of µ, .44.
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Derive the coefficient of friction between the mass and the surface.
 * 4) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">see calculations above
 * 5) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Compare your coefficient of friction with that of all groups doing this lab. (Be sure to post a data table with the class values.)
 * 6) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">see percent difference and table above
 * 7) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">A “car” goes around a banked turn.
 * 8) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Find an __expression__ for its maximum velocity, in terms of variables only.
 * 9) [[image:Screen_shot_2012-01-05_at_10.26.01_AM.png]][[image:Screen_shot_2012-01-05_at_10.26.47_AM.png width="71" height="141"]]
 * 10) [[image:Screen_shot_2012-01-05_at_10.27.03_AM.png width="71" height="81"]]
 * 11) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">[[image:Screen_shot_2012-01-04_at_1.45.01_PM.png width="127" height="41"]]
 * 12) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">How do you think the graph would change if you performed the same procedure but with an angled surface, instead of the level surface we used?
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Now that we have this expression, we needed to find the maximum, granted that there was a given angle. Since in this case, we were not given an angle, we substitute it for theta. Below is our result.
 * 2) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">[[image:Screen_shot_2012-01-06_at_8.39.59_AM.png width="159" height="255"]][[image:Screen_shot_2012-01-05_at_10.22.14_AM.png width="149" height="190"]]
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">[[image:Screen_shot_2012-01-05_at_10.24.04_AM.png width="200" height="76"]]
 * 4) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">[[image:Screen_shot_2012-01-04_at_9.34.38_AM.png width="251" height="71"]]
 * 5) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">this our our result for a banked angle!!!!

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

Our hypothesis was wrong; we hypothesized that the maximum velocity would decrease as the radius increased, though through our data we show that the maximum velocity actually increases as the radius increases. With a larger radius, the mass is farther from the center and therefore covering more distance and a greater centripetal force would be needed for the mass to reach its maximum velocity. We also hypothesized about banking angles, and although we didn't perform an experiment on it, we believe our hypothesis would still be correct. The coefficient of friction from our graph was found because the graph follows the equation of y=Ax^B. The graph has the x-value represents the radius and the y-value represents the maximum velocity. Since the maximum velocity is equal to the sqroot of (R)(g)(µ), the exponent (or B-value) on the x-value should be 0.5 and A is equal to the sqroot of (g)(µ). Therefore, using this, we were able to calculate the value of the coefficient of friction. Also, since maximum velocity is a square root equation, the graph should appear as one. Since our graph still takes the general shape of a square root equation, it shows that our lab was relatively successful. The percent error between the theoretical exponent (0.5) and the exponent from our graph (0.3847) was 29.97% which is pretty high. In addition, the percent error between the coefficient of friction of the graph (experimental) and the coefficient of friction from our calculations (theoretical) was 25%. These high percent errors were due to the many sources of error in the lab. One possible source of error is human reaction time between when the mass flew off the rotational turntable and when the person watching said stop, and also between when the person said stop and when the other person stopped the DataStudio from recording data. An extra period could have been in the time, which would have thrown off the answer as the period we used could be the one after the mass flew off instead of right before. Another source of error could be with the voltage, as the voltage wasn't exactly the same each trial. Also, the voltage could have been turned up too quickly and therefore the velocity increased too quickly to be recorded. These sources of error could be corrected in a future lab by using different tools. Instead of manually increasing the voltage, we could use a machine that increases voltage at a constant pace ensure the velocity would be accurately recorded on data studio. The human reaction time could be eliminated by having a different tool that would immediately stop the timing once the mass flew off. If these errors were all corrected, our coefficient of friction and our exponent would be far closer to the theoretical values.