Group2_2_ch4

Group Members: Ben Weiss, Dani Rubenstein, Danielle Bonnett, Julia Sellman toc

= Gravity and the Laws of Motion Lab = Danielle Bonnett- Task A Ben Weiss- Task B  Dani Rubenstein- Task C  Julia Sellman- Task D

In this lab, the following objectives had to be met:
 * __Objectives__**
 * 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 the lab
 * Determine if mass has an effect on the acceleration of an object

Before this lab could begin, several hypotheses had to be made that offered predictions of how the objectives would be solved.
 * __Hypotheses and Rationales__**
 * If the value of acceleration due to gravity is calculated, then it will be about 9.8 m/s^2. This is a rational hypothesis because in previous experiments (such as the free-fall lab), the class has calculated the acceleration due to gravity as being 9.8 m/s^2.
 * If acceleration of an object increases, then the incline angle must also increase. This would make sense because the class has found in previous labs that the acceleration at a degree of 0º would be 0 m/s^2, while acceleration at a degree of 90º (or pure free-fall) is 9.8 m/s^2. As the angle increases and gets closer to 90º, it is reasonable to believe that the acceleration will also increase to eventually reach 9.8 m/s^2.
 * **Because the third objective only requires creating a graph, a hypothesis is not needed.**
 * If one attempts to determine if mass has an effect on the acceleration of an object, one will find that there is no effect at all. This would make sense because the class has seen in other activities (especially the egg-drop activity) that regardless of the mass of an object, the object will always free-fall at an acceleration of 9.8 m/s^2.

To determine whether or not the hypotheses above were true, tests involving incline angle had to be performed. Before the angle could be set up, the mass of a ball that was given first had to be measured with an electric balance. From here, a ramp with a length of 1.20 m was set up so that it would be at an angle in relation to a table. This angle could be changed by changing the height at which the higher end of the ramp was (this length could be measured with a ruler and the resulting angle could be measured with a protractor). After this, the ball could be rolled down the ramp with the total time it took to reach the other end of the ramp being measured by a stopwatch.
 * __Methods and Materials__**

When set up, the materials looked like this: From here, the ball was able to roll in the manner shown below: media type="file" key="Rolling Ball.mov" width="300" height="300"

Ultimately, after having calculated the length of the ramp, the total height of the ramp, and the time it took for the ball to reach the other end, one could use kinematics equations to calculate acceleration for that particular run. After doing so with several different angles, one could put this data on a graph and estimate the acceleration at 90º or at free fall.


 * __Calculations, Data, and Analysis__**

Link to Document: Gravity and the Laws of Motion Data: This data table shows our results after setting the height to a certain distance, rolling the ball down, and calculating different parts. It shows all of our trials which are also categorized into four different groups (used different colors) to show that they all were set to the same height.

Graph: __**Analysis:**__

This graph shows that (when the line is extended to sin of Theta=1), our acceleration due to gravity would be 6.11 m/s/s. However, this graph does not show our y intercept equal to zero, which is needed because the acceleration at an angle of 0º is 0 m/s/s. When we set the intercept equal to zero, we saw the result of 7.16 m/s/s, and that is the magnitude we used while completing our other calculations.

Sample Calculations:

Sample Calculation to Find Average Time: Second Set of Trials that were set at 0.25 m Sample Calculation to Find Acceleration: 1.68 seconds at a height of 0.15 m (Trial 2) Sample Calculation to Find the Average Acceleration: Third Set of Trials that were set at 0.30 m Sample Calculation to Find Sin of Theta (using the trig definition): Fourth Set of Trials that were set at 0.36 m Percent Error: Although this percent error seems to be quite large, there are good reasons for why this result was obtained. Because we were not able to actually set the ramp to 90 degrees and have it be in free-fall, we only were able to get this result from looking at a graph based on previous results. Although the graph did give us accurate results, they were not completely precise due to the fact that we did not have direct calculations for certain points.

Percent Difference from Class Average:

Class Data: From this class data, we were able to observe many things. With exception to the smallest mass, all groups showed a consistent pattern with the ratios between the mass and the experimental g. For example, the heaviest mass had the highest g and it decreased as the mass decreased. Our group shows to be continuous with this pattern, as we had the fourth smallest mass and had the fourth smallest g value as well. Also, the second data table shows, just like the laws of inertia state, that mass does not affect the acceleration of an object. Although all the masses were different, all had accelerations that were very close to each other. This shows that acceleration is always the same of an object in free fall (or an object rolling down a ramp) and it does not matter if one object has a greater mass than the other.

Free Body Diagram: Although this free-body diagram looks simple, there is more that is actually occurring in the situation. The two forces that are acting on this ball are weight force and normal force. Both of these forces play a part in allowing the ball to roll down the ramp. As the weight force as both an x and a y component, one has to be cancelled out to allow the ball to roll down. Since the y component is cancelled out by the normal force from the ramp, it is evident that it is the x component of the weight force that allows the ball to roll down. Also, we can use the x component and Newton's Second Law to determine acceleration. We can use the equation f=ma to solve for this.

Example of Finding Acceleration (from this information): Data taken from the 0.30 trial By using Excel, for this trial, we found the average acceleration to be 1.705 m/s/s. Although this number was not exact to our calculated one, it was close, which shows our accuracy in completing both the Excel method and the method taken from Newton's second law.


 * __Discussion Questions__**
 * 1. Is the velocity for each ramp angle constant? How do you know?** Velocity for each ramp angle would not be constant. This would be the case because at each ramp angle, the ball is accelerating and changes its velocity as it moves.


 * 2. Is the acceleration for each ramp angle constant? How do you know?** The acceleration for each ramp angle is constant. This is clear based on the calculated acceleration for each angle in the data table above. While there may have been slight differences between the calculated acceleration of certain runs, there were no drastic outliers that might put the results in question. As a result, any slight difference that there might be would be due to experimental error.


 * 3. What is another way that we could have found the acceleration of the ball down the ramp?** Yes, we could have used another kinematics equation, such as a = (vf-vi)/t. Although this would be another way to find acceleration, we would have had to find the final velocity to solve this equation.


 * 4. 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?** By consistently raising the height of the ramp, making it closer to 90 degrees, Galileo observed that the acceleration would increase as he went. When the ramp was closest to 90 degrees, he observed that the acceleration was very close to 9.8 m/s/s. By following previously made patterns and taking this observation into consideration, Galileo was able to determine g by rolling balls down an inclined plane.


 * 5. 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?** Theoretically, the mass of an object should not affect its rate of acceleration down the ramp, but when friction and air resistance play a role in an object's movement, the acceleration may be affected. The mass of an object should never affect the motion of an object in free-fall; the acceleration of that object will ALWAYS be 9.8 m/s2.

We hypothesized that the value of the acceleration would be approximately 9.8 m/s2. This rationale was realistic, because in previous experiments like the freefall lab, we have calculated that the acceleration was around that value. We did also hypothesize that as the incline increased, the acceleration value would get closer to 9.8 m/s2 as the angle got closer to 90 degrees. These hypotheses were approximately correct. We were able to find that the acceleration at 90 degrees would come out to be about 7.16 m/s2, which isn’t exact, although the value does come somewhat near that of 9.8 m/s2. The differences probably stem from error throughout the lab that should be accounted for. Each time that we increased the angle of elevation of the ramp, we found that the acceleration increased continually. For example, when the ramp had a sin (theta) value of 0.125, the average acceleration was 1.056 m/s2, though when the sin (theta) value was 0.250, the acceleration value increased to 1.705 m/s2. There was definitely a direct correlation between the increase in the size of the angle and the increase of the acceleration, which was found throughout all of our results. We also hypothesized that mass would have no effect on the acceleration of an object. At first we began to question this hypothesis because we found that when comparing the different ball masses, different accelerations did result. For example, our group had a ball mass of 0.016 kg and we had an acceleration of 7.16 m/s2, and when compared to another group with a ball with the mass of 0.226 kg, it had an acceleration of 8.135 m/s2. The rest of the class results did show that for the most part, as the mass increased, so did the acceleration, but we did learn that this was mostly due to friction. The friction probably did account for the slight differences in the accelerations, while if there was no acceleration, theoretically, the accelerations would come out to be the same. Though, we were told to ignore the minimal friction that could have occurred between the ball and the ramp throughout the lab, which does relate to mass. This friction could have caused the accelerations to be slightly lower than what they would have been without any friction at all. This is why it does make sense that our acceleration at 90 degrees is lower than 9.8 m/s2. Even though we found it to be 7.16 m/s2, which is a significant difference and has a percent error of 27%, it still is a realistic value due to the fact that we didn’t take into account the friction present throughout the experiment. Compared to the rest of the class, we only got a percent difference of 7.9%, so that shows that our results were relative to those that everyone else got. We also didn’t account for air resistance, which could have also lowered the value of the acceleration slightly as well. Other sources of error could have been from the fact that the ball could have been veering slightly to one side of its course, causing even more friction with the wall of the ramp, and therefore further slowing its acceleration. Another source of error could have been the timing, which might not have been completely exact, being that our best contraption was a simple manual timer. Ways to help decrease error could be using some kind of better ramp that would have less friction with the ball and using a more advanced timer like a sensor on the computer that could tell when the ball had reached the bottom of the ramp.
 * __Conclusion__**

=**Newton's Second Law Lab**=

Ben Weiss- Task A Julia Sellman- Task B Danielle Bonnet- Task C Dani Rubenstein- Task D

In this lab, the only objective is to determine the relationship between system mass, acceleration, and net force.
 * Objectives**

- If acceleration's relationships to net force and system mass is determined, then acceleration will be shown to be directly porportional to the net force and inversely porportional to the system mass. The formula created for Newton's Second Law, **net force= mass x acceleration**, which has been used in class demonstrates this.
 * Hypothesis**

- If acceleration vs. net force and acceleration vs. mass graphs are made, then the graph for acceleration vs. net force will show a linear relationship between acceleration and net force, while the acceleration vs, mass graph will show that acceleration exponentially decreases in relation to mass. This would be the case because the graphs would be representative of the relationships detailed in the first hypothesis.

- The mass of all objects, including the carts, the weights, and the hanging mass was recorded first by measuring them on an electronic scale. Then, the USB that would open the program needed for this experiment was plugged into the computer. Next, Data Studio was opened in order to initiate the program, on which acceleration could be measured. The metal track was then placed on the table, along with the pulley, which was secured by the screw. Next,the string was put over the pulley and hung down through the pulley, off of the side of the table. The 10g, 10g, and 5g weights were placed on the cart on the cart, which was released, letting the string run through the pulley. After three different trials using this set-up, the needed information was recorded for all three. The 5g weight was then transferred to the hanging mass (the opposite end) and then accelerations were recorded for three trials with this set-up. The two 10g weights were then transferred one by one, after which Data Studio recorded three trials of acceleration for each one. With these different accelerations, average acceleration was able to be calculated, which in turn could be used to create a linear net force vs. acceleration graph. Then, for another series of tests, blocks were put on top of the cart, leaving the weights from the first series of tests attached on the hanging weight. From here, Data Studio was able to record another series of accelerations, which led to new average accelerations, which could be used to make an exponentially decreasing total mass vs. acceleration graph.
 * Methods and Materials**

media type="file" key="Movie on 2011-11-30 at 08.37.mov" width="300" height="300" This video shows the cart accelerating across the table due to the hanging mass.
 * Procedure**

After running several tests with varying cart weights and hanging weights which all added up to the same total weight, then different total weights, it was possible to measure and calculate net force, theoretical acceleration, experimental acceleration, and average acceleration. All measurements and calculations can be found below: After this, it was possible to graph (for the first four sets of trials) a net force vs. average acceleration graph and (for the final three sets) a total mass vs. average acceleration graph. The two graphs can be found below:
 * Data and Graphs:**
 * Average Acceleration For Trial 1 Calculation:**


 * Net Force Calculation:**


 * Percent Error for Acceleration vs. Net Force:**
 * Percent Error for Acceleration vs. Mass:**

Explain your graphs:  1) 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 slop should be equal to this quantity. What is the meaning of the y-intercept value? 2) 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. 3) 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.
 * Analysis:**
 * For the Acceleration vs. Net Force graph, the trend line was linear. The actual value of the slope was 1.16896, which goes along with the value of 1/total mass. The observed value should have been around .530. A 11.24 % error was calculated for this, so the results still fit in the "20% error range." The meaning of the y-intercept is friction. In this lab, the friction should be negative, which explains why the y-intercept on our graph is negative. -f/total mass can be used to represent friction. The slope should be equal to this because of the calculation and the substitution of the equation in slope-intercept form that is below:[[image:Screen_Shot_2011-12-03_at_6.45.44_PM.png]]
 * The graph for the Acceleration vs. Mass was non-linear. The power on the x is -.866, but it really should be -1. The coefficient in front of the x corresponds to the net force, which is the weight of the hanging mass. The observed value from the graph was .2652, but it should actually be .294. With this information, a percent error of 9.86% was calculated. This value should be equal to this quantity because of the equation below:
 * [[image:Screen_Shot_2011-12-03_at_6.47.30_PM.png]]= A is equal to net force = mg
 * By adding friction, it would cause the acceleration to drop. This would be due to it going against the tension force of the string. In order to create the same acceleration, you would need a bigger force because friction opposes the motion of force. Friction can definitely be a source of error in this experiment. It may have been found on the cart, which would have caused it to slow down a little bit. The slope was too big because there was little percent error. If friction was involved in the lab, then it would be the (f/m) value, (-0.0189), which can be seen in the graph above.

It was hypothesized that the acceleration would be directly proportional to the object's net force and inversely proportional to the object's mass. To prove this hypothesis correct, a lab was conducted that used a cart, weights, a hanging mass, a pulley, and a ramp. By using these materials and moving the weights from the cart to the hanging mass, the net force, theoretical acceleration, experimental acceleration, and average acceleration of six different sets of trials were recorded and calculated. After completing the lab and analyzing the results, it was clear that this hypothesis was correct. It was also correctly predicted that the acceleration vs. net force graph would be linear and that the total mass vs. acceleration would have a exponentially decreasing slope. In addition, the percent error for both graphs shows that the numerical results were precise as well. For the acceleration vs. net force graph, a percent error of 11.24% was calculated, which falls within the 20% error range. As there are many places where a source of error could have affected our results, a percent error of 11.24% is very successful. For the acceleration vs. mass graph, an even smaller percent error of 9.86% was calculated. Like the previous percent error, this percent error falls within the 20% range, proving the accuracy of these results. Additionally, the r squared values also show that the results were precise, as the r squared values were both above 99% on both of the graphs, showing that the data was extremely accurate. Although the percent errors and r squared values were idealistic, there were numerous sources of error that contributed to the fact that the results did not have 0% error. The first source of error was found in the string that was used to cause the tension between the cart and the hanging mass. For the lab to be successful, the string had to be perfectly parallel to the ramp that the cart was moving on. Although the string came pretty close to being parallel, even a slight incline or decline in the strings position could have affected the final results. Also, the hanging mass sometimes either hit the ground before Data Studio was stopped or came in contact with the wire on the pulley while a trial was underway. This was somewhat able to avoided this by holding the wire away and being more precise about when the data stopped being recording, but it was not able to fall completely perfectly. If this lab could be redone, there are a myriad of actions that could be taken to fix these sources of error. For example, a tool, such as a protractor or another measuring device, could be used to make sure the string was perfectly parallel with the horizontal ramp. Also, the environment could be set up so that it would be impossible for the hanging mass to come in contact with either the ground or the wires from the pulley. This lab is important to understand because it demonstrates the relationship between net force, acceleration, and mass. Without knowing this vital information, a lot of everyday applications would not be possible. For example, this "drop-and-pull" situation is important to understand if you work as an engineer or in a factory, where machines that demonstrate this situation are present. If some object was being used to hold up another object in a drop and pull situation, it would be important to know if the object would accelerate or not once released, as the person setting up the situation might be aiming to avoid this.
 * Conclusion**

=**__Coefficient of Friction Lab__**= __Period 2__ __Date Completed:__ 12/7/11 __Date Due:__ 12/8/11

__Task A__: Dani Rubenstein __Task B:__ Danielle Bonnett __Task C:__ Julia Sellman __Task D:__ Ben Weiss

__**Objectives:**__
 * To measure the coefficient of static friction between surfaces
 * To measure the coefficient of kinetic friction between surface
 * To determine the relationship between the friction force and the normal force.

__**Hypothesis:**__
 * As normal force increases, so does the friction force, meaning that they will be directly proportional.
 * The coefficient of static friction and kinetic friction will be between 0 and 1 because that's the normal range.
 * The coefficient of friction and the mass are directly related, so as the mass increases, the coefficient of friction will as well.

__**Materials:**__ The materials that we used for this lab were a Pasco Force Meter, USB link, friction cart, miscellaneous asses, string, an aluminum track, and a clamp.

__**Video:**__ media type="file" key="Friction Lab Video.mov" width="300" height="300"

__**Procedure:**__ 1) Mass the friction dynamics cart. 2) Place the cart on the surface and put a 500g mass in it. 3) Tie a short 15cm string to the block at one end, and to the Pasco Force Meter on the other end. 4) Plug the force meter into your computer. Choose Data Studio, and then click"Create Experiment". 5) Go to SETUP and check //Force-Pull Positive// and uncheck //Force-Push Positive.// 6) On the graph display, click the y-axis label to change the name to //Force - Pull Positive.// 7) Leaving the string slack, press the button "zero" on the sensor. 8) Press START on Data Studio, and gently pull the block with the force sensor. 9) Highlight the straight line part on the graph and click the net force symbol, and then select the MEAN as the value for Tension at Constant Speed. 10) Highlight the maximum point and record the value as the maximum tension. 11) Repeat twice more with the same mass. 12) Repeat steps 8-12 adding more mass each time in large increments
 * Be sure to pull with a very slow constant speed once it starts to move.
 * Hold the string parallel to the board.

First, the mass of a cart was measured on an electronic scale (the mass was found to be about .093 kg). Next, the cart was placed onto an aluminum track that was clamped onto a table, after which a 500 g (or .500 kg) mass was placed in the cart. From here, one end of a short 15 cm string was tied onto the cart, while the other end was tied onto a Pasco Force Meter. This Force Meter would make it possible to measure the tension in the string, which would provide the friction of the cart. To do this, the Force Meter was plugged into a laptop with a USB, after which Data Studio was turned on. After setting up an experiment, with settings to enable the program to make graphs of tension, the cart was pulled via the string in order to measure mean and maximum tension. To calculate mean tension, the straightest part of a specific graph was highlighted, then a "net force" button was clicked giving the desired value. The highest point on the graph was maximum tension. To see sample graphs, go to //Data Tables and Graph//. To vary up the results, different masses were added to the cart. From here, average maximum and mean tensions were found by adding all the calculated values for a specific mass, then dividing by three. To find the co-efficient of friction (using the equation f=
 * __Materials and Procedure:__**

__**Data Tables and Graph:**__


 * Data Table of Maximum Tension on the Cart**


 * Data Table of Mean Tension on the Cart**


 * Graph Comparing Both Mean and Maximum Tension vs. Normal Force**
 * (Maximum Tension = Static Friction and Mean Tension = Kinetic Friction)**


 * Class Data:**

__**Analysis:**__
 * **Compare the slope of line with calculated m s average (% difference).**
 * Static Friction
 * [[image:Screen_shot_2011-12-07_at_6.40.22_PM.png width="382" height="49"]]
 * [[image:Screen_shot_2011-12-07_at_6.31.53_PM.png width="175" height="75"]]
 * Kinetic Friction
 * [[image:Screen_shot_2011-12-07_at_6.40.22_PM.png width="382" height="49"]]
 * [[image:Screen_shot_2011-12-07_at_6.37.06_PM.png]]
 * **Compare your result with the class results.**
 * Static Friction
 * [[image:Screen_shot_2011-12-07_at_6.40.22_PM.png width="382" height="49"]]
 * [[image:Screen_shot_2011-12-07_at_4.50.34_PM.png width="204" height="91"]]
 * Kinetic Friction
 * [[image:Screen_shot_2011-12-07_at_6.40.22_PM.png width="382" height="49"]]
 * [[image:Screen_shot_2011-12-07_at_4.51.29_PM.png width="192" height="100"]]

__**Discussion Questions:**__
 * 1) **Why does the slope of the line equal the coefficient of friction? Show this derivation.**
 * 2) The general line equation is y=mx +b. We know that the y-intercept for this equation will be 0, so therefore b=0. This leaves us with the equation y=mx. We know further that our y-axis shows our force of friction while the x-axis shows our normal force. Therefore, because we know that the equation of friction is f=µ*N, the coefficient of friction must be equal to the slope.
 * 3) **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) The coefficient of friction between the material and the aluminum track is approximately somewhere in between .25 and .4, for static friction and between 0.1 and 0.3 for kinetic friction according to []. We found that our coefficient for static friction was approximately 0.1622, which is slightly off from the .25 or to be exact, 0.0878 off. On the other hand, we found that our coefficient for friction for the kinetic friction was 0.1034. That one fell within the category that was specified on the website. It makes sense that the static friction's coefficient variable is larger than that of kinetic friction because kinetic friction is moving, therefore having less friction, while an object with static friction is at rest, and has more.
 * 5) **What variables affected the magnitude of the force of friction? What variables affected the magnitude of the coefficient of friction?**
 * 6) The variables that affected the magnitude of the force of friction are the coefficient of friction, as well as normal force, considering the formula for the force of friction is µ *N. The variables which affect the coefficient of friction are the normal force and the friction itself. This is because f/N= µ . When the friction force is larger and the normal force is smaller, the u will be bigger. Though, when the force of friction is smaller and the normal force is larger, the coefficient will be smaller.
 * 7) **How does the value of coefficient of kinetic friction compare to the value for the same material’s coefficient of static friction?**
 * 8) The value of the coefficient of kinetic friction is 0.1034 and the coefficient of static friction is 0.1622. The static friction coefficient is slightly larger by .0588. This makes sense because kinetic friction will be slightly less, for the object is able to move. On the other hand, static friction's coefficient is smaller because an object that is not moving has more friction than one that is moving.

__**Conclusion:**__ It was hypothesized that normal force and friction force would be directly proportional to one another, that the co-efficients of both static and kinetic friction would be between 0 and 1, and that the co-efficient of friction increases as the system mass increases. To prove these hypotheses correct, an experiment had to be performed in which both maximum tension and mean tension were calculated for a mass pulled by a string. The purpose of doing this was to find static friction (which is equivalent to maximum tension) and kinetic friction (which is equivalent to mean tension); tension and friction are equivalent because there is zero acceleration (T-f=0), which provides T=f when f is added on both sides). After different maximum tensions and mean tensions were calculated and measured for different masses, a kinetic friction vs. normal force (equivalent to the mass' weight) and a static friction vs. normal force graph could be made. The resulting graph, which was linear, demonstrated that as normal force increases, so does friction force (in both cases), proving the first hypothesis correct. From here, the slope of each linear graph could be calculated, which ended up being the co-efficient of friction in both graphs. The co-efficient of static friction was calculated as being .1622, while the co-efficient of sliding friction was calculated as being .1034. These values are both in between 0 and 1, providing the second hypothesis correct. At the same time, the results of the lab demonstrated that a greater mass would require a greater tension, leading to a greater friction (due to the T=f equation)**.** This proves that the third hypothesis is correct.

In this experiment, though the results were extremely accurate, there was some error. This was evidenced by the calculated percent difference between the slopes and the calculated co-efficients and the percent difference between the results of the rest of the class and the results of this group. For example, the percent difference between the slope and calculated co-efficient for static friction was 3.21%, while the percent difference between the slope and calculated co-efficient for kinetic friction was 1.35%. The percent difference between the class results and the results of this group were 5.81% and 8.98% for static and kinetic friction respectively. One potential source of this error could have been the angle of the string that was providing tension. It was supposed to be at an ideal angle of 0º, but during the experiment, it may have been slightly higher. Another source of error could have been from the pulling of the cart. It is possible that the person pulling the cart did not have a steady hand at all times, leading to the possibilities of the string being shifted and/or the cart being pulled at a non-constant speed. To minimize this error if we were to repeat this lab, a protractor could be used to measure the angle of the string and some sort of device that would make sure that the cart moved at a constant speed and that the string did not shift could be used to pull the string, instead of a human hand.

This lab can be applied in the real world. This lab provided a small demonstration of how to calculate the co-efficient of friction between two different surfaces, which can be applied to any two surfaces outside of the lab. For example, it is possible to calculate the co-efficient friction between the tires of a car and the road underneath them using the methods of the lab. As a result, this lab gives a greater understanding how touching objects interact with each other in the real world.