Group6_4_ch4

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Hy[p toc = = =Gravity and the Laws of Motion = Hella Talas Period 4 11/18/11 Group 6: Hella Talas, Jonathan Itskovitch, Lauren Barinsky, Jake Aronson

Task A: Lauren Task B: Hella Task C: Jake Task D: Jon


 * Objectives: **
 * 1) Find the value of acceleration due to gravity
 * 2) Determine the relationship between acceleration and incline angle.
 * 3) Use a graph to extrapolate extreme cases that cannot be measured directly in the lab.
 * 4) Determine if there is an effect of mass on acceleration down the incline.


 * Purpose and Rational: **
 * Acceleration due to gravity is 9.8 m/s/s because of the results of our previous free fall lab.
 * <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">The larger incline angle the larger acceleration because there is less equilibrium between gravity and normal force, and because the weight of the ball pulling itself towards the center of Earth. When the incline angle is 0, normal force from the ramp is pushing straight upwards and gravity is pushing straight downwards, and there is equilibrium. As the incline angle increases, gravity's influence increases because the normal force is not directly opposing it anymore, resulting in an increasing acceleration.
 * <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">We are going to extrapolate extreme cases in this lab. We will theoretically calculate points beyond what was measured, and assume a common trend, in order to predict the graph.
 * <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Yes, because mass is indirectly proportional to acceleration. The more massive the object is, the larger the acceleration will be.


 * <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Method and Materials: **

<span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Supplies used in this lab include a ball, a ramp linked to a clamp, a meter stick, a stopwatch, and an electronic scale. <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">To begin the lab, set up a ramp linked to a clamp. Measure the length of the ramp via a meter stick, which will serve as the distance travelled by the ball. Find the mass of the ball with an electronic scale. The first height to be tested is 0.15 m from the table. Place the ball at the top of the ramp and allow it to roll down the ramp until it reaches the bottom. Using a stopwatch, record the time it takes for the ball to travel the length of the ramp. To more accurately determine when the ball reaches the bottom, a barrier can be placed at the end so that it is known that the end is reached when the ball hits the barrier. A tissue box is used for this in this experiment. Record the time for five trials at the first height. Four more heights are chosen and five trials are repeated for each height. There will be a total of 25 trials for this experiment. media type="file" key="physics trial ball ramp.m4v" width="300" height="300"

<span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">**Observations and Data:**

<span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Mass of the ball: 0.0846 kg

__TABLE: Experimental Results and Accompanying Calculations__

__GRAPH:__

Analysis of the Graph: The graph is a constant, linear graph. It shows a constant relationship that, as the sin of theta increases, so does the acceleration of the ball. The slope of the graph, 11.451, is related to the acceleration due to gravity. The y-intercept is related to friction, but isn't actually friction. The y-intercept should theoretically be at 0, if there is a frictionless surface, but this isn't the case. Y is the acceleration, and x is the sin of theta. The R 2 value of 0.999 suggests that the trendline is very accurate according to our data.

Excel Spreadsheet of Data:

<span style="background-color: transparent; color: #000000; font-family: Times New Roman; font-size: 15px; text-decoration: none; vertical-align: baseline;">Analysis:
 * 1) Class Data (in order of mass, low to high)

Free Body Diagram:

The weight of the ball, specifically the x component of the weight, in conjunction with the imbalance between the weight and normal force is what causes the ball to roll down the ramp. We used h=15cm to test this - theta is 6.89 degrees. By doing this, we get an acceleration of 1.17 m/s/s, which is above our 0.84m/s/s. Though it is slightly off, this difference is due to friction. This shows that F=ma is an accurate equation for solving acceleration.


 * <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Discussion Questions: **

<span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">1. Is the velocity for each ramp angle constant? How do you know? <span style="background-color: #ffffff; color: #000080; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;"> a. No, the velocity for each ramp angle is not constant. According to the table, if one were to divide distance over time to find average velocity, one would notice that as the angle increases, the velocity increases but at a slower rate. This is because the average times are decreasing with a slower rate over time as the angle increases.

<span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">2. Is the acceleration for each ramp angle constant? How do you know? <span style="background-color: #ffffff; color: #000080; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;"> a. No, the acceleration for each ramp angle is not constant; it is only about the same within the trials of the same angle. Using the kinematics equation, d=vit+1/2at^2, one would notice that acceleration equals 2d/t^2. Using this equation, one would notice that the acceleration increases as the angle increases. Also, using the equation F=ma, one would realize that, though the mass is the same, the applied forces are not, so the acceleration cannot be constant. The reason for forces increasing with steeper angles is because the normal and weight forces become more unbalanced more quickly, and so the net forces increase. It is also because of the weight itself, and the gravity pulling the ball down towards the center of Earth.

<span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">3. What is another way that we could have found the acceleration of the ball down the ramp? <span style="background-color: #ffffff; color: #000080; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;"> a. We could have used the formula F=ma to find acceleration. Knowing the mass of the ball in kilograms, we could have measured the force exerted onto the ball in Newtons, and simple algebra would determine the acceleration.

<span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">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? <span style="background-color: #ffffff; color: #000080; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;"> a. It was possible for Galileo to determine g when he rolled the balls down the inclined plane. By carefully measuring theta, the height, and assuming a frictionless surface, he rolled balls down and up ramps and expected the ball to stop moving at the original height, even when the masses of the balls were different. This was the case. This led Galileo to believe that all objects affected by gravity should free fall at the same rate every time. Galileo could have used calculations we knew now to determine acceleration due to gravity, but he did not have such tools.

<span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">5. Does the mass of an object affect its rate of acceleration down the ramp? Should it affect the motion of an object in the same manner? <span style="background-color: #ffffff; color: #000080; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;"> a. Yes, the mass of an object has a massive (no pun intended) effect on the rate of acceleration down the ramp. Newton provided us with the equation F=ma. The mass is inversely proportional to the acceleration, so a bigger mass should decrease acceleration. And it should affect the motion in the same manner, but it does not. In this lab, we ignored the friction force acting upon the balls. More massive balls are less affected by friction, so they can accelerate faster. Since the ball is on an incline, we can separate the motion into x and y components, and use the equation F=ma to find the x and y components of the ball. For x, it should be gsintheta, and for y it is gcostheta. Because we used the equation y=mx+b for the graph, and y is the acceleration, the equation goes as a=gsintheta+b, and b is the friction-related forces changing the values of acceleration.


 * <span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Conclusion: **

<span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">Yes, our hypotheses were correct. Although our lab results showed that acceleration due to gravity is 11.451 m/s/s, it is 9.8 meters per second squared, as has been proven by our previous labs on free fall. All actual free-falling objects in the real world should be compared to the theoretical value of acceleration, 9.8, for percent error. Also, having a larger incline angle does mean a larger acceleration. The normal force and weight become less balanced quicker, and more net forces are acting upon the ball quicker, so the object does accelerate faster. Our data shows acceleration increases with larger angles. And yes, of course, the mass does have an effect on acceleration. Theoretically, higher mass balls accelerate slower. This is proven by Newton’s Second Law, stating the mass is inversely proportional to acceleration. However, the class data proves otherwise. This is because we ignored the FRICTION force resisting the motion. Higher mass balls are less effected by friction, meaning they can accelerate faster.

<span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">As for experimental error, we got a 9.18% margin of error, which is pretty good. There are sources of error that describe this, however. First of all, our timer could have began the time late or early, and recorded the time incorrectly. This could have skewed the data and resulted in an inaccurate result of acceleration. Secondly, the ball could have rolled off the ramp and resulted in the timers stopping time only after the ball hit the ground. This, again, leads to inaccurate data. Thirdly, the height of the ramp to the ground could have been measured incorrectly, leading to an incorrect theta and desired acceleration values.

<span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">However, there are ways to address this error, and fix the issues stated above. There should be 2 timers, not 1, to average out the time and get a more accurate reading. Also, put a tissue box or other object to prevent the ball from rolling off, and also makes it easier to see when the ball actually reaches the end of the ramp (the ball hits the box and bounces up). Finally, use very accurate measuring devices to accurately measure the height of the ramp to the ground to get the correct theta value.

<span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">A real life application has to do with skateboarding, going down ramps to do tricks. The ramps are on a certain angle, and the skater goes down the ramp. Obviously, the steeper the angle, the more acceleration the skater has, and the more distance the skater can cover to do awesome tricks! However, the steep angle may make the skater accelerate too much, and cause him/her to fall off. This proves to be important for skaters who do so professionally, because they need to know the dangers and risks of the tricks they desire to perform.

=Newton's Second Law= Lauren Barinsky Period 4 12/2/11 Group 6 Members: Lauren Barinsky, Hella Talas, Jonathan Itskovitch

Task A: Hella Task B: Lauren Task C: Jonathan Task D: Lauren

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

As force increases, acceleration increases. As mass increases, acceleration decreases. Acceleration increases as force increases and mass decreases. F = ma, so mass and acceleration are inversely proportional when force is constant (curved graph), and force and acceleration are directly proportional when mass is constant (linear graph). A larger mass needs a larger force to be accelerated equally.
 * Hypotheses:**

The materials used in this experiment include a dynamics cart, masses, track, photogate timer, USB link, Data Studio, super pulley with table clamp, string, mass hanger and masses, and a mass balance.
 * Method and Materials:**

Attached the photogate to the pulley and plug the USB link into the computer. Open Data Studio and select "Digital Input." Remove the displays of the position-time and the acceleration-time graphs. The slope of the velocity-time graph will be used to find the acceleration. Attach one end of the the string to the cart and the other end to the mass manger. Put the string over the pulley with the cart on the track and the mass hanger hanging off. Make sure that the track is level and that the string is parallel to the track.

To test the relationship between acceleration and force, place two 10g and one 5g masses on the cart. Place the cart on the track at the farthest distance that enables the mass hanger to hang without touching anything. Press "Start" on Data Studio and let the cart go. Press "Stop" before the cart reaches the end of the track and make sure the cart does not hit the pulley. Repeat this three times. Find the linear trendline for each trial and record the slopes. Hide the trials to get a clear graph.

To increase the force acting on the system, take the 5g mass and place it on the mass hanger instead. This way, the force is increased but the total mass remains constant. Repeat the previous steps, recording the results of three trials with the new force. Return the 5g mass to the cart and put a 10g mass on the mass hanger. Record the results of three trials. Put the 5g mass on the mass hanger with the 10g mass. Record the results of three trials. Put the 5g mass back on the cart and put both 10g masses on the mass hanger. Record the results of three trials.

To test the relationship between acceleration and mass, place the three 498g and one 501g masses on the cart and a 5g and 10g mass on the mass hanger. Record the slopes from three trials like when the relationship between acceleration and force was being tested. Remove one 498g mass from the cart and do three trials. Remove another 498g mass and do three trials. Remove the last 498g mass, leaving the 501g mass on the cart, and do three trials. Keep the 10g and 5g mass on the mass hanger throughout these trials to keep the force constant.

media type="file" key="Movie on 2011-12-02 at 12.17.mov" width="270" height="270"


 * Observations and Data:**

Mass of cart: 0.498 kg Mass of mass hanger: 0.005 kg

Example Data Studio Graph- Total Force vs. Acceleration, Trial 1:

__Table: Comparing Total Force and Acceleration__

__Table: Comparing Total Mass and Acceleration__

Data Spreadsheet:

Percent Error for B Coefficient:

Net Force Sample Calculation:

Other sample calculations are shown in the analysis.


 * Analysis:**





1) Theoretical acceleration:

Percent error between theoretical and experimental acceleration: <span style="font-family: arial,helvetica,sans-serif;">

2) The slope of the trendline is linear, meaning that there is a constant relationship between the acceleration and net force; that is, as the force increases, so does acceleration. Newton’s Second Law tells us these two properties are directly proportional. The actual slope of the line is derived from the inverse of the total mass of the system. This does make sense, considering the numbers we had and the slope of the graph. If 1.838 is the slope of the graph, then the inverse is 0.544 kg. The total mass of the system is 0.528 kg.



Considering the percent error between the actual and experimental values, the slope of the line, 1.838, makes total sense. The y intercept of the equation is derived from the friction of the system; actually it is the friction over the total mass of the system. This makes sense because the intercept is negative, and friction goes in the opposite direction of the system. Also, this equation makes sense when manipulating the equation, where x is force and y is acceleration: This is derived from the equation:

B ecause the net force is x, it only makes sense that the slope is the inverse of the total mass. Also, the net force is the weight of the hanging mass.

3) This graph is hyperbolic. As the x increases, the y decreases but in an ever-slower rate each time. Assuming the net force is the same, the mass is inversely proportional to acceleration. Since we get the inverse of the mass, the power on the x should be a -1. That makes sense when going back to Newton’s Second Law equation, making mass x and acceleration y:

Therefore, the coefficient in front of the x is the net force. Since we’ve discussed earlier that the net force is the weight of the hanging mass, and that it is the same in this experiment, we can find percent error between the weight of the actual and theoretical weights. The actual weight was 0.01, and the graph tells us it was 0.01161.

Percent Error for A Coefficient:

A 16.1% error is not bad, so this can tell us that the coefficient of the x is the net force.

4) Friction should decrease the acceleration. A bigger force is needed to restore the acceleration. This makes sense, because the theoretical acceleration values we had were significantly higher than the actual. That is because the theoretical ignored friction, and friction decreases acceleration. So let us see how the theoretical value changes when friction is included:

Theoretical Acceleration Calculation (REDO WITH FRICTION)



Yes, friction is a BIG source of error in this experiment. The theoretical value is the exact same number as the actual, showing the massive (no pun intended) effect friction has on the acceleration value.


 * Conclusion:**

Our hypotheses were correct. With a constant mass, the force and acceleration are directly proportional to each other and produce a linear graph. Their ratio does not chance. When force increases, acceleration increases, and vice versa. With a constant force, the product of mass and acceleration does not change (because F=ma), so mass and acceleration are inversely proportional to each other and produce a curved graph. When mass increases, acceleration decreases to keep the force constant. When acceleration increases, mass decreases. This is all proven by our data and the graphs that it produces. As the total force was increased by 0.049 N, the acceleration increased by about 0.09 m/s/s. As the total mass was increased by 0.498 kg, acceleration decreased but by a lesser amount each time.

When comparing force and acceleration, our percent errors ranged from 8.049 to 29.744. They were higher when the force was lower because friction was able to have a larger influence on its motion. When comparing mass and acceleration, our percent errors ranged from 14.469 to 38.363. They were higher when the mass was larger because the heavier cart caused friction to have a larger influence on its motion. Our percent error was 16.1 for net force and 35.4 for the B coefficient. Our percent error for the slope of the a vs. F graph was 1.6. Our results were fairly accurate, but they were most accurate in the later trials when friction had less of an influence.

One source of error could be in the release of the cart. If the cart was accidentally pushed backwards or forwards a little bit, Data Studio used the faulty data points to create a linear trendline that is used to find the experimental acceleration (slope). To fix this, we could have some sort of gate in front of the cart that would open/retract on our command. This way, our hands would not be able to affect the motion of the cart and there would be a smooth start every time. Another source of error could be the swinging of the mass hanger. When the hanger is still, all of the W force acting on it is pulling in the Y direction, which is ideal. If the hanger is swinging as a result of a previous trial, the W has X and Y components, making it so that not all of the force is acting on the system the way we want it to be. To fix this, we could connect the gate mechanism mentioned previously to an apparatus that holds the mass hanger in place and releases it the instant the gate is opened. This would ensure that the hanger will not swing and the whole W force will be utilized.

The concepts illustrated in the lab can be applied anywhere. When driving, we need to apply a larger force and press the gas pedal harder to make the engine turn faster if we want to accelerate faster. If I apply the same force with a car full of people (larger mass), I will not accelerate as fast as I did with only me in the car. More massive objects need larger forces to be accelerated as much.

=Lab: Coefficient of Friction=

Task A: Lauren Task B: Jonathan Task C: Hella

Objectives: Hypotheses: Materials and Methods: media type="file" key="Movie on 2011-12-07 at 11.14.mov" width="300" height="300"
 * To measure the coefficient of static friction between surfaces
 * To measure the coefficient of kinetic friction between surfaces
 * To determine the relationship between the friction force and the normal force.
 * To measure the coefficient of static friction between surfaces, it is necessary to know the maximum tensions of the duration of the pull for each mass, and find the slope of these. It should be assumed that the coefficient should be between 0 and 1, and higher than the kinetic friction coefficient.
 * To measure the coefficient of kinetic friction between surfaces, it is necessary to know the mean tensions of the duration of the pull for each mass, and find the slope of these. It should be between 0 and 1 and lower than the static friction coefficient.
 * As the normal force increases, so does the friction force. This makes sense because if there is more contact between two surfaces, there should be more friction to resist the change in motion. They are also directly proportional.
 * First, mass the friction cart. Then, put the cart on a surface and place a 500-g mass in it (the data will be compared to the mass plus to mass of the bucket, not just the mass itself). Attach this bucket to a 15cm string, which is connected to a force meter, which will measure the tension pull force exerted when moving the cart across the surface, an aluminum track - this is used to make the cart be pulled in a straight line.The track is held down to the table with a clamp. The force meter gets plugged in via USB to a computer so it is possible to create this experiment in Data Studio. When this program is opened, uncheck Force-Push Positive and replace with Force-Pull Positive. This will create the proper tension versus time graph. Then, zero out the tension by pressing the zero button on the meter. Once this is ready, you can start pulling the bucket with the force meter, which will automatically plot the data points on the graph. It should be pulled very slowly and at constant speed, and make sure the string is parallel to the board. When the points are plotted, find the mean tension by highlighting all of the constant speed points. Also find the maximum tension. This whole process should be repeated adding more miscellaneous masses each time.

Sample Graph: Tension Versus Time Data Table: Static Friction Data Table: Kinetic Friction Graph: Static v Kinetic Friction Before we get to the explanation, let us look at these 2 linear equations: From this derivation, we can assume that friction is the y axis, and Normal is on the x-axis. This makes sense, because that is what is on the graph. Now, the friction equation can be written like this, too: This allows us to deduct that the b, or y-intercept is equal to 0, as is in both graphs, and the coefficient of friction is equal to m, or the slope.
 * Analysis of the Graph:**

Free-Body Diagram: Friction Cart

Note: We can assume that that the acceleration on the x and y is equal to 0. That is because the y forces are balanced and there is no motion on the y. Also, though the cart is moving on the x, it is doing so at constant speed, meaning no acceleration. Friction Coefficient of Friction Normal Force Average Tension
 * Sample Calculations:**

Percent Difference – Average Coefficient of Static Friction v Slope Our average coefficient value was 0.142, and the slope of the graph was 0.1366. At a mere 3.47% difference, the results are clearly precise.

Data Table: Class Data Percent Difference – Average Coefficient of Static Friction v Class Average Coefficient of Static Friction

Our average coefficient value was 0.142, and the class average coefficient value was 0.156. The percent difference resulting is 9.28%, which is pretty good. But this is okay because our values for static and kinetic were proportionally lower than the class average, so it must have been due to a different magnitude of push force on the friction cart.

Because the y intercept is zero, the equations of our lines are, y = .1366x and y = .1024x. One can see that this is in slope intercept form and in the same form as the formula f = µ N. This would suggest that our y values on our graph are friction and our x values are normal force. This is proven because this is exactly what our graph showed; y = µx. When looking at this interpretation, it is obvious that µ is the slope, because it is the place of m (slope) in the equation y= mx + b.
 * Discussion Questions:**
 * 1) Why does the slope of the line equal the coefficient of friction? Show this derivation.**

http://www.tribology-abc.com/abc/cof.htm The theoretical coefficient of static friction between our material and the aluminum track is between 0.25 and 0.4. Our results proved to be slightly less than .25 because our average coefficient of static friction was 0.142. Also, the theoretical coefficient of kinetic friction is between 0.1 and 0.3. We achieved a very similar coefficient, .103.
 * 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!**

This lab proves that the variables that affected the magnitude of the force of friction are the coefficient of friction and normal force. This is due to the fact that the formula for the force of friction is f = µN. In the same way, friction itself and normal force are the variables that affect the coefficient of friction because of this formula.
 * 3) What variables affected the magnitude of the force of friction? What variables affected the magnitude of the coefficient of friction?**

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 12px;">During this lab, we ended up with .142 for the coefficient of static friction and .103 for the value of the coefficient of kinetic friction. The source found compares the two by showing that kinetic friction is less than static friction, which supports our results.
 * 4) How does the value of coefficient of kinetic friction compare to the value for the same material’s coefficient of static friction?**

This lab certainly satisfied our objectives, and proved our hypotheses correct. Our first hypothesis stated that to calculate coefficient of static friction, one needs to know the maximum tension, and it should be higher than kinetic friction value. We were able to find maximum tension, and we were right that max tension would yield coefficient of static friction, specifically, 0.1366. Static friction is always higher than kinetic friction. Our second hypothesis said that measuring kinetic friction would be derived from mean tension, and should be lower than static friction. We were able to find our kinetic friction, at 0.1024, and was lower than 0.1366. We were right about this statement. Our last hypothesis said that normal force increases with the friction force. We were correct about this as well. Looking at the graph we made, a constant, increasing line shows the linear, direct relationship between normal and friction forces. Friction is equal to the coefficient of friction times the normal force. It does make sense that the more contact there is between surfaces and more rubbing, then there should be more resistance to motion. Plus, we know we are right because of our low percent differences.
 * Conclusion:**

The percent differences in our lab were 3.47% and 9.28%, which is very good and under the 10% mark. However, there still could have been sources of error. One error was when the string was being pulled along the horizontal. Determining this was just our perception; while our angle could have been close to 0, there still probably was an angle of the tension. Which means that there are x and y component to deal which, and this could completely throw off the data if the angle is off 0. Another error was also upon pulling the cart, because it was probably accelerating. We tried to move it as much as constant speed as possible, but it is impossible to make it perfectly constant speed. The fact that there was acceleration could completely change data; ideally it should be 0.

There are ways to fix these errors, however. As for the first error, one could tie the string to a pole, that is measured out vertically from the track so it stays parallel. Pulling this pole at constant speed would eliminate the need for component calculations. As for the second error, it is possible to use the CMVs we have used early in the year to move the friction cart at constant speed, and attach the string to it.

There are several real-life applications of this lab, such as in skiing. It is important to know the coefficient of kinetic friction when moving down the track with different skis with different waxes, generating different coefficients of friction. It is important to know which ski/wax combo fits with a certain track the best.