Group1_2_ch4

For **Group 1: Sammy Caspert, John Chiavelli, Andrew Chung, Jenna Malley** toc =**__ Gravity and the Laws of Motion __**= Task A: Sammy Caspert Task B: Jenna Malley Task C: John Chiavelli Task D: Andrew Chung

__**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 direction in the lab.
 * 4) Determine if mass has an effect on the acceleration of an object.

__**Hypothesis:**__
 * 1) The acceleration of gravity is 9.8 m/s^2 as we proved in the free-fall lab that we did earlier in the year.
 * 2) As the incline angle increases, so does the acceleration of an object. With a horizontal angle, an object has an acceleration of 0 while an object in free fall has an acceleration of 9.8. In between that incline angle range as the angle approaches 90 degrees from 0 degrees, the acceleration approaches 9.8 from 0.
 * 3) The mass and acceleration of an object have in inverse relationship as proven by the equation "F=mg". When the force is constant, the mass of an object increases as the acceleration of it decreases; visa-versa.

__**Materials:**__
 * Metal ball
 * Electronic balance
 * Ramp
 * Stopwatch
 * Meter Stick

__**Methods:**__ First we took the mass of the metal ball and found it to be 0.00898 grams. Then we went to the ramp to set the top of it where the ball will start its roll to .15 m. Since the ramp is 3-dimensional, we meausred the bottom side of it to the .15 meters. We started each ball roll at the top, which according to the measuring device on the ramp was 0.12 meters. Then we started our experiment. Three seperate times, we placed the ball at the top of the ramp and recorded how long it took to get to the bottom. After we did it three times for the height of .15 meters, we redid the process three times for an initial height of 0.20 meters, and then three times for an inital height of 0.30 meters. Now with time, distance, and height, we were able to find sin(theta), which is equal to "height/distance". In addition to that, we found the acceleration of each trial, and then witihn each height, we found the average acceleration of the three trials.

Below is a video of the ball rolling down the ramp:

media type="file" key="Gravity and Laws of Motion.mov" width="240" height="240"

__ **Data Table:** __ __link to document: __

__**Calculations:** __   __**Graph:**__ link to document:
 * Final Velocity Example Calculation: **
 * Acceleration Example Calculation: **

__**Analysis:**__ As per the graph, our experimental value of the acceleration of gravity is 8.7899 m/s2. This was derived from the equation y=8.7899x, which corresponds to our graph of acceleration vs. sin theta. The theoretical value of the acceleration of gravity is 9.8 m/s 2 . If the y-intercept had not been set to 0, the equation would be: y=9.8849x-0.2141. The significance of the y-intercept would be in the event of friction.



 By evaluating the class data, it can be proposed that mass does not have an effect on the acceleration of gravity. In addition, the data reflects the idea that mass does not affect acceleration.
 * Class Data: **





<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;"> <span style="font-family: 'Times New Roman',Times,serif; font-size: 14px;">The weight of the force is causing it to roll down the ramp. The entire force of weight is responsible. The x-component of the weight force vector enables us to use Newton's Second Law of Motion to calculate acceleration. The y-component of the weight force vector is balanced by the normal force. When compared to our calculated average incline for the .150m trial, the //F=//m//a// acceleration value, they are relatively close, but not close to being exact. <span style="color: #000080; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">__**Discussion Questions:**__ <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**1. Is the velocity for each ramp angle constant? How do you know?** <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">The velocity for each ramp angle is not constant. This is because acceleration and time differs as the angle changes.
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Free-Body Diagram Depicting Motion Above **

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**2. Is the acceleration for each ramp angle constant? How do you know?** <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">No, the acceleration value for each ramp is not constant. We know this because the value changes as the angle changes.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**3. What is another way that we could have found the acceleration of the ball down the ramp?** <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">A second way we could have found the acceleration of the ball would have been to use the formula for acceleration. Using the formula:, we could have determined the same value for the acceleration.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**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="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Galileo was able to time the position or distance covered by the ball on an incline (vertical free fall would have been too fast), and therefore could translate his time ratios and distances into a kinematic equation. He is known to have used the time-squared law of uniformly accelerated objects to determine the acceleration of gravity. He could have also used the kinematics equation we employed above:, which would have yielded a relatively similar answer. Understanding that the largest possible angle was ninety degrees, and that its sine value is 1, he was probably able to determine that the value of gravitational acceleration was around 9.8 m/s<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%; vertical-align: super;">2.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**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?** <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">No, the mass of an object does not affect its rate of acceleration down the ramp. Yes, as an object's mass in free fall will not affect its rate of acceleration. This is because acceleration due to gravity is entirely independent of mass.

<span style="color: #000080; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">__**Conclusion:**__

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Our initial hypothesis stated that the acceleration due to gravity would be 9.8 m/s^2. We calculated this value through the use of various labs throughout the year and found it to be the acceleration due to gravity for an object in free fall. Thus, using this experiment, we hoped to achieve similar results to the labs already done. We similarly believed that the angle of the ramp had an effect on the acceleration of the object. We also believed that mass and acceleration had an inverse relationship, as shown by the equation force = mass x acceleration. We ran the experiment three times at three different heights and angles and recorded the values. Once graphed, these values showed that our acceleration due to gravity was 8.79 m/s^2, a value relatively close to 9.8 m/s^2. Furthermore, the data also shows that when the angle of an incline increases, the acceleration approaches the acceleration due to gravity. This makes sense, because as the angle reaches 90 degrees the incline ceases to be an incline and becomes vertical. Our initial hypothetical belief that the acceleration due to gravity is 9.8 m/s^2 rang true once again. Our second belief that the angle of the incline caused the acceleration to either increase or decrease also turned out to be true. We found this out through the various experiments we ran involving moving the incline to different heights and recording the time it took the ball to reach the end of the ramp. For instance, at the angle (sin theta) of .125 we found the average acceleration to be 1.039. When we increased the angle to .167 the average acceleration became 1.407. When the angle was increased once more to .250 the average acceleration became 2.266. The data that the class collected as a whole has led our group to believe that mass indeed does not play as big a role in acceleration down an incline as we would have thought. This is surprising because it challenges and disproves our initial belief that as the mass of the ball increases, the acceleration decreases.

After comparing our theoretical and actual calculations, we achieved a percent error of 10.31%. This value is due to the various sources of error present in this lab. For example, friction exists between the ball and the incline. This most likely resulted in the ball not falling as quickly as it should have, which would have skewed acceleration and time values. Furthermore, it is very possibly that the person dropping the ball could have added additional unwanted force that could decrease the time the ball fell down the incline. Furthermore, the timing of the ball could be inaccurate due to mechanical failures on the stop watch that would prevent an accurate reading. If we were to re-do this experiment to make it less error-prone, there would be several changes that we would make. First, we would see if we could purchase an incline that has very little to no friction. This would allow for an accurate reading. We would also use a computerized device that could stop a stopwatch the instant that the ball reached the end of the incline. This would remove errors on the part of the stopwatch and the human administering the stopwatch. Finally, we would decrease the width of the incline so that the ball didn't roll from side to side which could increase the time it takes for the ball to reach the end of the ramp.

=Newton's Second Law=

Task A: Andrew Chung Task B: Sammy Caspert Task C: Jenna Malley Task D: John Chiavelli


 * Objectives**


 * 1) To find the relationship between acceleration and net force
 * 2) To find the relationship between acceleration and mass


 * Hypothesis**


 * 1) The graph of acceleration versus net force will be linear. We believe this because acceleration is caused by a difference in the net force of an object. Thus, as the acceleration increases the net force will increase.
 * 2) The graph of acceleration versus mass will be a straight horizontal line. This is because masses of objects fall (accelerate downward) at the same rate.


 * Materials**
 * 1) Ramp
 * 2) Dynamics Cart
 * 3) Free Weight
 * 4) String
 * 5) Photogate timer
 * 6) PasPort


 * Procedure**


 * 1) Place the ramp on the table.
 * 2) Attach the photogate timer directly in front of the ramp.
 * 3) Place the dynamics cart on the ramp.
 * 4) Place the free weights on the ramp.
 * 5) Attach string to the dynamics cart that goes over the photogate timer and is attached to a free weight holder.
 * 6) Let the cart fall and record the data with no weight on the holder.
 * 7) Now, add a 5g weight to the holder, let it fall, and record the data.
 * 8) Do step 7 three times.
 * 9) Remove the 5g weight and put it back in the cart.
 * 10) Place a 10g weight from the cart on the holder, let it fall, and record the data.
 * 11) Do step 10 three times.
 * 12) Add the 5g weight from the cart to the freeweight holder, let it fall, and record the data. Make sure you keep the 10g weight from step 9 on there.
 * 13) Do step 12 three times.
 * 14) Remove the 5g weight from the holder and add the 10g weight to the holder, let it fall, and record the data. Make sure you keep the 10g weight from step 13 on there.
 * 15) Do step 14 three times.
 * 16) Add the 5g weight from the cart to the holder, let it fall, and record the data. Make sure you keep the weights from step 15 on there.
 * 17) Do step 16 three times.
 * 18) Add one 250g weight to the cart while keeping the rest of the weights on the holder. This will be for the net force calculations.
 * 19) Let the weight fall and record the data.
 * 20) Complete step 19 three times.
 * 21) Add another 250g weight to the cart while keeping the rest of the weights on the holder. This will be for the net force calculations.
 * 22) Let the weight fall and record the data.
 * 23) Complete step 22 three times.
 * 24) Now remove one 250g weight, add a 500g weight to the cart. Let it fall and record the data.
 * 25) Complete step 24 three times.
 * 26) Add another 250g weight to the cart. Let it fall and record the data.
 * 27) Complete step 26 three times.

media type="file" key="Movie on 2011-11-30 at 08.37.mov" width="300" height="300"
 * Video**

__Net Force vs. Acceleration__ __Mass vs. Acceleration__
 * Calculations:**

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">**Average Acceleration Calculation** <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">**Net Force Calculation**

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">**Percent Error Calculation for Linear** <span style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">**Percent Error Calculation for Non-Linear** <span style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">**What should the slope be for a linear line? Calculation** <span style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">**Discussion Questions and Analysis**


 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">Explain your graphs:
 * 2) <span style="font-family: Arial,Helvetica,sans-serif;">If linear: What is the slope of the trendline? To what actual observed value does the slope correspond? How does it compare to this actual observed value (find the percent error between the two)? Show why the slop should be equal to this quantity. What is the meaning of the y-intercept value?
 * 3) <span style="font-family: Arial,Helvetica,sans-serif;">The graph of acceleration vs net force is linear. The slope of the trendline of this graph is 1.1318. This calculated value comes from the observed/measured value of the inverse of the hanging weight. We found our hanging weight to be .531 kg, and the inverse of this is 1.88.
 * 4) <span style="font-family: Arial,Helvetica,sans-serif;">Our percent error calculation shows that we have about a 40% error for this value . From this, we can assume that our numbers were slightly off, most likely due to errors in measurements.
 * 5) <span style="font-family: Arial,Helvetica,sans-serif;">The slope should be equal to this quantity because of the calculations. We demonstrated this in the calculation titled "What should the slope be for a linear line?". This also shows what the y-intercept should be equal to, which is [[image:f_over_m_neg.png width="35" height="31"]], or negative friction over the total mass.
 * 6) <span style="font-family: Arial,Helvetica,sans-serif;">If non-linear: What is the power on the x? What should it be? What is the coefficient in front of the x? To what actual observed value does the coefficient correspond? Find the percent error between the two. Show why this value should be equal to this quantity.
 * 7) The graph of mass vs acceleration was non-linear. The power on the x is -2.011, however, it should b<span style="font-family: Arial,Helvetica,sans-serif;">e -1. The coefficient in the equation of this graph corresponds to the net force, which in this case is the weight of the hanging mass.
 * 8) <span style="font-family: Arial,Helvetica,sans-serif;">The percent error of this is about 70%. This fairly large percent error can be contributed to many sources, including errors in measuring and miscommunication.
 * 9) <span style="font-family: Arial,Helvetica,sans-serif;">This value should be equal to this quantity because of this equation: [[image:where_a_is_equal_to.png width="222" height="44"]].
 * 10) <span style="font-family: Arial,Helvetica,sans-serif;">What would friction do to your acceleration? Would you need a bigger or smaller force to create the same acceleration? Was your slope too big or too small? Can friction be a source of error in this experiment? Redo the calculation of acceleration WITH friction to show its effect.
 * 11) <span style="font-family: Arial,Helvetica,sans-serif;">Friction would lower the acceleration because it would go against the tension force of the string. You would need a bigger force to create the same acceleration due to this (unless you had a smaller mass). Friction could be a source of error in this lab because it's impossible to completely eliminate it, so it may slow down the cart a little bit. Our slope was too small, which is why we had a percent error, and this is most likely because of friction.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;">**Conclusion**

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">As far as results are concerned, our first hypothesis was correct, while the second was not. We successfully predicted that the graph of average acceleration v. net force would be linear, however incorrectly hypothesized that the graph of average acceleration v. total mass would also be linear. In fact, the graph of average acceleration v. total mass depicts a downward exponentially curved non-linear function. Our first graph of acceleration v. net force proved that as net force increases, so does acceleration. The second graph of acceleration v. total mass shows that as the mass increases, acceleration decreases exponentially. In terms of error, our percent error concerning the slope value of the average acceleration v. net force graph was 39.89%. This figure is pretty good considering the varying sources of error throughout the laboratory. The percent error for the graph of average acceleration v. total mass was 70%. This represents a significant of error, no doubt due to the potential for error consistently found throughout the lab. Throughout the laboratory, there were several sources of potential error. A primary source of error would be if the tension string was not completely parallel to the dynamics cart track. If the cable was not always taut, the acceleration values recorded could be slightly off. This could naturally occur after myriad test runs, yet should be evaluated before each trial in the future. Another problem involving the cable would be if it was not level with the height of the cart. To prevent this from interfering with the results, we were successful in adjusting the Photogate timer, yet a standard level could be an insightful tool to ensure better results. Additionally, if the table and cart track was not completely level, it would disrupt the motion, and ultimately acceleration values of the experiment. We had taken advantage of the knob on the track enabling us to create a parallel relationship between the track and table, yet the judgement solely based on eyesight is not always correct. To address this possible cause of error, we change the lab by instituting a procedure step that would require a contractor's level be used in order to be more accurate. Although not relevant in all areas of the workforce, understanding the relationship between system mass, acceleration, and net force is critical to the success of a machinery taken for granted like an elevator or a construction crane. The engineers and craftsmen who design such contraptions must take into account the net force of an full elevator of people or of a destructive wrecking ball, as well as its impact on acceleration of the mass. The "drop and pull" dynamic is a fairly common portrayal and framework that is applied to various areas of everyday life.

=__<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Lab: Coefficient of Friction __=

Task A: John Chiavelli Task B: Andrew Chung Task C: Sammy Caspert Task D: Jenna Malley

__**<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">Objectives: **__ <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">- To measure the coefficient of static friction between surfaces <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">- To measure the coefficient of kinetic friction between surfaces <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">- To determine the relationship between the friction force and the normal force

__**<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">Hypothesis: **__ <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">-The coefficient of friction for both static and kinetic friction will be between 0 and 1. As the mass increases, so will the coefficient of friction because of their direct relation to each other.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">- The relationship between frictional and normal force will be directly proportional. This is because as normal force increase, so does frictional force (//f//=//u//N).

__**<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">Materials: **__ <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">The materials and equipment we used were a Pasco Force Meter, USB link, "friction" dynamic cart, miscellaneous masses, string, an aluminum track, and a clamp.

__**<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">Methods: **__<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;"> After recording the mass of the cart, and placing the mass inside of it, we attached the force meter and cart with mass with string. After each trial, we recorded the maximum tension and the mean value for tension and constant speed. We then plugged these values into our various data tables and then transferred the data to the Excel spreadsheet to create the graphs. We then were able portray the relationship between frictional and normal force. Also, the slope enabled us to determine the coefficient value of static and kinetic friction.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">

<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">media type="file" key="Movie on 2011-12-07 at 08.35.mov" width="300" height="300"

__**<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">Procedure: **__ <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">1. Mass the "friction" dynamics cart <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">2. Place the cart on the surface and put a 500g mass in it <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">3. Attach a 15cm string to one end of the cart and the other to the Pasco Force Meter <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">4. Insert Force Meter into computer, choose DataStudio, and click "New Experiment" <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">5. Go to "SETUP", check "Force-Pull Positive", and uncheck "Force-Push Positive" <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">6. On graph display, click y-axis label in order to change the label to "Force-Pull Positive" <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">7. Leaving the string slack, press the "Zero" button on the sensor <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">8. Press "Start" on DataStudio, and gently pull the block with the force sensor (with slow constant speed, maintaining a parallel string to surface) <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">9. As per the graph, highlight the straight line section and click the net force symbol, followed by selecting the MEAN as the value for tension and constant speed <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">10. Highlight the maximum point and record the value as the maximum tension <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">11. Repeat trial five times with same mass <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">12. Repeat steps 8-12 adding more mass in large increments

__**<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">Data Tables: **__

__**<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">Graph: **__

__**<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">Analysis: **__
 * || StaticFriction (Max T) || KineticFriction (Mean T) ||
 * My Group || 0.151 || 0.1023 ||
 * Class Average || 0.1674 || 0.1026 ||






 * Free Body Diagram of the Cart**

__**<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">Discussion Questions: **__

**<span style="font-family: 'Times New Roman',Times,serif;">1. Why does the slope of the line equal the coefficient of friction? Show this derivation. **

**<span style="font-family: 'Times New Roman',Times,serif;">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! ** As for static friction, the coefficient of friction is supposed to be between 0.25 and 0.4. However, are coefficient of friction was lower at 0.151. For kinetic friction, the coefficient of friction is supposed to be between 0.1 and 0.3, and our coefficient of 0.123 happened to fall in that range. Our source for finding the theoretical coefficent of friction between the cart and track was http://www.tribology-abc.com/abc/cof.htm.

**<span style="font-family: 'Times New Roman',Times,serif;">3. What variables affected the magnitude of the force of friction? What variables affected the magnitude of the coefficient of friction? ** Being that friction is equal to weight, which is equal to mass*gravity, the magnitude of the force of friction is affected with a positive correlation by the mass inside the cart. It is also affected by the coefficient of friction. What affected the coefficient friction was again the mass of the cart in addition to the magnitude of the friction.

**<span style="font-family: 'Times New Roman',Times,serif;">4. How does the value of coefficient of kinetic friction compare to the value for the same material’s coefficient of static friction? ** <span style="font-family: 'Times New Roman',Times,serif; font-size: medium;">In this lab, our group got a 0.1023 for the value of coefficient of kinetic friction. For the value of coefficient of static friction we got 0.151. According to the website and following the trend of the class' results, our value for kinetic friction was supposed to be less than static friction, which is what we got.

__**<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">Conclusion: **__

This experiment successfully proved our hypothesis, which stated that the coefficient of friction for both static and kinetic friction will be between 0 and 1. Additionally, we were also able to show that as the mass increases, so will the coefficient of friction because of their direct relation to each other. It's because of this that the relationship between frictional and normal force ended up being directly proportional, because of the equation that is used to find friction.

In this situation we were able to find out that tension force is equal to friction force, so we knew that tension force would be equal to the coefficient of friction times normal force. This is why in our equations, the coefficient for static friction was .151 and the coefficient for kinetic friction was .1023. These values help to support our hypothesis because they are above zero but below one.

The fairly low percent error (.29%) that we calculated for kinetic friction shows that our results were fairly accurate in terms of what the class got for kinetic friction. However, for static friction we got a percent error of nearly 10%. Although this is a fairly low number, it still shows that some errors were made. Most of the errors were probably due to the impossibility of pulling the spring scale in a perfectly straight, horizontal line. Additionally, minor accelerations (decreasing and increasing when we were pulling) could have thrown of our data.

This situation can be applied to real life, for instance, when you need to measure the force that something can hold or pull and how friction will effect it. For example, if a truck was pulling a wagon. You would need to know how friction was going to effect the wagon you were pulling to be able to determine the necessary tension. Knowing the friction coefficient between the wagon's tires and the road could help you determine this.