SpencerRachelDylanSammy

toc = = = = = ** Lab: Acceleration Down an Incline ** = Rachel, Sammy, Spencer, Dylan Period 2 Due date: 12/21/10


 * Objective: **To find how acceleration of an object down an incline depends on the angle of the incline.

**Hypothesis**: As the angle of incline gets larger or smaller, the acceleration will get larger or smaller respectively.

**(Rationale):** Because of the equation,, we can see if gravity, mass, and m stay constant, theta and acceleration have a direct relationship. As theta increases or decreases, acceleration will do the same.

An object placed on an incline will often down. The rate the object does this is dependent upon how much of an incline the surface is at. This can be measured using angles. The larger the angle usually the faster the object will slide down the inclined surface and the same goes for the smaller angle. This is due to an unbalanced force., according to Newton’s Second Law. We tested this law in our lab to figure out the relationship between acceleration of an object down an incline and the angle of the incline.
 * Introduction:**

Data:

13 Degrees- 15.5 Degrees- 17 Degrees- 18 Degrees- 20 Degrees- 22 Degrees

Part A Data Table


 * Band Thickness = 0.005 m |||| Mass of block/fence = 573 g ||  ||   ||   ||   ||   ||   ||   ||   ||   ||
 * Angle (Degrees) || Height (m) || Acceleration 1 (m/s^2) || Acceleration 2 (m/s^2) || Acceleration 3 (m/s^2) || Acceleration 4 (m/s^2) || Acceleration Average (m/s^2) || Angle (Radians) || Sin(Angle) || Mu || Cos(Angle) || g || Acceleration ||
 * 13 || 0.314 || 0.066 || 0.053 || 0.042 || 0.045 || 0.103 || 0.227 || 0.225 || 0.193 || 0.974 || 9.800 || 0.358 ||
 * 15.5 || 0.366 || 0.244 || 0.245 || 0.223 || 0.335 || 0.524 || 0.271 || 0.267 || 0.193 || 0.964 || 9.800 || 0.793 ||
 * 17 || 0.398 || 0.368 || 0.336 || 0.265 || 0.335 || 0.652 || 0.297 || 0.292 || 0.193 || 0.956 || 9.800 || 1.053 ||
 * 18 || 0.423 || 0.474 || 0.436 || 0.538 || 0.425 || 0.937 || 0.314 || 0.309 || 0.193 || 0.951 || 9.800 || 1.226 ||
 * 20 || 0.456 || 0.536 || 0.497 || 0.530 || 0.674 || 1.119 || 0.349 || 0.342 || 0.193 || 0.940 || 9.800 || 1.571 ||
 * 22 || 0.505 || 0.859 || 0.775 || 0.830 || 0.772 || 1.618 || 0.384 || 0.375 || 0.193 || 0.927 || 9.800 || 1.914 ||

Class Data


 * Name || Slope (m/s^2) || y-intercept || R^2 || Slope w/ y-int = 0 ||
 * Rachel || 9.738 || -2.113 || 0.980 || 2.912 ||
 * Evan || 10.476 || -1.854 || 0.998 || 4.030 ||
 * Nicole || 9.039 || -1.959 || 0.978 || 3.720 ||
 * Justin || 8.724 || -1.744 || 0.978 || 2.310 ||
 * Andrew || 13.406 || -3.673 || 0.984 || 3.380 ||
 * Ryan || 11.223 || -2.529 || 0.970 || 2.630 ||
 * Emily || 10.089 || -2.054 || 0.999 || 2.230 ||
 * Jessica || 9.716 || -1.874 || 0.982 || 3.680 ||
 * Jae || 10.393 || -2.681 || 0.989 || 4.360 ||
 * Deanna || 9.870 || -2.264 || 0.989 || 3.010 ||
 * Chris || 10.089 || -2.052 || 0.989 || 4.300 ||
 * Eric || 10.038 || -2.340 || 0.995 || 4.210 ||
 * Sam || 12.299 || -3.063 || 0.994 || 4.150 ||
 * Average || 10.392 || -2.323 || 0.986 || 3.456 ||


 * Derivations:**

Theoretical Acceleration for Part A Theoretical Acceleration for Part B




 * Sample Calculations:**


 * Discussion Questions:**

1.) The slope of this graph is the gravitational force on the system. Based on the equation derived in the pre-lab; a=gsin(pheta)-µgcos(pheta), when a=y, g=slope, and sin(pheta)=x, µgcos(pheta)=y-intercept.

2.) If the mass of the cart was doubled the velocity should increase so the acceleration should remain constant but at a higher value. Weight and velocity are directly related so as one increases, the other one does too

3.) There is no way that friction is the reason there was this difference because friction doesn't effect anything other than forces on the x axis plane.

Percent Error Calculation Between Slope of Graph and Gearth:

Percent Difference Calculation: In conclusion, our actual results supported our original goal. We figured in our hypothesis and seen in calculations above, that the theoretical slope would be 9.8. Although our 9.7376 accounts for a .64% error from that original goal, our lab results account for friction and other problems that could have gone wrong. Something that could have gone wrong in this lab was definitely human error. The cart didn't always move straight, and this could have been due to the way we set up the cart, ramp, or tape that was on the cart in our trials. Also, there will always be human error when measuring. When measuring the height of the ramp and the angles, because these tools are hand held and different for every group, error could have come from that. Our sensor proved to be not working properly for a lot of this experiment. When we finally fixed it, the numbers began to become like more we expected. If the sensor was working properly the entire time, our results may have been closer to 9.8. Although we had a percent error, we conclude that the lab supported our introduction and hypothesis and we calculated accurate results.
 * CONCLUSION:**

= Lab: Coefficient of Friction =

[[image:RACHELSAMMYSPENCERDYLANGRAPHSSSS.png width="800" height="527"]]
Free Body Diagram

Since the force of tension is our y-value and the weight (mass times gravity) is our x-value, the coefficient of the static friction is the slope of the line weight v tension. In our experiment, our coefficient of static friction is 0.205. For kinetic fiction, it is the exact same thing. Since it is going at a constant speed, acceleration is 0 for both the x and y formulas therefore leading to the same formula as we used for station friction. Our coefficient of kinetic friction was 0.1934. The coefficient for static friction will always be greater than that of kinetic friction because for static, we use the maximum and for kinetic all of the points are taken into consideration and averaged out, therefore making it a lower number (more shallow slope).

__Data__



Percent Error
Static Friction Kinetic Friction

4. How does the value of coefficient of kinetic friction compare to the value for the same material’s coefficient of static friction? The value of coefficient of kinetic friction is lower than the value of coefficient of static friction for the same material. This is due to the fact that when an object has kinetic friction (already in motion) their is less of a force keeping the block on the track. When an object is not moving at all, it will take more of a force in order for it to start moving.

5. Did putting the track on an incline significantly change the coefficient of friction? Why or why not? Putting the track on an incline did change the coefficient of friction. It was slower than when the track wasn't on an incline. This is because the force of gravity on the block of wood was more significant when it was on an incline. The equation for incline friction uses mg cosine and theta for the y axis and theta sine mg for the x axis.

= **Lab: Atwoods Machine** = **Due Date:** **Objective:** What is the relationship between net force and acceleration **Introduction:** **Materials:** Atwood's machine, clamp,rod,stand,2 mass hangers, masses, photogate, string

**Procedure:** =25 Grams:= =20 Grams:= =15 Grams:= =5 Grams:= file:///Users/groovygirlsiw/Desktop/physics%20excel.jpg =0 Grams:= ==
 * 1) Set up apparatus, and excel worksheet
 * 2) Put 355g on each side (Mass A and Mass B), and 25 g on one side. (Mass B) This makes total mass 735g
 * 3) Do 3 trials. Record data in excel sheet.
 * 4) Take 5g off one side (Mass B) and add it to the other mass (Mass A).
 * 5)  Do 3 trials . Record data in excel sheet.
 * 6) Take 5g off one side (Mass B) and add it to the other mass (Mass A).
 * 7) Do 3 trials. Record data in excel sheet.
 * 8) Take 5g off one side (Mass B) and add it to the other mass (Mass A).
 * 9) Do 3 trials. Record data in excel sheet.
 * 10) Take 5g off one side (Mass B) and add it to the other mass (Mass A).
 * 11) Do 3 trials. Record data in excel sheet.
 * 12) Take 5g off one side (Mass B) and add it to the other mass (Mass A).
 * 13) Do 3 trials. Record data in excel sheet.

= = In this lab, we determined the relationship between force and acceleration in order to prove Newton's second law. Newton's second law states that Force = mass (times) acceleration. The hypothesis says that according to Newton's Second Law, if the force is changed and the total mass is kept the same, then the acceleration should change proportionately according to the equation F=ma. The graph we generate should be linear. As the difference in the masses increases, the acceleration increases as well. This is due to their inverse relationship. When reconfiguring the equation we can also find that force and acceleration is directly proportional. Using an Atwood machine, we proved Newton's second law to be true. After conducting the experiment, our hypothesis was proved correct because force and acceleration increased and mass stayed the same.Our graph also proved our hypothesis to be true. The line is a linear line, with a positive slope. It shows that when the y value (slope) increases, the x value (acceleration) increases too. On the graph, there is an R^2 value is extremely close to 1, which shows that the data points fit the trend of the line very well.
 * Graphs:**
 * Conclusion:**

1. Explain your graph(s) thoroughly! a. If linear: What is the slope of the trendline? To what actual observed value does the slope correspond? How does it compare to this actual observed value (find the percent error between the two)? Show why the slope should be equal to this quantity. What is the meaning of the y-intercept value? b. 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.
 * Follow up questions:**

2. 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.  Friction would cause the acceleration to decrease. You would need a bigger force to create the same acceleration you want or are testing. The slope of the graphs was too small because on a velocity time graph acceleration is the slope, and since the pulley is not frictionless it decreases the acceleration (slope). Friction can be one source of error in this experiment because our calculations does not account for the friction.

3. Discuss the precision of your data. Because our R^2 value is very close to 1, our data is very close to accurate. This is expected because all of the masses were known and the mass of the pulley was extremely small. Also, the data studio which calculated the acceleration works perfectly.

4. The real pulley and mass arrangement is not as simple as we assumed. In fact the pulley is not massless and frictionless means that it does require a net “torque” (a turning force) to make it rotate – this is supplied by the tension in the string. The rotational inertia of the pulley then adds an equivalent mass to the total mass being accelerated, where the equivalent mass for the pulley is approximately equal to ½ of the mass of the pulley. If the mass of each pulley is 5.6 g, could the pulley mass account for a significant potion of your error in the experiment? By adding the mass of the pulley to the total mass it will decrease the acceleration a little bit. Because we used such heavy masses, half of 5.6 is 2.8 grams, which will not effect our acceleration so much but will decrease it a little. **WITH PULLEY:**

**WITHOUT PULLEY:**

= = =**Lab: Newton's Second Law**= acceleration and net force?
 * Due Date:** 12.01.10
 * Objective:** What is the relationship between system mass,

Indroduction: In this lab we are trying to find and prove the relationship between system mass, acceleration and net force. We hypothesize that the relationship between net force and mass/acceleration are direct. This data we collect will therefore show us a linear graph. We also hypothesize that the relationship between acceleration and mass will be indirect. Once this data is collected, we will most likely end up with a power curve.

Materials: dynamics cart, masses, track, photogate timer, data studio, super pulley with clamp, base and support rod, string, mass hanger and mass set, wooden or metal stoping block, mass balance, level


 * Procedure :**
 * 1) Set up track with pully, dynamic carts, masses, and data studio
 * 2) Find the mass of the cart 0.494 kg
 * 3) Tie a 5g mass to the end of the string, and put 25g on the cart.
 * 4) Try the first trial to find the acceleration of the cart. (Do three trials)
 * 5) Take 5g off the cart and add it to the end of the string.
 * 6) Try second mass (Do three trials)
 * 7) Take 5g off the cart and add it to the end of the string.
 * 8) Try third mass (Do three trials)
 * 9) Take 5g off the cart and add it to the end of the string.
 * 10) Try fourth mass (Do three trials)
 * 11) Take 5g off the cart and add it to the end of the string.
 * 12) Try fifth mass (Do three trials)
 * 13) Take 5g off the cart and add it to the end of the string.
 * 14) Try sixth mass (Do three trials)
 * 15) Record data and compare it to calculations of actual acceleration.
 * 16) Set up pully and tie 20g to the end of the string, keeping that the constant mass. Put 1 kg(1000g) on the cart. Try first mass. Do three trials
 * 17) Take 200g off the cart. Try second mass (Do three trials)
 * 18) Take 200g off the cart. Try third mass. (Do three trials)
 * 19) Take 200g off the cart. Try fourth mass. (Do three trials)
 * 20) Take 200g off the cart. Try fifth mass. (Do three trials)
 * 21) Take 200g off the cart. Try sixth mass. (Do three trials)

We found the relationship between the acceleration of the cart and the force by keeping the total mass constant but changing the mass of the pully and therefore the cart.


 * Mass Pully (kg) || Mass Cart (kg) || Mass Total (kg) || Gravity (m/s^2) || Force (N) || Accel Trial 1 (m/s^2) || Accel Trial 2 (m/s^2) || Accel Trial 3 (m/s^2) || Accel (m/s^2) || Calculated Accel (m/s^2) ||
 * 0.005 || 0.519 || 0.524 || 9.8 || 0.049 || 0 || 0 || 0 || 0 || 0.09351145 ||
 * 0.01 || 0.514 || 0.524 || 9.8 || 0.098 || 0.0748 || 0.07 || 0.07 || 0.0716 || 0.187022901 ||
 * 0.015 || 0.509 || 0.524 || 9.8 || 0.147 || 0.15 || 0.2 || 0.17 || 0.173333333 || 0.280534351 ||
 * 0.02 || 0.504 || 0.524 || 9.8 || 0.196 || 0.22 || 0.22 || 0.22 || 0.22 || 0.374045802 ||
 * 0.025 || 0.499 || 0.524 || 9.8 || 0.245 || 0.33 || 0.33 || 0.33 || 0.33 || 0.467557252 ||
 * 0.03 || 0.494 || 0.524 || 9.8 || 0.294 || 0.41 || 0.45 || 0.4 || 0.42 || 0.561068702 ||

We found the relationship between the total mass and the acceleration of the cart by keeping the mass of the pully and therefore the force constant while changing the mass of the cart.


 * Mass Pully (kg) || Mass Cart (kg) || Mass Total (kg) || Gravity (m/s^2) || Force (N) || Accel Trial 1 (m/s^2) || Accel Trial 2 (m/s^2) || Accel Trial 3 (m/s^2) || Accel (m/s^2) || Calculated Accel (m/s^2) ||
 * 0.02 || 1.494 || 1.514 || 9.8 || 0.196 || 0.04 || 0.04 || 0.03 || 0.036666667 || 0.129458388 ||
 * 0.02 || 1.294 || 1.314 || 9.8 || 0.196 || 0.15 || 0.15 || 0.15 || 0.15 || 0.149162861 ||
 * 0.02 || 1.094 || 1.114 || 9.8 || 0.196 || 0.17 || 0.19 || 0.13 || 0.163333333 || 0.175942549 ||
 * 0.02 || 0.894 || 0.914 || 9.8 || 0.196 || 0.17 || 0.18 || 0.16 || 0.17 || 0.214442013 ||
 * 0.02 || 0.694 || 0.714 || 9.8 || 0.196 || 0.23 || 0.25 || 0.22 || 0.233333333 || 0.274509804 ||
 * 0.02 || 0.494 || 0.514 || 9.8 || 0.196 || 0.34 || 0.35 || 0.34 || 0.343333333 || 0.381322957 ||

The graph of acceleration versus fore was a linear fit model. The slope of the best fit line is the total mass of the objects used. Our trend line had a slope of 0.5827 (experimental value). However, our actual total mass was 0.524 (actual value). Our percent error was -10.07%. The y-intercept of 0.0535 is the value of the friction that played a factor in our experiment.

The graph of mass versus acceleration was a power fit model. The power on our x is -1.5874. It should be -1 that way it makes the x become 1/x. The coefficient in front of the x is the force of the weight hanging. With the F multiplied by the 1/x, it becomes F/x = a which is part of Newton’s second law. We got the F in our graph to be 0.1403 (experimental value) when the actual force was 0.196 (actual value). The percent error was 39.7%.


 * Conclusion:**
 * Our purpose in doing this lab was to prove Newton's Second Law which states that Force = Mass (times) Acceleration. The data we collected proves this with the exception of a small margin of human error. When we increased mass, acceleration decreased within the correct proportion, when we increased mass force increased as well within the correct proportion, and when we increased acceleration, force increased within the correct proportion. We tested these things three times each and used the average slope of velocity for the three. Our graph shows the correct fit regardless of the percent error. (By Dylan) **


 * Follow-up Questions: **

**1. Explain your graphs:**

**a. If linear: What is the slope of the trendline? To what actual observed value does the** **slope correspond? How does it compare to this actual observed value (find the percent** **error between the two)? Show why the slope should be equal to this quantity. What is** **the meaning of the y-intercept value?**

**b. 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.**

**2. 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.**

Friction would decrease the acceleration, because it adds resistance. You would need a bigger force to create the same acceleration. Our slope was smaller than what was needed due to the friction of the cart, especially because we did not account for it. This could be a source of error in the experiment because we ignored the friction, ignoring calculations needed to be done if there was friction. **Fr = μN**

 Fr - is the resistive force of friction <span style="font-family: Verdana,Arial,Helvetica,sans-serif; line-height: normal;">**μ-**coefficient of friction for the two surfaces <span style="font-family: Verdana,Arial,Helvetica,sans-serif; line-height: normal;">**N-**normal or perpendicular force pushing the two objects together

**Lab: Inertial Mass**

 * Objective:** Find the mass of an object only using its inertia.

Mass is solely dependent on the inertia of an object. Inertia is the resistance an object has to a change in its state of motion. The more inertia one object has the more mass and the same vice versa. A more massive object has a greater tendency to resist changes in its state of motion. In this lab, we found the relationship between mass and inertia using the vibration period of an object. Using this information we created an equation and through this we were able to calculate the mass of a rubiks cube, using only its' inertia.
 * Introduction:**

Inertial balance Varying Masses (50g, <span style="display: inline ! important;">100g, <span style="display: inline ! important;"> 200g)
 * Materials:**

Stopwatch Clamp


 * Procedure:**
 * 1) First set up the materials and choose one of the masses to find the period for. (50g)
 * 2) Release the inertial balance and count 10 periods. Time using the stopwatch.
 * 3) Record this into an excel worksheet.
 * 4) Do this three times with each mass and find the average time it takes.
 * 5) Repeat this step and find the periods for multiple masses to create a graph (100g, 150g,200g,250g,300g,350g,400g)
 * 6) After creating a graph, make a trendline.
 * 7) Then put the rubiks cube on the inertial balance and count 10 periods. Time using the stopwatch.
 * 8) After doing several trials, find the average time it takes for the rubiks cube, and compare it to the graph to predict the mass of the cube.
 * 9) Plug the trendline equation into your calculator and find the value when y=0.478


 * Trials:**


 * Mass (g) || Period (sec) || Trial 1 (sec) || Trial 2 (sec) || Trial 3 (sec) ||
 * 50 || 0.426 || 0.429 || 0.414 || 0.435 ||
 * 100 || 0.478 || 0.481 || 0.476 || 0.476 ||
 * 150 || 0.524 || 0.521 || 0.528 || 0.523 ||
 * 200 || 0.587 || 0.580 || 0.593 || 0.589 ||
 * 250 || 0.637 || 0.653 || 0.637 || 0.622 ||
 * 300 || 0.679 || 0.670 || 0.689 || 0.678 ||
 * 350 || 0.736 || 0.728 || 0.735 || 0.745 ||
 * 400 || 0.810 || 0.803 || 0.828 || 0.800 ||
 * ??? || 0.478 || 0.478 || 0.478 || 0.478 ||


 * RUBIKS CUBE = 99.3 g ||

[|intertia data]


 * Calculations/Graph:**


 * Conclusion:**

The graph we generated shows a linear relationship between mass and period. We have an r^2 value of .9965. This means that 99.65% of our data follows the trend of the line. The positive slope indicates that the bigger the mass an object has, the longer vibration period it will have. We used the equation of our graph (y=.0535x+.3688) to plug in the vibration period of a rubiks cube (.478) and find it's mass. Using this, we estimated that the mass of the rubiks cube is 99.3 grams, and in actuality it is 101.41 grams. According to our calculations and trials above, the percent error we came up with was a 2.08% error and we had a percent difference of 3.93%. These values show that our experiment was pretty much a success, but there are some things that could have contributed to why our calculations were slightly off. The major cause of getting a percent error is human error. It is almost impossible to start and stop the stopwatch at the exact times we were supposed to, and each trial could have been slightly off from the previous trial or the next trial. Also, the period could have been affected by the sliding of the weights. The paper-towel made the weights relatively sturdy, but sometimes they slid, causing the inertia balance to most likely become slightly off and the mass of the paper towel had a very minor effect as well.

<span style="font: 13px/19px Arial; margin: 0px;">No it did not play a part because the mass of an object is what effected the period of motion, and gravity effects mass in no way. It is a downward force and we were measuring vibrations (side to side movements).
 * Percent error:**
 * Percent Difference:**
 * Follow-up Questions:**
 * 1. Did gravitation play any part in this operation?Was this measurement process completely unrelated to the "weight" of the object?**

<span style="font: 13px/19px Arial; margin: 0px;">It lengthened the period of motion. On earth, inertial and gravitational mass are equal. Inertial mass is found by the equation m=F/a and gravitational mass is found by the equation M=F/g. On earth, the acceleration of any object is -9.8 (g) therefore the inertial mass equation becomes identical to the gravitational mass equation. It is much easier and much more accurate to find gravitational mass. To find gravitational mass you just need to use a balance because the machine knows to take gravity into play. This produces more precise answers than performing what we did today in the lab using an inertial balance, a stop watch, and a least squares regression line. The objective of the lab is to find the MASS of an object only using its inertia. Becuase mass measures how much inertia an object has, gravity has no affect on the goal of this lab. The results would not change, unless the question changed, for example how much would the rubiks cube weigh. This value would change due to the force of gravity changing. However because this isn't the question being asked, the result would stay the same.
 * 2. Did an increase in mass lengthen or shorten the period of motin?**
 * 3. How do the accelerations of different masses compare when the platform is pulled aside and released?**
 * The accelerations were different for all of the masses compared in the experiment. As the weight increased, the acceleration decreased. As the weight decreased, the acceleration increased **
 * 4. Do you imagine that the period would have been different if the side arms were stiffer? Would this change lengthen or shorten the period of the motion?**
 * If the side arms were stiffer, the period would still be the same. This is because the inertial balance measures how long it takes to complete one period. If the balance were stiffer, it would not go out as far as it did for the real thing. **
 * 5. Is there any relationship between inertial and gravitational mass of the object?**
 * 6. Why do we almost always use gravitation instead of interia as a means of measuring mass of an object?**
 * 7. How would the results of this experiment be changed if you did this experiment on the moon?**