Law Of Motion Lab
Lab: Newton’s Law of Motion
Section #: 404
Group #: 3
Experiment #: 3
Date :October 16, 2012
Newton’s Law of Motion
Your signature indicates that you have completely read the entire report and agree with everything here in. Failure to sign will result in a zero for your personal grade unless a formal exception is filed with your TA.
Please Print and Sign Full Name
Principal investigator:
Skeptic ________________________________________________________
Researcher:
TA:
Lab Report Score:________________
Role
I
DC
AD
RC
Q1
Q2
PI
PG
Legend:
I introduction
DC data and calculation
AD analysis and discussion
RC results and conclusion …show more content…
Q1/Q2 quiz/prelab
PI principal investigator points
PG personal grade (average of individual score and Lab Report Score)
Newton’s Law of Motion
Introduction
Objective In this experiment, the objective was to experiment research Newton’s Law of motion. A series of questions were asked under experimental implementation to decide whether Newton’s laws were valid or needed to be re-evaluated. In theory, his first law, “an object moves with constant velocity if and only if the net force acting on the object is zero,” his second law, “force=mass X acceleration” and his third law which states that, “ for two interacting objects, the force acting on object 1 due to object 2 is equal in magnitude and is opposite in direction to the force acting on object 2 due to object 1” should be validated in this experiment. The values should yield Newton’s results.
Procedure
Before the experiment was started, all the necessary equipment was gathered. Once the equipment was gathered Jessika went to be informed by Dr. Ellis about the necessary steps she needed to take to be the skeptic. Before any test could be run, Andrew tested the balance of the rail/track to ensure it wouldn’t throw off the data information. Once the track was balanced, Matt placed the CBR unit at the end of the track behind the rail and connected it to two calculators at different times so that the programs would be on the calculators. The cart was then placed in the middle of the track and the CBR program was initiated for take off. Once started, the cart was pushed to the opposite end of the CBR. This step was repeated many times until the group was comfortable using the apparatus. Once the group was ready to proceed, Matt ran three trials in order to get the data for the time vs. position graph. After each trial Matt handed the calculator to Andrew so that the data could be recorded and analyzed on the computer. Andrew connected the calculator to the computer and ran the Ti-connect program. Andrew then opened up Excel and exported the data from the calculator to the Excel spreadsheet and inserted a graph. The graph was edited to exclude the data points (not part of the motion of interest). The graphs for each of these 1st three trials are recorded and shown in graphs [1,2,3] respectively in the data and calculations segment for the time vs. position. Andrew reported to the lab room Tuesday, October 16, 2012 at 8:00 a.m. to complete the second half of the lab. Five trials containing the velocity vs. time graph were recorded with each time containing a different weight. The first trial was with the hook by itself plus the string, attached to the cart. The weight for the first trial was 0.05 kg (hook only). The data was recorded from the CBR and calculator and put into the computer onto excel. The second trial’s weight contained the hook (0.05 kg) + the weight (0.02 kg) equaling 0.07 kg. This data was also recorded and entered into excel. The third trial was conducted the exact same way with a different weight: hook (0.05 kg) + weight (0.03 kg) equaling 0.08 kg. The fourth trial in was done in the same fashion with these new sets of weight: hook (0.05 kg) + weight (0.04 kg) equaling 0.09 kg. The final trial consisted of the same procedure as the previous ones with much greater weight: hook (0.05 kg) + weight (0.06 kg) totaling 0.11 kg. These five trials represent velocity vs. time and are recorded and displayed in [graphs 4,5,6,7,8] in the data and calculations segment below.
Materials:
1 TI calculator (serial# 2385094906S-0407H)
1 CBR Unit (serial #TICBR-54)
1 Cart with reflector plate (serial #ME9430)
1 set of metal weights
1 Track with pulley (serial #ME9430)
1 String
1 Triple beam balance
1 Carpenter’s Level
Mass pan
References:
Ellis, Steve L. Physics 211: Laboratory Manual. University of Kentucky Department of Physics and Astronomy: Van-Griner, 2013. Print.
“Physics 211 Lab.” Ellis, Steve Course BlackBoard. University of Kentucky. Appendices B, C, F, G.
Post-Lab Meetings:
Thursday, October 11,20120- Lab was performed.
Tuesday, October 15, 2012- Matt, Jessika and Andrew got together after recitation to discuss the report and put together a plan of action
Tuesday, October 16, 2012- Andrew went to finish the experiment at 8:00 a.m.
Tuesday, October 16, 2012- Lab members met at the William T. Young Library beginning at 6:30pm to continue to work on data and calculations and put lab together.
Monday, October 22, 2012- Lab members met after recitation at 6:30 to discuss what remained on the lab.
Data and Calculations These graphs shows below are the given data records of the experiment for Newton’s Law of motion. The first three document the Position vs. Time graph. These graphs show the motion of the cart as it comes forward, bounces off the rail bumper, and returns to its origin. They answer whether or not the cart will stop without a force pushing it forward. The second section of graphs deals with velocity and time. These graphs are needed as acceleration is calculated and recorded for Table A. In order to find the acceleration of the cart, the equation [Equ. 1] is used. This equation takes the weight in kg of each trial, times the gravity divided by the weight of the cart plus the weight of the cart. These calculations produced [Table A] recorded below the graphs. Here is how the equation was used: mass weight of trial 1= 0.05, gravity= 9.81 m/s divided by the mass of the cart (0.6651 kg) plus mass weight of trial 1= 0.05. This is the resulting equation for trial 1 in the equation format: . Thus .686 m/s is the acceleration for the first trial. This equation is used for trials 2-5 as well only the weight of the trials will be different. The other four accelerations were calculated using this equation. The table shows that as the object gets heavier, the acceleration also increases.
[Graphs 1-3] Time Vs. Position:
[Graph 1a Trial 1]
[Graph 1b trial 1]
[Graph 2a trial 2]
[Graph 2b trial 2]
[Graph 3a trial 3]
[Graph 3b trial 3]
Velocity Vs. Time Graphs: [Graphs 4-8]
[Graph 4trial 4]
[Graph 5 trial 5]
[Graph 6 trial 6]
[Graph 7 trial 7]
[Graph 8 trial 8]
This equation is used for [graphs 1a-3b]: =acceleration. Taking the mass weight tied to the string divided by the total mass weight plus the mass of the cart gives you the acceleration.
The same holds true for the acceleration that corresponds to the mass proportion on the y axis.
[Table A.]
Mass Used (kg)
Calculated Acceleration
0.05 kg
0.686 m/s
0.07 kg
0.933 m/s
0.08 kg
1.05 m/s
0.09 kg
1.170 m/s
0.11 kg
1.40 m/s
Mass of Cart is: kg
Discussion and Analysis
Part 1
Uncertainty in Distance:
In part 1 of the experiment distance vs. time was plotting using the CBR and Microsoft Excel. The farther away the target was from the CBR, the larger the uncertainty. The CBR uncertainty is within 1% of the range (Appendix). The range is the total distance the cart traveled and it can be calculated by the change in displacement. Data from Trial 1 was used to find the uncertainty.
Forward Movement
1.17607m-.64512m=.53095m
Uncertainty:
=+.0053m
Backward Movement
1.17607m-.443186m=.732884m
Uncertainty=+. 0073m
Displacement (m) (m)
Forward Motion
.53095
+.0053
Backward Motion
.732884
+.0073
Uncertainty in Time:
The CBR device sends out the same number of pulses regardless of the time the cart is traveling. The uncertainty is found by calculating the difference in 2 times.
Forward Movement
Backwards Movement
The total time for backward movement can be calculated by taking the total time the cart was moving and subtracting the forward movement time (where the max point is on the graph). Since the CBR sends out the same number pulses both uncertainties are the same for time, regardless of direction.
3.6019s-1.55904s=2.04286s
Time (s) (s)
Forward Movement
1.55904
+.05376
Backward Movement
2.04286
+.05376
Uncertainty in Velocity:
The velocity was calculated using the distance vs. time graph.
Forward Direction
Backward Direction
Uncertainty in Velocity using graph
Velocity (m/s) (m/s)
Forward Direction
.764
+.03345
Backward Direction
.487
+.01767
Uncertainty in Velocity using Max-Min Method:
The uncertainty in velocity can also be found by using the max-min method; the values necessary can be obtained from the graphs.
The slope was calculated using the min and max points on the trend line for series 1 and the y-intercept. Series 2 shows the maximum slope and series 3 shows the minimum. X and Y error bars are on the graph, they are just difficult to see. The uncertainties for time and distance were used to specify the value for the error bars.
Note: X and Y error bars are on graph, they are just too small to see. Series 3 shows maximum slope and series 2 shows the minimum.
V(m/s) (m/s)
Velocity Forward
.764
+.0279
Velocity Backward
.487
+.0093
Uncertainty in Velocity due to Friction:
Friction can also cause uncertainty within the data. Friction uncertainty can be calculated by using tension. T=.456N as calculated in the Results and Conclusions. The mass of the cart is equal to .6651kg, as stated in the Data and Calculations.
Total Uncertainty in Velocity: Total Uncertainty in Velocity for Forward Direction:
.03345+.0279+.00026=+.06161m/s
Total Uncertainty in Velocity for Backward Direction:
.01767+.0093+.00026=+.02723m/s
Total Uncertainty in Velocity:
Velocity (m/s) (m/s)
Forward Direction
.764
+.06161
Backward Direction
-.487
+.02723
Uncertainty in Mass:
The final length minus the initial length can calculate the uncertainty in the length of the string.
Length of string after being tied to cart and weight: 1.42m
This value will give one uncertainty associated with the mass.
There is also uncertainty associated with the measuring equipment used to calculate the mass of the string. The uncertainty associated with this value is +.5 of the smallest unit of measurement.
Total Uncertainty in Mass:
Part 2
The acceleration of the cart was calculated in part 2 using 5 different masses. The acceleration can be measured using the Velocity vs. Time graph(s).
Uncertainty in Acceleration:
Mass 1:
Acceleration Uncertainties
Mass Used (kg)
Calculated Acceleration (m/s2) (m/s2)
0.05 kg
0.686
+.1625
0.07 kg
0.933
+.2214
0.08 kg
1.05
+.2492
0.09 kg
1.170
+.2777
0.11 kg
1.40
+.3323
Uncertainty due to slant
There could be uncertainty associated with the track not being completely horizontal, however in this case this was negligible. A level device was used to make sure the track was horizontal. The bubble in the level device was in between the two bars, therefore the slant was considered negligible.
Uncertainty in Velocity:
They uncertainty in velocity is the uncertainty of the CBR, which is given as .01m/s.
Time Uncertainty
The uncertainty in time remains the same for part 2.
Gravity can be determined by comparing acceleration and mass ratio. Theoretically, this number should not be significantly different than the local gravity calculated in lab 1.
Gravity was determined in lab 1. “Free Fall”, using Google earth, and is shown below.
The local gravity of the laboratory was necessary to take into account because depending on where the location is on Earth the gravity deviates from 9.8m/s2.
λ =38.020905˚ a=5.278895*10-3 β= 2.3462*10-5 ge= 9.7803185 ms-2
Local gravity (g)= 9.799m/s2 + .001m/s2
This information was obtained from the online Appendix F and Google Earth.
The uncertainty of Gravity was obtained by plugging in the givens, ge, β, and a in the equation above then finding the latitude and longitude for a location within 10 miles east and 10 miles west of where the actual experiment took place. Each value was subtracted from the actual local gravity then standard deviation was used to find the uncertainty.
Local Gravity for Tates Creek Village(West) :(g)=9.798m/s2
Local Gravity for Tin Roof (East): …show more content…
(g)=9.799m/s2
To find the gravity associated with this experiment, this equation can be used:
Uncertainty of Experimental Gravity:
Uncertainty in gravity can also be found using the min-max method from the acceleration vs. mass ratio.
Series 2 shows the maximum slope and series 3 shows the minimum. X and Y error bars are included.
Uncertainty by min-max method:
Total uncertainty associated with gravity:
Total Gravity with Uncertainty:
g (m/s2)
Gravity from Experiment 1
9.799
+.001
Gravity from Experiment 3
9.81
+.3321
Ranking of Uncertainties:
To rank the uncertainties in the experiment the ratio of the uncertainties must be found, otherwise it would be impossible to tell with different units for each uncertainty. To do this the relative uncertainty can be found.
Example of relative uncertainty:
For gravity, relative uncertainty=
Ranking
Uncertainty
Relative Uncertainty
1
Velocity
.1365
2
Mass
.0368
3
Time
.037
4
Gravity
.0341
5
Distance
.0100
Percent Difference:
Percent difference of Velocity:
Percent difference of Gravity:
Results and Conclusions
Statement of Results:
The objective was to incorporate Newton’s laws of motion into the experiment by comparing the forward and backward velocities and accelerations. Part one of the lab was to establish the difference in the velocities of the cart before it hit the barrier and after it hit. According to Newton’s third law the object should be equal in magnitude and opposite in direction. Part two’s goal was to relate Newton’s 2nd law (F=ma) to the experiment to make it valid.
The measurements in Part 1 was recorded with the calculator after the cart was pushed in the forward direction, hit the barrier and came back to the initial position in the backward direction. There were several uncertainties in calculations due to equipment error or random error. The results of uncertainty were calculated in the Analysis and discussion portion. The velocity forward in the 1st displacement vs. time trial was .764m/s. The velocity in the backward direction was -.487m/s. The uncertainty for the velocity in the forward direction was +.15501. The uncertainty in the backwards direction was +.02503. The Analysis and Discussion section explain how these values were retrieved. The % difference of the velocity forward and velocity backwards was 44.28%. The measurements of acceleration in part 2 was 6.86m/s2+.1625 for the hanger (.05kg),.933m/s2+.2214 for the 1st weight (.07kg), 1.05m/s2 + .2492 for the 2nd weight(.08kg),1.170m/s2+ .2777 for the 3rd weight(.09kg), and 1.40m/s2+ for the 4th weight(1.1kg). (The hanger was used for measurement because the weight hooked to it)
Forward and backward velocity:
Part 1: These two values were compared along with their uncertainties to determine whether or not they overlapped. All the information requiring the displacement vs. time graph was derived from the 1st trial.
Number line:
The number line indicates that the values for forward and backward uncertainties do not overlap. The Secondary analysis is included at the end of the report.
Gravity number line:
The uncertainty for gravity, indicated by the number line overlap for the two experimental values. The percent difference for gravity is .1122%.
Conclusions:
The results in the number line for velocity indicate that there was larger error than expected causing the velocities and there uncertainties to not allow an overlap. This could be caused by random or systematic error. The team will go back and review the lab and all the specific steps used to acquire this outcome.
Secondary Analysis: The team concluded that there was systematic error related to the track and the barrier.
There was a transfer of momentum from the car to the track during the trials. Every time the cart would come in contact with the barrier the track would shift slightly. Also the barrier would move back and forth when the cart would hit it. There is also some friction on the cart that cannot be accounted for. When the spring on the cart compresses against the barrier, energy escapes the system causing the kinetic energy in the backward direction to be less than the forward direction. Correcting this error would be a very difficult task. In order to do so the team would have to lock the track to the table, which would have to lock to the floor, the floor would have to lock to the ground, and the ground to the Earth. This would be an almost impossible task.
Questions:
1.) According to Graphs 1-3 (displacement vs. time) all 3 graphs indicate that the velocities were comparatively constant in both the forward and backward direction. This was true because the slope of the line was
linear.
2.) The velocity from the x-t graph was calculated to be .764m/s in the foreword direction, and .487m/s in the backward direction. The reason the force changed direction and magnitude was because the equal and opposite force was exerted on the cart by the wall. The shape of the graph looked like an upside down V, the top point on the graph was right before the cart hit the wall.
3.) The cart bounced back slower because of uncertainties in the backward direction. According to Newton’s third law the barrier should exert the same amount of force back on the cart causing its velocity to be the same (neglecting outside forces).
4.) .It was very important to make sure the rail was completely horizontal during the x-t graph because if there would have been an incline, the velocities would not have been constant. Therefore, they were constant due to the complete linear path travel (no y-direction). If gravity acts on the cart then it would give the cart an acceleration causing the velocity to not be constant.
5.) The string exerts a tension force. This force is derived from the equation below:
Tension:
A.)
This calculation for Tension was comes from the acceleration of the first trial .05kg.
B.) If the gravity force (9.8m/s2) is used as acceleration and .05kg as the mass then tension force value will be close to the force value of the cart times the .05kg mass’s acceleration(.686m/s2).
6.) The cart and the weight are connected physically (a system)by a string so they will share the same acceleration value.
7.) The string allows the cart to accelerate by connected it to a weight. If the string was not used in the experiment then the cart would stand still and the acceleration would equal 0.
Ex.)
Section #: 404
Group #: 3
Experiment #: 3
Date :October 16, 2012
Newton’s Law of Motion
Your signature indicates that you have completely read the entire report and agree with everything here in. Failure to sign will result in a zero for your personal grade unless a formal exception is filed with your TA.
Please Print and Sign Full Name
Principal investigator:
Skeptic ________________________________________________________
Researcher:
TA:
Lab Report Score:________________
Role
I
DC
AD
RC
Q1
Q2
PI
PG
Legend:
I introduction
DC data and calculation
AD analysis and discussion
RC results and conclusion …show more content…
Q1/Q2 quiz/prelab
PI principal investigator points
PG personal grade (average of individual score and Lab Report Score)
Newton’s Law of Motion
Introduction
Objective In this experiment, the objective was to experiment research Newton’s Law of motion. A series of questions were asked under experimental implementation to decide whether Newton’s laws were valid or needed to be re-evaluated. In theory, his first law, “an object moves with constant velocity if and only if the net force acting on the object is zero,” his second law, “force=mass X acceleration” and his third law which states that, “ for two interacting objects, the force acting on object 1 due to object 2 is equal in magnitude and is opposite in direction to the force acting on object 2 due to object 1” should be validated in this experiment. The values should yield Newton’s results.
Procedure
Before the experiment was started, all the necessary equipment was gathered. Once the equipment was gathered Jessika went to be informed by Dr. Ellis about the necessary steps she needed to take to be the skeptic. Before any test could be run, Andrew tested the balance of the rail/track to ensure it wouldn’t throw off the data information. Once the track was balanced, Matt placed the CBR unit at the end of the track behind the rail and connected it to two calculators at different times so that the programs would be on the calculators. The cart was then placed in the middle of the track and the CBR program was initiated for take off. Once started, the cart was pushed to the opposite end of the CBR. This step was repeated many times until the group was comfortable using the apparatus. Once the group was ready to proceed, Matt ran three trials in order to get the data for the time vs. position graph. After each trial Matt handed the calculator to Andrew so that the data could be recorded and analyzed on the computer. Andrew connected the calculator to the computer and ran the Ti-connect program. Andrew then opened up Excel and exported the data from the calculator to the Excel spreadsheet and inserted a graph. The graph was edited to exclude the data points (not part of the motion of interest). The graphs for each of these 1st three trials are recorded and shown in graphs [1,2,3] respectively in the data and calculations segment for the time vs. position. Andrew reported to the lab room Tuesday, October 16, 2012 at 8:00 a.m. to complete the second half of the lab. Five trials containing the velocity vs. time graph were recorded with each time containing a different weight. The first trial was with the hook by itself plus the string, attached to the cart. The weight for the first trial was 0.05 kg (hook only). The data was recorded from the CBR and calculator and put into the computer onto excel. The second trial’s weight contained the hook (0.05 kg) + the weight (0.02 kg) equaling 0.07 kg. This data was also recorded and entered into excel. The third trial was conducted the exact same way with a different weight: hook (0.05 kg) + weight (0.03 kg) equaling 0.08 kg. The fourth trial in was done in the same fashion with these new sets of weight: hook (0.05 kg) + weight (0.04 kg) equaling 0.09 kg. The final trial consisted of the same procedure as the previous ones with much greater weight: hook (0.05 kg) + weight (0.06 kg) totaling 0.11 kg. These five trials represent velocity vs. time and are recorded and displayed in [graphs 4,5,6,7,8] in the data and calculations segment below.
Materials:
1 TI calculator (serial# 2385094906S-0407H)
1 CBR Unit (serial #TICBR-54)
1 Cart with reflector plate (serial #ME9430)
1 set of metal weights
1 Track with pulley (serial #ME9430)
1 String
1 Triple beam balance
1 Carpenter’s Level
Mass pan
References:
Ellis, Steve L. Physics 211: Laboratory Manual. University of Kentucky Department of Physics and Astronomy: Van-Griner, 2013. Print.
“Physics 211 Lab.” Ellis, Steve Course BlackBoard. University of Kentucky. Appendices B, C, F, G.
Post-Lab Meetings:
Thursday, October 11,20120- Lab was performed.
Tuesday, October 15, 2012- Matt, Jessika and Andrew got together after recitation to discuss the report and put together a plan of action
Tuesday, October 16, 2012- Andrew went to finish the experiment at 8:00 a.m.
Tuesday, October 16, 2012- Lab members met at the William T. Young Library beginning at 6:30pm to continue to work on data and calculations and put lab together.
Monday, October 22, 2012- Lab members met after recitation at 6:30 to discuss what remained on the lab.
Data and Calculations These graphs shows below are the given data records of the experiment for Newton’s Law of motion. The first three document the Position vs. Time graph. These graphs show the motion of the cart as it comes forward, bounces off the rail bumper, and returns to its origin. They answer whether or not the cart will stop without a force pushing it forward. The second section of graphs deals with velocity and time. These graphs are needed as acceleration is calculated and recorded for Table A. In order to find the acceleration of the cart, the equation [Equ. 1] is used. This equation takes the weight in kg of each trial, times the gravity divided by the weight of the cart plus the weight of the cart. These calculations produced [Table A] recorded below the graphs. Here is how the equation was used: mass weight of trial 1= 0.05, gravity= 9.81 m/s divided by the mass of the cart (0.6651 kg) plus mass weight of trial 1= 0.05. This is the resulting equation for trial 1 in the equation format: . Thus .686 m/s is the acceleration for the first trial. This equation is used for trials 2-5 as well only the weight of the trials will be different. The other four accelerations were calculated using this equation. The table shows that as the object gets heavier, the acceleration also increases.
[Graphs 1-3] Time Vs. Position:
[Graph 1a Trial 1]
[Graph 1b trial 1]
[Graph 2a trial 2]
[Graph 2b trial 2]
[Graph 3a trial 3]
[Graph 3b trial 3]
Velocity Vs. Time Graphs: [Graphs 4-8]
[Graph 4trial 4]
[Graph 5 trial 5]
[Graph 6 trial 6]
[Graph 7 trial 7]
[Graph 8 trial 8]
This equation is used for [graphs 1a-3b]: =acceleration. Taking the mass weight tied to the string divided by the total mass weight plus the mass of the cart gives you the acceleration.
The same holds true for the acceleration that corresponds to the mass proportion on the y axis.
[Table A.]
Mass Used (kg)
Calculated Acceleration
0.05 kg
0.686 m/s
0.07 kg
0.933 m/s
0.08 kg
1.05 m/s
0.09 kg
1.170 m/s
0.11 kg
1.40 m/s
Mass of Cart is: kg
Discussion and Analysis
Part 1
Uncertainty in Distance:
In part 1 of the experiment distance vs. time was plotting using the CBR and Microsoft Excel. The farther away the target was from the CBR, the larger the uncertainty. The CBR uncertainty is within 1% of the range (Appendix). The range is the total distance the cart traveled and it can be calculated by the change in displacement. Data from Trial 1 was used to find the uncertainty.
Forward Movement
1.17607m-.64512m=.53095m
Uncertainty:
=+.0053m
Backward Movement
1.17607m-.443186m=.732884m
Uncertainty=+. 0073m
Displacement (m) (m)
Forward Motion
.53095
+.0053
Backward Motion
.732884
+.0073
Uncertainty in Time:
The CBR device sends out the same number of pulses regardless of the time the cart is traveling. The uncertainty is found by calculating the difference in 2 times.
Forward Movement
Backwards Movement
The total time for backward movement can be calculated by taking the total time the cart was moving and subtracting the forward movement time (where the max point is on the graph). Since the CBR sends out the same number pulses both uncertainties are the same for time, regardless of direction.
3.6019s-1.55904s=2.04286s
Time (s) (s)
Forward Movement
1.55904
+.05376
Backward Movement
2.04286
+.05376
Uncertainty in Velocity:
The velocity was calculated using the distance vs. time graph.
Forward Direction
Backward Direction
Uncertainty in Velocity using graph
Velocity (m/s) (m/s)
Forward Direction
.764
+.03345
Backward Direction
.487
+.01767
Uncertainty in Velocity using Max-Min Method:
The uncertainty in velocity can also be found by using the max-min method; the values necessary can be obtained from the graphs.
The slope was calculated using the min and max points on the trend line for series 1 and the y-intercept. Series 2 shows the maximum slope and series 3 shows the minimum. X and Y error bars are on the graph, they are just difficult to see. The uncertainties for time and distance were used to specify the value for the error bars.
Note: X and Y error bars are on graph, they are just too small to see. Series 3 shows maximum slope and series 2 shows the minimum.
V(m/s) (m/s)
Velocity Forward
.764
+.0279
Velocity Backward
.487
+.0093
Uncertainty in Velocity due to Friction:
Friction can also cause uncertainty within the data. Friction uncertainty can be calculated by using tension. T=.456N as calculated in the Results and Conclusions. The mass of the cart is equal to .6651kg, as stated in the Data and Calculations.
Total Uncertainty in Velocity: Total Uncertainty in Velocity for Forward Direction:
.03345+.0279+.00026=+.06161m/s
Total Uncertainty in Velocity for Backward Direction:
.01767+.0093+.00026=+.02723m/s
Total Uncertainty in Velocity:
Velocity (m/s) (m/s)
Forward Direction
.764
+.06161
Backward Direction
-.487
+.02723
Uncertainty in Mass:
The final length minus the initial length can calculate the uncertainty in the length of the string.
Length of string after being tied to cart and weight: 1.42m
This value will give one uncertainty associated with the mass.
There is also uncertainty associated with the measuring equipment used to calculate the mass of the string. The uncertainty associated with this value is +.5 of the smallest unit of measurement.
Total Uncertainty in Mass:
Part 2
The acceleration of the cart was calculated in part 2 using 5 different masses. The acceleration can be measured using the Velocity vs. Time graph(s).
Uncertainty in Acceleration:
Mass 1:
Acceleration Uncertainties
Mass Used (kg)
Calculated Acceleration (m/s2) (m/s2)
0.05 kg
0.686
+.1625
0.07 kg
0.933
+.2214
0.08 kg
1.05
+.2492
0.09 kg
1.170
+.2777
0.11 kg
1.40
+.3323
Uncertainty due to slant
There could be uncertainty associated with the track not being completely horizontal, however in this case this was negligible. A level device was used to make sure the track was horizontal. The bubble in the level device was in between the two bars, therefore the slant was considered negligible.
Uncertainty in Velocity:
They uncertainty in velocity is the uncertainty of the CBR, which is given as .01m/s.
Time Uncertainty
The uncertainty in time remains the same for part 2.
Gravity can be determined by comparing acceleration and mass ratio. Theoretically, this number should not be significantly different than the local gravity calculated in lab 1.
Gravity was determined in lab 1. “Free Fall”, using Google earth, and is shown below.
The local gravity of the laboratory was necessary to take into account because depending on where the location is on Earth the gravity deviates from 9.8m/s2.
λ =38.020905˚ a=5.278895*10-3 β= 2.3462*10-5 ge= 9.7803185 ms-2
Local gravity (g)= 9.799m/s2 + .001m/s2
This information was obtained from the online Appendix F and Google Earth.
The uncertainty of Gravity was obtained by plugging in the givens, ge, β, and a in the equation above then finding the latitude and longitude for a location within 10 miles east and 10 miles west of where the actual experiment took place. Each value was subtracted from the actual local gravity then standard deviation was used to find the uncertainty.
Local Gravity for Tates Creek Village(West) :(g)=9.798m/s2
Local Gravity for Tin Roof (East): …show more content…
(g)=9.799m/s2
To find the gravity associated with this experiment, this equation can be used:
Uncertainty of Experimental Gravity:
Uncertainty in gravity can also be found using the min-max method from the acceleration vs. mass ratio.
Series 2 shows the maximum slope and series 3 shows the minimum. X and Y error bars are included.
Uncertainty by min-max method:
Total uncertainty associated with gravity:
Total Gravity with Uncertainty:
g (m/s2)
Gravity from Experiment 1
9.799
+.001
Gravity from Experiment 3
9.81
+.3321
Ranking of Uncertainties:
To rank the uncertainties in the experiment the ratio of the uncertainties must be found, otherwise it would be impossible to tell with different units for each uncertainty. To do this the relative uncertainty can be found.
Example of relative uncertainty:
For gravity, relative uncertainty=
Ranking
Uncertainty
Relative Uncertainty
1
Velocity
.1365
2
Mass
.0368
3
Time
.037
4
Gravity
.0341
5
Distance
.0100
Percent Difference:
Percent difference of Velocity:
Percent difference of Gravity:
Results and Conclusions
Statement of Results:
The objective was to incorporate Newton’s laws of motion into the experiment by comparing the forward and backward velocities and accelerations. Part one of the lab was to establish the difference in the velocities of the cart before it hit the barrier and after it hit. According to Newton’s third law the object should be equal in magnitude and opposite in direction. Part two’s goal was to relate Newton’s 2nd law (F=ma) to the experiment to make it valid.
The measurements in Part 1 was recorded with the calculator after the cart was pushed in the forward direction, hit the barrier and came back to the initial position in the backward direction. There were several uncertainties in calculations due to equipment error or random error. The results of uncertainty were calculated in the Analysis and discussion portion. The velocity forward in the 1st displacement vs. time trial was .764m/s. The velocity in the backward direction was -.487m/s. The uncertainty for the velocity in the forward direction was +.15501. The uncertainty in the backwards direction was +.02503. The Analysis and Discussion section explain how these values were retrieved. The % difference of the velocity forward and velocity backwards was 44.28%. The measurements of acceleration in part 2 was 6.86m/s2+.1625 for the hanger (.05kg),.933m/s2+.2214 for the 1st weight (.07kg), 1.05m/s2 + .2492 for the 2nd weight(.08kg),1.170m/s2+ .2777 for the 3rd weight(.09kg), and 1.40m/s2+ for the 4th weight(1.1kg). (The hanger was used for measurement because the weight hooked to it)
Forward and backward velocity:
Part 1: These two values were compared along with their uncertainties to determine whether or not they overlapped. All the information requiring the displacement vs. time graph was derived from the 1st trial.
Number line:
The number line indicates that the values for forward and backward uncertainties do not overlap. The Secondary analysis is included at the end of the report.
Gravity number line:
The uncertainty for gravity, indicated by the number line overlap for the two experimental values. The percent difference for gravity is .1122%.
Conclusions:
The results in the number line for velocity indicate that there was larger error than expected causing the velocities and there uncertainties to not allow an overlap. This could be caused by random or systematic error. The team will go back and review the lab and all the specific steps used to acquire this outcome.
Secondary Analysis: The team concluded that there was systematic error related to the track and the barrier.
There was a transfer of momentum from the car to the track during the trials. Every time the cart would come in contact with the barrier the track would shift slightly. Also the barrier would move back and forth when the cart would hit it. There is also some friction on the cart that cannot be accounted for. When the spring on the cart compresses against the barrier, energy escapes the system causing the kinetic energy in the backward direction to be less than the forward direction. Correcting this error would be a very difficult task. In order to do so the team would have to lock the track to the table, which would have to lock to the floor, the floor would have to lock to the ground, and the ground to the Earth. This would be an almost impossible task.
Questions:
1.) According to Graphs 1-3 (displacement vs. time) all 3 graphs indicate that the velocities were comparatively constant in both the forward and backward direction. This was true because the slope of the line was
linear.
2.) The velocity from the x-t graph was calculated to be .764m/s in the foreword direction, and .487m/s in the backward direction. The reason the force changed direction and magnitude was because the equal and opposite force was exerted on the cart by the wall. The shape of the graph looked like an upside down V, the top point on the graph was right before the cart hit the wall.
3.) The cart bounced back slower because of uncertainties in the backward direction. According to Newton’s third law the barrier should exert the same amount of force back on the cart causing its velocity to be the same (neglecting outside forces).
4.) .It was very important to make sure the rail was completely horizontal during the x-t graph because if there would have been an incline, the velocities would not have been constant. Therefore, they were constant due to the complete linear path travel (no y-direction). If gravity acts on the cart then it would give the cart an acceleration causing the velocity to not be constant.
5.) The string exerts a tension force. This force is derived from the equation below:
Tension:
A.)
This calculation for Tension was comes from the acceleration of the first trial .05kg.
B.) If the gravity force (9.8m/s2) is used as acceleration and .05kg as the mass then tension force value will be close to the force value of the cart times the .05kg mass’s acceleration(.686m/s2).
6.) The cart and the weight are connected physically (a system)by a string so they will share the same acceleration value.
7.) The string allows the cart to accelerate by connected it to a weight. If the string was not used in the experiment then the cart would stand still and the acceleration would equal 0.
Ex.)