Buggy Lab : Done By Aditya Tipre, Adithya Kalyan, and Tyler (Conducted on September 14th, 2021)
Focus Problem
Controlling Variables
Data Collection
Procedure
Raw Data
|
Processed Raw Data
Processed Data
* For this experiment Time trial 1 was 1 second, Time trial 2 was 5 seconds, Time trial 3 was 10 seconds, and time trial 4 was 15 seconds.
- In order to process this raw data we had to take the sum of a particular trial and divide by three to get the mean
- For example, for trial one you would add 45+40+38=123, and then divide by three to get a mean of 41
- Repeat this process with each Trial to process the raw data
- Assumptions made during this experiment include, the starter's release reaction time, the timer's ability to say start and stop on time, and the stopper's reactions time.
Processed Data
* For this experiment Time trial 1 was 1 second, Time trial 2 was 5 seconds, Time trial 3 was 10 seconds, and time trial 4 was 15 seconds.
Time Trial number |
Distance Traveled (cm) |
1 |
41 |
2 |
194.3333 |
3 |
386.6666 |
4 |
601.6666 |
Graphical Representation of Data
Equation for graph (*x means position)
x=39.92t-3.448
Slope = 39.92 cm/s
Y int = -3.448
GRAPHICAL ANALYSIS: This is a position time graph, it is used to show an objects position relative to a certain time, and the slope is the velocity. With this we can Conclude that the average velocity of this Buggy was 39.92 cm/s (as indicated by the slope). The Y axis of this graph is the prediction the model makes for how far the buggy goes at 0 seconds, and in this case the model predicts that after 0 seconds the Buggy travels -3.448cm. This is merely an experimental value, (aka what the model predicts) it is not what happens in real life.
What does this mean? Conclusions drawn from evidence.
Conclusion
Evaluation of Procedure
- Our results conclude that there is a clear positive relationship between Position and time
- As indicated by the slope of the graph, we can conclude that as time increases position increases
- More generally, as time changes position changes.
- This same process could be used to conduct the same experiment on different moving objects
- The purpose of this lab was to find a relationship between position and time, as long as the same process is followed and variables are controlled in a similar manner, experiments done with other moving objects should yield the same result.
Conclusion
- Essentially, this experiment was conducted to find a relationship between time and position. As we can see from both data tables and graphs, we can conclude that as time changes position changes. In all 3 different time trials, none yielded the same average, in fact, each showed an increase in distance, from 41 cm, to 194.333, to 386.6666, to 601.6666. The direct increasing relationship between time and position prove that as time changes, position changes.
Evaluation of Procedure
- In my opinion, our procedure was an organized one which eliminated many sources of possible error out.
- I feel the highlight of our procedure was dividing the labor into 3 separate parts helped to factor out the possibilities of reaction time error to the highest degree possible
- I felt our procedure also allowed us to maintain control of our variables
- However, no procedure is perfect and ours is no different.
- A suggestion I would incorporate into this experiment is the replacement of hand held timing to technology based timing, like they have and track and field events, this makes the timing of the event much more accurate.
- Another suggestion I have is to add a track, which forces the buggy to go straight. On the flat surface we noticed that as the buggy travels a longer distance it diverges from its path a little bit; a straight track could help to increase accuracy.
The Cart on Ramp - Done by Aditya Tipre, Adithya Kalyan, and Leyton Shroff
Focus Problem and Variables:
Method to Control variables
Data Collection:
The Procedure:
Labeled Diagram of Setup:
- The main question we wanted to figure out was how does time effect the velocity of the car. Our group had the following Variables, Independent Variable: Time (s), Dependent Variable: Position(m), Controls: Ramp, Force with which Car was applied on Ramp, Starting position, Final position, Scale of reference (measured in cm), Environment, Friction.
Method to Control variables
- In order to control our variables for the maximum accuracy we set all all our logger pro videos to the same origin and frame in order to make our results more dependable and accurate, additionally the person who releases the car only does so when the recorder signals him to do so. This as a result, helps our time measurement more accurate.
Data Collection:
- Our Procedure for collection included the following.
- The Recorder of the Video sets up his laptop in order to take a clear video of the cart rolling down the ramp.
- Once the recorder is ready, he signals the dropper to drop the car down the ramp, upon being signaled the dropper drops the car.
- The Stopper then stops the car once the car reaches the bottom of the ramp.
- Once the trial is complete, the recorder stopped recording
- After the video was complete it was uploaded into Logger Pro and the following process was followed: 1.) The Beginning of the Video was set to be the first frame 2.) The origin was set to the top of the ramp (Where the Cart started) 3.) The axis were adjusted to be in line with the ramp.
- After the setup was complete, the video was played in Logger Pro, and the Cart's position marked at every frame.
- This data was then fed into a table
- From the Data Table, Logger Pro's software generated a position/time graph, and a Velocity/time graph.
The Procedure:
- Following the previously listed procedure, we managed to find many key components of the Focus questions.
- By using Logger Pro, our group was able to formulate an a position time graph.
- By using the slope of the position time graph, Logger Pro's software also was able to formulate a velocity time graph
- Essentially, using the slope of these two graphs we can calculate both the average velocity and average acceleration of the Cart (Velocity = Slope of position/ time graph & and Acceleration = slope of velocity/time graph.
- Unfortunately, we could only run one trial.
Labeled Diagram of Setup:
Recorded Raw Data:
How raw data was processed:
Processed Raw Data:
- The Raw data was inputted into Logger Pro's software, and provided with very accurate x values. Using Logger Pro's software also eliminates the possibility of having a wrong displacement. Some Assumptions that were made included the the positioning of the axis. While we tried our best, it is impossible to have a perfect axis and perfect origin, therefore the values wont be perfect, they will be accurate but not a accurate as can be.
Processed Raw Data:
Graphs and Graphical analysis:
Velocity Time Graph Position Time Graph
Velocity Time Graph Details:
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Position Time Graph Details:
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GRAPHICAL ANALYSIS:
Conclusion drawn from Evidence:
Conclusion:
Procedure Evaluation:
Improvements:
- Position Time Graph
- The sign of the line of best fit (y=-0.4669t^2-0.02667+0.00435), combined with slope of the graph having a non linear slope indicates that the object (Cart) is moving in the downwards motion and accelerating downwards as well. The Y intercept of 0.00435, means the model predicts that at 0 seconds the buggy will have traveled 0.0435 meters after traveling for 0 seconds. As is known, this is not true, it is only what the model predicts and therefore it is an experimental value. Experimental Values almost always contradict what happens in real life as it this number is only made by the Software's expectation as to what should happen.
- Velocity Time Graph
- The equation for the line of best fit for this graph is Vx=-0.9780m/t/t-0.002559. It is a line with a linear, negative slope. The Equation tells us that for every 1 second traveled, the cart accelerates at a constant rate of -0.9780m/t/t, the sign indicates that the acceleration is in the downwards direction. The Y intercept of this Equation indicates that at 0 seconds the model predicts that the cart will have a velocity of -0.002559, as mentioned previously this is just a experimental value so it is alright for it sound off.
Conclusion drawn from Evidence:
- As both models prove, as time increases, the velocity of the car increases. As seen by the Position Time Graph we can see that the velocity increases exponentially (Quadratic Model) in the negative direction indicating that as time goes on the the velocity seems to get faster. The Velocity Time Graph proves that there is a constant acceleration (Linear slope), confirming that the velocity increases as time increases.
Conclusion:
- As shown by this experiment, there is a clear relationship between time and velocity. As time increases velocity increases. As shown by our two models, both show an increase in velocity as time goes on. Due to our research and graphs, we can conclude that this trend should continued unless stopped by an outside force ( In our case the stopper at the end of the ramp). While we only had time to do one trial, we can say with fair confidence that, while it may offer some extra variability, all other trials would have emulated the same trend/relationship between Time and Velocity. The only instance in which this statement did not hold true was until it was acted upon by an outside force, until then this relationship should hold true for all other circumstances.
Procedure Evaluation:
- Under the given circumstances, our procedure was as efficient and accurate as it could have been, however it doesn't free it from flaw. The most noticeable and prominent flaw in our procedure was the lack of trials. Anything can happen only once, therefore a singular trial is bound cause unreliability when analyzing results. Another source of error originates from aligning the origin and axis for the video Analysis. As mentioned previously, we aligned the axis as best was we could have, however, this does not mean it was perfect. Even the slightest misalignment can make our results unreliable. Those are the two most noticeable flaws in our procedure.
Improvements:
- One Improvement that I would highly suggest is the inclusion of additional trials. This would remove any potential source of doubt that experimenters may have when looking at their data. Doing multiple trials of an experiment would either prove or disprove a pattern, making it an imperative step of any experiment design. That is why I would suggest the use of multiple trials.
Unbalanced Forces Lab: Done by Aditya, Aayush, Muskan, and Gabby.
Research Questions:
- Does the acceleration of an object depend on the Net Force acting on it?
- Does the acceleration of an object depend on the Mass of it?
Variables and Controls (Includes the variables for both experiments:
- Independhent Variables: Net Force, Mass
- Dependent Variables: Acceleration
- Controls: Total Mass of the Entire System ( Cart and Hanger ), Mass of Hanger, The Cart, The Hanger, Ramp, Pulley, Sensor for tracking Velocity
- Process for Controlling Variables: In order to produce Fair and Accurate results, we ran each trial in each respective experiment on the same track (Pulley System) and had no objects interfering with it. Therefore, the speed of the car will not be affected by outside factors, giving better control of variables, and thus giving better results.
- Net Force Lab - In this we made sure the mass of the entire system was constant throughout the lab, that mass being 1680g. In this lab, Our groups changed the location of the Weights, transferring weight from the Cart on to the hanger. For each trial, we transferred weight from the cart onto the hanger, and pushed the cart forward, tracking its velocity using a sensor. Once the trial was over, the sensor (Which was plugged a laptop) created a velocity time graph. Using Logger Pro, our group used the slope of the velocity time graph to determine the acceleration for each trial.
- Mass Lab - In this lab, Our group changed the total mass of the system. We did so by increasing the weight of the cart. Our group did not change the mass of the hanger in order to have a constant, thus producing a more reliable result. For Every Trial, our group increased the weight of the cart, and saw how it affects acceleration. Data collection was the same in this experiment as it was in the last experiment.
- Net Force Lab: In this lab we measured acceleration in relation to net force, in order to see how it changes when cart is released. We measured it by putting a cart and a hanger to make a pulley system. Making sure the weight of the whole system adds up to 1680 g. With each trial we took weight off the cart, and added it to the hanger. For each trial, a sensor was used to track velocity, and make a velocity time graph. Once the velocity time graph was made in Logger Pro, we found the slope which gave us the acceleration.
- Mass Lab: In this lab we measured the affect Mass has on acceleration. The group changed the mass of the cart, while keeping the mass of the hanger constant, with each trial we added weights onto the cart. We found acceleration using the same process as stated before.
* Both labs had same setups, only that in Net force lab, weights were added to both the cart and the hanger, whereas the in the Mass lab weights were just added on the cart*
Raw Data for Both Labs:
- Raw Data for Net Force Lab
Mass of Cart (g) |
Mass of Hanger (g） |
Total mass of Pulley System (g) |
Acceleration (m/s^2) |
1630 |
50 |
1680 |
0.283 |
1580 |
100 |
1680 |
0.5838 |
1530 |
150 |
1680 |
0.8567 |
1520 |
160 |
1680 |
0.9452 |
1510 |
170 |
1680 |
1.032 |
1550 |
130 |
1680 |
0.781 |
1560 |
120 |
1680 |
0.6842 |
1620 |
160 |
1680 |
0.31 |
1610 |
170 |
1680 |
0.472 |
Mass lab: *Trials are not presented in order*
Mass of Cart (g) |
Mass of Hanger (g) |
Mass of Pulley System (g) |
Acceleration (m/s^2) |
1500 |
50 |
1550 |
0.33 |
500 |
50 |
550 |
0.74 |
550 |
50 |
600 |
0.66 |
600 |
50 |
650 |
0.55 |
700 |
50 |
750 |
0.4 |
900 |
50 |
950 |
0.54 |
1400 |
50 |
1450 |
0.34 |
1600 |
50 |
1650 |
0.295 |
1700 |
50 |
1750 |
0.33 |
1800 |
50 |
1850 |
0.3 |
1900 |
50 |
1950 |
0.26 |
2430 |
50 |
2480 |
0.253 |
Processed Raw Data:
- Here is the processed Raw Data for the Net Force Lab: For this data set, we processed the raw data into Net Force by multiplying Mass of System by the respective Trials acceleration ( following the equation F net= Mass x Acceleration )
Mass of Cart (g) |
Net Force (N) |
Acceleration (m/s^2) |
1630 |
0.49 |
0.283 |
1580 |
1.176 |
0.5838 |
1530 |
1.47 |
0.8567 |
1520 |
1.568 |
0.9452 |
1510 |
1.666 |
1.032 |
1550 |
1.274 |
0.781 |
1560 |
1.176 |
0.6842 |
1620 |
0.588 |
0.31 |
1610 |
0.686 |
0.472 |
Processed Raw data for the mass lab: In order to process this data, The total mass of the system was converted into kg
Total Mass of the System (kg) |
Acceleration (m/s^2) |
1.55 |
0.33 |
0.55 |
0.74 |
0.6 |
0.66 |
0.65 |
0.55 |
0.75 |
0.4 |
0.95 |
0.54 |
1.45 |
0.34 |
1.65 |
0.295 |
1.75 |
0.33 |
1.85 |
0.3 |
1.95 |
0.26 |
2.48 |
0.253 |
Graphs and Graphical Analysis:
- Graph of the Net force lab
Graphical Analysis + Conclusion:
- In this Graph the group modeled Net force and acceleration in order to clearly see the relationship between the two. Firstly, our group decided to go with a proportional model (y=Ax) as the proportional model goes through the point (0,0). The group choose this model because this point is logical, when Net Force is zero, the forces are balanced meaning that objects cannot accelerate, because to do so objects need to feel an unbalanced push or pull, and when the Net force is zero there is no unbalanced push or pull. Therefore, the object cannot accelerate when net force equal zero ( 0 Net Force = No Acceleration) and this is why the our group believes the proportional model works best. The Equation of the line of best fit is Acceleration = 0.5912(N), Slope = 0.5912. The translation of this equation is that the model predicts that for each 1 N increase is Net Force, Acceleration will increase by 0.5912 m/s^2. As seen on the graph, the line of best fit has a positive slope, Indicating that the relationship between Net Force and Acceleration are both proportional and positive. As the Net force increases, the Acceleration increases.
Graphical Analysis of the Mass lab:
Graphical Analysis + Conclusion:
- In this Graph, Our group graphed Total Mass and Acceleration in order to see the relationship between the two. In order to simplify the graph, the group converted all of the Total Masses of the Systems from grams to kilograms. For this Graph, the group decided the proportional model (y=Ax^b). The group choose this model, because it agrees with the laws of Physics. Acceleration = Fnet/Mass, so like the equation the proportional model is asymptotic at y=0. The slope of the line is -0.4203. This means that for every 1kg increase in Mass, the acceleration will decrease by 0.4203 m/s^2. The interpretation of the slope combined with the line of best fit indicate that mass and Acceleration are inversely related. When mass increases, Acceleration decreases. This conclusion is in agreement with the laws of physics, when we look at the equation a= Fnet/ m , we can see that are conclusion ( As mass increases, Acceleration decreases holds true).
Synopsis of Conclusions:
- Net Force Lab: As Net Force increases Acceleration increases
- Mass Lab: As Mass increases Acceleration decreases
Evaluation of Procedure:
- Our Procedure contained some flaws which prevented the experiment from yielding the most accurate results. First off, for both labs the hanger hit the floor before the cart could be stopped, this caused the cart to slow down mid-trial and therefore introduced another origin of doubt into the results. The Second area of doubt is that for each mass, only one trial was performed. As stated in class, anything can happen just once, in order to disprove notions of a fluke, you need to perform multiple trials. Our Group was not given the opportunity to do so. Our 2 biggest areas of uncertainty were the Hanger hitting the floor before the cart and the lack of Trials.
How to Improve the Experiment:
- Firstly, having more trials throughout the experiment is the biggest suggestion for improvements. It will eliminate a big area of uncertainty encountered by all groups. Also, improvements regarding the actual pulley System itself will significantly improve the experiment. The first improvement would be to set it up to a height where the cart could reach the end of the track and the hanger not hitting the floor. Another improvement would be to increase the divot of the pulley system's wheel. The divot in which the string sat proved to be not deep enough as it came off of the wheel every trial. Therefore increasing the walls of the wheel could help to remove uncertainty from the results.
Whirly Durly Lab: Conducted by Aditya Tipre, Leyton Schroff, Edward Li:
Research Question:
- What affect does velocity have on the acceleration of an object moving in a circular clockwise motion.
- Independent: Speed (amount of rotations per minute)
- Dependent: Acceleration (meters per second^2)
- Controls: Radius and Mass of object
- In terms of materials, we were given an object, some string, a meter stick, and a metronome. Using the meter stick, we measured 0.5 m, and made a mark. That radius was going to be kept constant for all 5 trials. Then, we turned on our metronome and set it to our desired BPM. Leyton then turned on his phone, and got his timer ready. Edward got ready to count the rotations. After getting accustomed to the speed of the metronome, Aditya gave Leyton the sign to start his timer for some amount of seconds. During this time frame, Edward counted the amount of revolutions that occurred within the seconds. Edward then toke note of the revolution in an excel sheet. The three of us then used our excel sheet to convert the unprocessed raw data to processed raw data. Following that, we plotted the points in logger pro.
- Record the mass of the object (20 g)
- Record radius
- Set metronome to a desired pace (BPM)
- Had one person (Aditya Tipre) spin the mass in a clockwise motion at the rate set by the metronome, while Leyton Schroff for timed for x seconds, and Edward Li counted the the amount of rotations that occurred in those seconds.
- Edward Li recorded the data and calculated the acceleration.
- This process was repeated 5 times
Unprocessed Raw Data:
Further Calculations:
- Found speed using the following formula.
- For acceleration, we used Newtons law Fnet=ma. During circular motion, when an object is swinging by a string, the net force acting on the object is its tension force. Therefore, for this situation acceleration = Tension force/mass.
- Processed Raw data
NOTE: Speed and Acceleration were calculated using the processes explained in the FURTHER CALCULATIONS SECTION:
- Graph
f
Graphical Analysis:
- For the graph, we decided to go for a proportional fit with the equation being y=Ax^2(A=1.474). This makes the most sense, as when you have no velocity (x=0), you will have no acceleration (y=0). The proportional fit makes sure the line goes through the point (0,0). Therefore, making it the most sensible choice for this type of situation. Since it is a graph with x^2 the slope is ever changing, however, as clearly shown by the graph, the slope is positive for all x in the domain. This certifies that relationship between speed and acceleration, is a positive and proportional one. Essentially, as speed increases so to does acceleration.
NOTE: THROUGH THIS EXPERIMENT THE FOLLOWING EQUATION WAS DERIVED
Conclusion and how results of lab apply to general case:
Evaluation of procedure:
- Through performing this lab, we learned about how speed affect acceleration in an object. As seen by the graph, the relationship between the two is both positive and proportional. As speed increases so does Acceleration. This is not only indicated by the upwards slope of the trendline, but also by the table. As the speed increases, so to does acceleration. In our five trials, we increased the speed each time, hence why the relationship was both Positive and proportional. However, in the general case, this relationship is proportional. This holds true because the inverse is also true (Meaning if Speed decreases so will acceleration. Essentially, through this lab, we are studying centripetal acceleration. The formula for centripetal acceleration is Ac=v^2/r. Where v= speed (Velocity), and r is the radius of orbit. The equation backs up the result found in the experiment. For the sake of this lab, we kept radius at a constant length of 0.5cm, so r is staying the same. The experiment only dealt with speed (v) and how it relates to Centripetal Acceleration. Therefore, for this experiment the affect of r on Centripetal Acceleration does not need to be discussed. As seen in the equation v is in the "numerator part" of the equation, hence, an increase in v leads to an increase in Centripetal Acceleration, and a decrease in v leads to a decrease in Centripetal Acceleration.
Evaluation of procedure:
- Our planned procedure was solid, and in my opinion a perfectly good plan of action. However, like most things the theoretical didn't match up with the actual. First off, the timing. Often, Leyton would start the timer 1 to 2 s after Edward said go. In the directions for the assignment, we were only supposed to spin the object for 15 seconds, however, Leyton kept the timer on for varying amounts of time. As time went on, It was difficult for Aditya to keep the mass swinging at the constant rate. Additionally, Edward would occasionally lose counts and give us estimates of how many resolutions occurred. The group also had limited trials, only 5. All of these contributed to our low confidence in the results. We are confident with the relationship found, however we are not confident in our numbers.
- In my opinion, increasing the amount of trials would be extremely beneficial to the experimenter's confidence. In addition to more Trials, I would suggest involving more trials with different controls and different I.Vs. For example, for our first set of trials, radius would be kept constant, and in the second set velocity kept constant. Just so we as scientists can see how different variables affect an objects centripetal acceleration. By comparing this results, we can have increased confidence in our findings about the affects of different variables have on Ac.
