UNIT 1
AP Physics 1 - Mr. Frost G Block
The following Section is devoted to my labs that we perform in AP Physics 1 during the first unit. Each will be organized here in chronological order.
BUGGY LAB 09/14/21
Jack Hughes, Leyton Shroff, Eddie Li
Research Question and Introduction
Before performing the Buggy Lab, our group came up with the following research question:
How does time affect position?
Variables
In order to discover the answer to this question, we first had to classify our variables. The independent variable we chose was time, and the dependent variable that we wanted to measure was position. It was important to make sure our experiment was properly controlled in order to ensure the accuracy of the results. The controls of our experiment were the surface our buggy moved on, using the same buggy for each data point, the initial position of the buggy, and performing each measurement in the same environment.
Ensuring that each variable was properly controlled was very important in order to isolate the relationship between our independent variable and dependent variable. Controlling the buggy that we used in the experiment as well as the surface that the buggy travelled on was relatively simple. We just kept track of our own buggy without sharing, and we allowed the buggy to travel on the tile floor and nowhere else. We did not leave the classroom, so we also maintained constant environmental factors. In order to use the most precise starting point as possible, we marked a point on the floor and had the buggy start from that point every time.
Data Collection
In order to collect our data, we used a stopwatch to keep track of time and a meter stick in order to measure the change in position of the buggy after a certain amount of time. Because we wanted to discover how time affects position, we let the buggy travel for a given amount of time that was calculated by the stopwatch, and then measured the change in position with our meter stick. This allowed us to plot our data with position as a function of time and point us towards a possible conclusion for the experiment and answer the research question.
Procedure
We measured the position of the Buggy from the starting point after a set amount of time
We used a stopwatch to calculate time (seconds)
We used a meter stick to measure the change in position from the starting point in centimeters
See next page for diagram
Presentation of Data
(See next page for photo)
The data recorded during this lab did not need any further processing, seeing as time was recorded using a stopwatch and the position was measured from the same beginning point (0). This means that the raw data is synonymous with the processed data for this experiment. The uncertainty for the measurements were limited; one person was responsible for timing each trial, and one person was responsible for taking the position measurements. The uncertainty for each trial relates to the reaction time of the timer and accuracy of when they stopped the car to be measured. The timing could have been between hundredths of a second off, and the accuracy of each measurement was limited by the accuracy of our meter stick and human error.
Graphical Analysis
(See next page for photos)
x= 15.04t - 10.39 (x,t) (position [cm], time [sec])
Xf = v*Δt +xi (Formula for position)
The slope of the line of best fit can best be interpreted as the change in position in one second. This means that every second, the position of the buggy changes 15.04 centimeters. Furthermore, we concluded that the velocity of the buggy was 15.04cm/sec. The y-intercept of the line of best fit is -10.39, which means that the model predicts at 0 seconds, the position of the buggy will be -10.39 centimeters. This shows that our data was not entirely accurate, because the position should be 0 cm when time is 0 sec, but it is just the y-intercept of the model.
Conclusion
The buggy travels at a constant speed, and so the distance the buggy travels is directly related to the amount of time it travels. We discovered that the equation for position was Xf = v*Δt +xi , and I was able to use the slope of my line of best fit of the data to conclude that the velocity of the buggy in our lab was around 15.04cm/second. The change in time was what affected the distance travelled for the buggy when the velocity was constant, and due to the fact that the starting point was held constant, my lab group was able to calculate the final position of the buggy by labeling our starting position as 0 centimeters and simply measuring the distance. Velocity multiplied by time has a direct influence on the position of an object, and this can be related to the calculation of any of the variables in the equation for any other scenario where time, position, and velocity are factors. It can also be applied that for the position of an object moving at a constant velocity over time, its model will be approximately linear.
Evaluation of Procedures
There were some sources of uncertainty for the data collected in this experiment. The reaction time of our timer, Leyton, could have affected the stopping distance of where we measured the buggy from the initial position. His human error in the stopping and starting of the stopwatch is worth noting because it could have affected the accuracy of the data regarding the distance traveled in a certain amount of time. It could have thrown off the distance we measured by more than we were supposed to or less than we were supposed to, so it had a strong effect on the variability of the data.
Another source of uncertainty in this experiment was the fact that our buggy was visibly slower in some trials than others. It could not be pinpointed why the buggy was varying in its power output, but it could have had an effect on the accuracy of the data.
The third source of uncertainty for the experiment was the accuracy of our measurements for distance. I used a meter stick to measure distances that were much larger than 100 centimeters, so I had to mark and move the meter stick on multiple occasions. It is quite possible that during some of these trials our measurements were not as accurate as we would have liked.
Improving the Investigation
In order to improve the accuracy of the investigation, we could have done a few things better. Instead of using a meter stick that was not long enough to record our position change, we could have used a larger tape measure that we would not have had to move so much in order to get a correct measurement. Also, we could have used a timer instead of a stopwatch so that the timing was calculated accurately and the only degree of uncertainty would be when the buggy was stopped and not when the timer shouted out “stop.” This would have made our data more accurate and could have led to more accurate findings regarding the velocity of our buggy.
BUGGY LAB PHOTOS
These are the photos for the buggy lab
CART ON RAMP LAB
Jack Hughes, Gabby Shapcott, Andy Chen, Eddie Li 09/24/21
Research Question and Introduction
By performing the Cart on Ramp Lab, we wanted to answer the following research question:
How does time affect the position of a cart on a ramp?
Variables
In order to answer this question, we first classified our variables. The independent variable was time, and the dependent variable was the position of the cart. We wanted to control other variables in this experiment to explicitly determine the relationship between time and position, and not have any other factors influencing the experiment. The controls of our experiment were using the same cart in our videos, the angle of the ramp, having the same person release the cart each time, the initial position of the cart, not recording any data until the cart had left the releasers hands, and not recording any data after the cart had touched the receivers hands, and maintaining a constant environment for the experiment.
Ensuring that each variable was properly controlled was very important in order to isolate the relationship between our independent variable and dependent variable. The use of one person to release the cart made sure that each release was as similar as possible. By keeping a marked initial position of the cart, it ensured that regardless of which video group members analyzed, the results would be similar. We also did not record any data while the cart was touching anyone’s hands, in order to make sure each data point corresponds to the motion of the cart. We did not leave the classroom, so we also maintained constant environmental factors.
Data Collection
In order to collect our data, we used foam blocks to hold up a phone and record a video of a cart moving down a ramp. We used a meter stick so that we could scale our video with logger pro, and recorded a video of this experiment. Logger pro’s video analysis feature was what we used to create our data.
Procedure
Video the cart moving down the ramp
Use meter stick to scale video
Use logger pro software in order to create and analyze data.
See Diagram
Presentation of Data
The raw data for this lab would be our initial video of the cart moving down the ramp. It has no values other than the time of the video, but was able to be manipulated using logger pro’s video analysis software to give us some data points.
The processed raw data was calculated through the use of logger pro. I set my axis as the length of the track, and the origin as the front of the cart in the video. I adjusted the data time and the video time so that 0 seconds for my data aligned with the exact frame that the cart was released. Also, I used the meter stick to calibrate the distance in the video. Upon the movement of the cart, I was able to plot points of its movement frame by frame until just before it was touched by the receiver at the end. The software recorded the horizontal and vertical positions in relationship to my origin as well as the horizontal and vertical velocity over time. (See Data Table below)
Graphical Analysis
ΔV/Δt=a (Acceleration formula)
Vf= a*Δt + Vi (Final Velocity)
x= -0.1047t² - 0.2491t + 0.04811 (Position/Time)
V= -0.04161t - 0.3057 (Velocity/Time)
(See Graphs below)
The slope of the curve of the position vs. time graph can be interpreted as the velocity. The slope is getting steeper due to the quadratic nature of the curve, and this means that the cart is speeding up over time. The cart is also moving in the negative direction. The y intercept of the position vs. time graph is 0.04811, which means that the model predicts at 0 seconds, the position of the cart will have travelled 0.04811 meters. This shows that our data was not entirely accurate, because the position should be 0m when time is 0 sec, but it is just the y-intercept of the model.
The slope of the velocity vs. time graph can be interpreted as the acceleration of the cart on the ramp. This means that the cart accelerates at a rate of about 0.04161m/s² in the negative direction. The y intercept of the graph details that the initial velocity of the cart is expected to be -0.3057m/sec. This reflects the uncertainty in the data because when the cart is not moving yet at zero seconds, the velocity should be zero.
Conclusion
By reviewing the graphs of my data and creating lines of best fit, I can conclude that the position of a cart on a ramp is affected by the acceleration of the cart and time spent accelerating. Because the ramp for our cart was less steep than the others, it is highly likely that our acceleration was less than other groups, and that our cart spent more time on the ramp than most. The acceleration of the cart influenced the time it took to travel down the ramp because in our case it was a constant increase in velocity/ time. The larger the acceleration, or the more steep the curve, the less time that the cart will have to travel to achieve the same position on the graph.
Evaluation of Procedures
There were some sources of uncertainty for the data collected in this experiment. The accuracy of the data collected by the software was much more accurate than using our own judgement, yet the judgement of selecting my points on the software could have been inaccurate. The video was really hard to pick exactly where the front of the cart was and it was a little blurry.
Another Source of uncertainty for this experiment was the fact that the software only recorded at a rate of 30FPS. This is very accurate, yet is still another source of error. It creates a very small degree of uncertainty to the data.
Improving the Investigation
In order to improve the accuracy of the investigation, we could have done a few things better. One major improvement that we could have had for this experiment was having a higher quality camera with more resolution record our trials, as well as have the classroom properly lit so the cart’s movement is much clearer. This could involve professional lighting and a very slow motion camera (and be very expensive) but it could improve upon my results.
CART ON RAMP LAB PHOTOS
These are the photos for the cart on ramp lab
UNIT 2
AP Physics 1 - Mr. Frost G Block
The following section is devoted to my labs that I will perform in AP Physics 1 during the second unit. Each will be organized here in chronological order.
UNBALANCED FORCES LAB
By: Jack Hughes, Luke Treese, and Tyler Frojmovich
10/21/21
During the Unbalanced Forces Lab, our group had two research questions that we wanted to explore during two experiments:
Experiment 1: How does the acceleration of an object depend on the net force acting on it?
Experiment 2: How does the acceleration of an object depend on the mass of it?
To answer these questions, we used a pulley system with a cart and a hanger as well as various weights for our trials. Using technology, we made measurements of acceleration with different combinations of weight by either removing weight from one part of the system and adding it to the other, or just adding and removing weight from the total system. For ease of navigating, I will be detailing both experiments and naming them "Experiment 1" and "Experiment 2". We plotted our independent variable against our dependent variable in order to make a conclusion about the relationship between each in their respective experiments.
Variables for Experiment 1
The independent variable for Experiment 1 was the net force of the pulley system. The dependent variable was the acceleration of the cart, which was measured during each trial. We kept the total mass of the system constant throughout each trial and only changed whether the mass was on top of the cart or on the hanger. We also made sure to use the same cart throughout all of our trials to make sure that all of our measurements were accurate.
Variables for Experiment 2
The independent variable for Experiment 1 was the total mass of the pulley system. The dependent variable was the acceleration of the cart, which was also measured during each trial. The net force of gravity was kept constant because no mass was added to the hanger, only the cart. We wanted to measure the effect that increasing the mass of the cart would have on the acceleration of the cart. Throughout this experiment the same cart was also used to ensure accuracy.
Procedure for Experiment 1
The mass of the entire system was measured using a digital scale, including the hanger, the cart, and all other masses.
The cart was placed on a track and connected to a hanger by a string, which was attached to a pulley.
The cart was released from our hands and moved down the track while being pulled down by the force of gravity on the hanger.
The velocity of the cart was measured using a motion detector and logger pro software and by calculating the slope of the velocity time graph the acceleration for each trial was discovered.
During each of the 9 trials, the masses were moved in between the cart and the hanger to measure the different accelerations when the hanger weighed more or less.
The force acting on the cart was measured using the equation Force of gravity= mass x acceleration.
Procedure for Experiment 2:
The cart was placed on a track and connected to a hanger by a string, which was attached to a pulley.
The cart was released from our hands and moved down the track while being pulled down by the force of gravity on the hanger.
The velocity of the cart was measured using a motion detector and logger pro software and by calculating the slope of the velocity time graph the acceleration for each trial was discovered.
Masses were weighed and added to the cart during each of the 8 trials to get a variety of different measurements.
The force acting on the cart was calculated for each trial using the equation Fg=m*g
(For the a photo of the lab set up and photos labeled of processed and raw data for both experiments, please see the attached gallery)
Raw Data Methods
The raw data for the lab was measured and calculated using various different instruments. To calculate the mass of the cart, hanger, and other relevant weights, an electronic scale was used and it recorded the mass of the objects in grams The uncertainty of our measurements could be attributed to the accuracy of the decimal place to which the scale measures, so each mass is within about 1 gram of its true mass.
In order to discover the acceleration of the cart, we used a motion detector and logger pro to calculate a velocity vs. time graph for each trial, and discovered the slope of the line of best fit at the points in time where the cart was accelerating. Because the technology was at times shaky, the uncertainty could lie with the ability of the motion detector to truly measure the velocity of the cart.
Processing the Data
The first step that was taken was to convert the measurements taken in grams into kilograms in order to make our force calculations easier. This can be generalized to any of the masses recorded in both experiments.
kg mass= g mass/1000
1.5=1500/1000
All of the masses had been converted to kilograms in order to perform the force calculations. Because all of the other forces were negligible in this case, we wanted to try and measure the force of gravity.
We used the equation Fg= mass x acceleration. The acceleration of gravity is about -10 m/s/s, and so for each calculation we plugged in the mass of the hanger to calculate the force acting upon the cart.
Fg = mass x acceleration
Fg = mass x -10
0.5= 0.05 x -10
(See the corresponding photo gallery for the labeled graphs)
Graphical Analysis Experiment 1
y=ax (proportional fit)
acceleration=0.5359(Net Force)
The fit used for this experiment was a proportional fit because the data appeared to have a strong linear association when plotted and it was concluded that the y intercept should be (0,0) because the acceleration of the cart will be 0 m/s/s when there is 0N of net force acting upon it to change its motion: this is because of Newton's first law. The slope of the best fit line, 0.5359, can be interpreted that for every 1N increase in net force, the acceleration of the cart will increase by 0.5359 m/s/s. Through this experiment, it was determined that acceleration is proportional to the net force acting on the object, and that the acceleration was equal to the net force times a constant value.
a= c x net force
Graphical Analysis Experiment 2
y=a/x (inverse model)
acceleration (m/s/s) = 0.3871/total mass (kg)
After trying a power model to represent the data, it was later discovered in the board meeting that an inverse model would be best to represent the data. There is no x and y intercepts for this fit, and the acceleration approaches infinity as total mass approaches zero, and the total mass approaches infinity as the acceleration approaches zero. It is important to note that when the total mass reaches a certain number, the acceleration of the system will be zero, but this is not represented by the model. Through this discovery, it can be concluded that there is an inverse relationship between the total mass and acceleration of an object, and the more mass that an object has, the more force that is needed to accelerate it. This is Newton's second law:
acceleration=net force/mass.
Conclusion
After performing both experiments and graphing our trials on logger pro, it was discovered that acceleration is proportional to the amount of net force acting upon the object, and acceleration is inversely related to the total mass of a system. From these conclusions, the equations for Newton's second law can be derived. The mass of the system in our first experiment was 1.68 kg, and because a= c(net force), it can be concluded that this value is 1/mass. The slope of the data for experiment 1 is about 0.54, which is very close to the calculated value of 0.595. The inverse relationship between acceleration and mass is reasonable because of the law of inertia, which states that objects are harder to accelerate the more mass that they have.
net force = mass x acceleration
acceleration= net force/mass
mass= net force/ acceleration
This lab could have used a number of different experiments in order to establish these relationships, and the results of these experiments are able to be used as knowledge for future calculations of mass, force, and acceleration that we may need to do in another lab.
Evaluating Procedures and Improvement
There were some sources of uncertainty that were previously mentioned in our methods of data collection. The accuracy of the scale could have affected the accuracy of our mass readings, and further affected the calculation of force for our trials. Also, despite the use of motion detector to calculate a velocity time graph for each trial, the readings were very messy and hard to interpret where the cart was truly increasing in velocity. It is possible that when creating a line of best fit for some of the velocity time graphs there was human error in recognizing which values should be included in the line of best fit. The slope of the best fit line was acceleration, and although no calculations were made using acceleration, it could have affected the accuracy of the data points and the values in the best fit models for both experiments.
One possible improvement to this experiment in the future would be to start the cart further away from the motion detector so it can get a more accurate reading without a crash in the beginning because it is too close. This would improve the accuracy of the acceleration for each trial and would make the data more precise.
UNBALANCED FORCES LAB PHOTO GALLERY
UNIT 3
AP Physics 1 - Mr. Frost G Block
The following section is devoted to my labs that I will perform in AP Physics 1 during the third unit. Each will be organized here in chronological order.
WHIRLY DURLY LAB
Jack Hughes, Matt Singer, Luke Treese
The main purpose of our Whirly Durly lab was to discover some factors that could affect "turning acceleration. Our group identified various factors of interest such as velocity, acceleration, radius length, mass of the tube topper, and using the same system for each one of our trials
After some discussion with my partners, we concluded that the best way to explore some of these factors was to explore the relationship between the velocity and Acceleration in a system.
Selection of Variables
We decided that the independent variable that we would measure would be velocity of the test tube topper, and the dependent variable for our experiment would be the acceleration of the test tube topper.
Control of Variables
The variables that our group wanted to make sure were adequately controlled was the radius length of the string that would be swinging the lab topper, as well as the mass of the lab topper. by marking the string with a orange marker, we were able to make sure that we swung the topper from that point each time, and we used the same topper for each trial so the mass remained constant. In order to keep the measurements consistent, we also measured the time for 20 rotations each trial.
The Procedure
In order to carry out an experiment that would accurately help determine the relationship between velocity and centripetal acceleration, we devised a plan that kept our controls constant, and would allow us to measure the velocity and acceleration for the lab topper.
1) Record the mass of the topper and the radius of the string into a spreadsheet, which will remain constant across all trials.
2) Mark the radius length as 0.5 meters with a marker and measuring the string with a ruler.
3) Attach a lab topper to one end of the string with paperclips.
4) Attach the other end of the string to a force detector which hooks up to logger pro software.
5) Using google metronome software, we were able to establish a pace for which the topper would be swung overhead.
6) Once the person swinging the pace of one rotation per beat, the timer would start and the force sensor would be activated.
7) Once the swinger had performed 20 rotations, the timer stopped the stopwatch and the force detector.
8) Record the raw data of Net Force, Time, metronome, and repeat for five different metronome BPM trials.
(Photos are attached in the Lab Gallery displaying our materials and the lab in action. The procedure is a bit long because I cannot accurately label the photos, so I just described the materials here)
Data Collection
The radius of the system was measured using a meter stick to be 0.5 meters. In order to discover the mass of the topper, we used a tabletop scale that would accurately measure mass, which was 0.019 kg. In order to discover the Net Force for the system, we used the force sensor and the logger pro software. The time that it took the swinger to complete 20 rotations was timed using a stopwatch, and the metronome data was easy to collect because we were able to set the computer to whichever value we needed.
Recorded Raw Data
(See Whirly Durly Lab Gallery for a detailed photo)
Processed Raw Data
(See the Whirly Durly Lab Gallery for a detailed photo)
In order to convert the values of our raw data into our independent and dependent variables, we used the spreadsheet software to repeat our calculations many times over. The basis of finding the acceleration was our Newton's second law equation Net Force = Mass x Acceleration. Because we had calculated the net force and mass of the topper for each trial, by completing the equation Acceleration = Net Force/Mass, we solved for the acceleration of our trials.
a = 0.8/0.019 = 42.11 m/s/s
In order to solve for the velocity of the topper during each trial, we needed to use the definition of a period in order to calculate the distance traveled in a given amount of time. The circumference of a circle is calculated c=2(pi)r, and in order to solve how much distance was covered during the 20 rotations, it was
20 x 2(pi)(0.5) = 62.83m
We took this distance that we travelled for each of the trials and divided it by the time we calculated for each trial.
62.83m/11.55s = 5.44 m/s
Some important uncertainties to address is the time between 20 rotations actually being completed and the timer being stopped. This would affect the velocity calculation for each trial. Also, the interpretation of the force sensor graph could have affected our calculation of the net force, which in turn would have affected our acceleration calculations.
Graphical Analysis
(See the Lab Gallery for an image of the graph)
The Graphical plot of our acceleration vs. velocity graph was best fit by a proportional quadratic fit y= Ax^2. We discovered this fit in class, and it helps us determine a relationship between the velocity and acceleration in circular motion. The x^2 represents the velocity because it is the independent variable, so we deduced the x^2 to be equal to v^2. The coefficient in the best fit equation was determined to be 1 divided by the radius of the system, although our calculations had some errors in them.
We derived the relationship between acceleration and velocity to be:
a= (1/r)v^2
for circular motion. This is the equation for centripetal acceleration.
Conclusion
By completing the Whirly Durly Lab, we were able to determine the relationship between centripetal acceleration and velocity for circular motion. This relationship can be expressed as ac= (1/r)v^2. Through our procedure and processing our data, we were able to determine this relationship. Because the x value (independent variable) is velocity, the x^2 in our best fit equation can be determined to be velocity squared. Through help from Mr. Frost (was not in class that day) we discovered that the A constant was 1 divided by the radius of the system. This relationship can be used in order to calculate some of our physics problems and help us discover other unknowns.
Evaluation of Procedures/Improvements
There were many different ways that the lab could have been improved in my opinion. First of all, performing the lab in an area that had much more space would have allowed us to perform more trials without a risk of hurting others because we could have used higher BPM metronomes and got a larger range of values. Also, we could have performed more trials in order for the data to be more precise and to discover any mistakes we could have made in the trials and conducted repeat trials. As for the measurement, the stopwatch timer could have been inaccurate because of human reaction time, and it affected our velocity calculations which made them less accurate. This human error must be acknowledged. Also, having a better method of reading the force sensor data could have led to much more accurate calculations. In conclusion, there was lots of uncertainty in the lab that could be mitigated next time it is performed.
