CART ON RAMP Lab Video analysis (9/24/21)- Katie, Carol, muskan
Research Question: How does time affect position of a cart on a ramp?
Variables:
-Independent variable= time
-Dependent variable= Position
-Control Variables= keep initial position the same,
Controls:
To maintain integrity of the experiment and collect data that is reliable and accurate as possible, we made sure to make our initial position at the top of the ramp, which we called 0 cm. To avoid inaccurate data, the person who let the cart go made sure not to exert any force onto the cart which would've made it go faster. Since we only did one trial and didn't do any measuring ourselves, there weren't many other controlled variables since we were only conducting the experiment one time.
Data Collection:
Since it would be very difficult and inaccurate to try to visually determine the position of the cart at different times as it went down the ramp, we set up a camera to record the cart going down the ramp. To insure the video had a measurement reference, we put a meter stick within the frame of the video, so when we uploaded it to the computer, it was able to give us data. Once the video was made (which was only a few seconds long), it was uploaded to LoggerPro, where we conduced a video analysis. The procedure of the video analysis is explained in more detail in the proceeding section.
Procedure:
1) To record the video, set up an iPhone camera in such a way that got the entire ramp and meter stick in the frame.
2)One person holds the cart at the top of the ramp, one person was at the bottom to catch the cart, and the other person is in charge of starting the recording.
3) When instructed, the person with the cart lets go, and let it slide to the bottom. When the video is topped, send to all lab members and upload to the LoggerPro application.
4) Create a new document and insert the movie.
5) Enable analysis of the video and sync graph to video, so time (t)= 0 lines up with the right part of the video.
6) Set the origin and the scale to obtain accurate data and provide a reference for the measurements.
7) Using the add points tool, click on a visible portion of the moving object at several seconds at each frame of the video to obtain data points. They should show up on the graph.
8) Finally, add a line of best fit to the graph and analyze.
*we only did one trial*
Diagram:
Variables:
-Independent variable= time
-Dependent variable= Position
-Control Variables= keep initial position the same,
Controls:
To maintain integrity of the experiment and collect data that is reliable and accurate as possible, we made sure to make our initial position at the top of the ramp, which we called 0 cm. To avoid inaccurate data, the person who let the cart go made sure not to exert any force onto the cart which would've made it go faster. Since we only did one trial and didn't do any measuring ourselves, there weren't many other controlled variables since we were only conducting the experiment one time.
Data Collection:
Since it would be very difficult and inaccurate to try to visually determine the position of the cart at different times as it went down the ramp, we set up a camera to record the cart going down the ramp. To insure the video had a measurement reference, we put a meter stick within the frame of the video, so when we uploaded it to the computer, it was able to give us data. Once the video was made (which was only a few seconds long), it was uploaded to LoggerPro, where we conduced a video analysis. The procedure of the video analysis is explained in more detail in the proceeding section.
Procedure:
1) To record the video, set up an iPhone camera in such a way that got the entire ramp and meter stick in the frame.
2)One person holds the cart at the top of the ramp, one person was at the bottom to catch the cart, and the other person is in charge of starting the recording.
3) When instructed, the person with the cart lets go, and let it slide to the bottom. When the video is topped, send to all lab members and upload to the LoggerPro application.
4) Create a new document and insert the movie.
5) Enable analysis of the video and sync graph to video, so time (t)= 0 lines up with the right part of the video.
6) Set the origin and the scale to obtain accurate data and provide a reference for the measurements.
7) Using the add points tool, click on a visible portion of the moving object at several seconds at each frame of the video to obtain data points. They should show up on the graph.
8) Finally, add a line of best fit to the graph and analyze.
*we only did one trial*
Diagram:
Recorded Raw Data: (recorded via LoggerPro Video Analysis)
Recorded Processed Data:
Since we only conducted one trial and only analyzed one video, there was no processed data inputted into the program.
Graph and Graphical Analysis:
Since we only conducted one trial and only analyzed one video, there was no processed data inputted into the program.
Graph and Graphical Analysis:
The first graph is a position time graph that shows the position of the cart on the ramp on different intervals of t (time in seconds). According to our best fit model, this data best represents a quadratic function with the equation X=-0.2118t^2-.12t-.0965. The y intercept is around -0.95, indicating that at t=0, the position is -.95, which makes sense considering that at t=0 position should theoretically be 0m as well. The slope is becoming steeper at time goes on, indicating that the velocity (which is shown in the second graph) is not constant. In the second graph, the velocity of the cart on the ramp is plotted against t (time in seconds). Here, we determined that the best line of fit for this model is in fact linear, with the equation of V=-.4x-0.1273. This indicates that the velocity is changing at a constant rate, meaning that the acceleration remains the same throughout the entire video. The velocity decreases, meaning that the speed is increasing towards the point of origin. There were 3 main equations that we derived from this lab. To find displacement of an object on a V-T graph, you must find the area of the equation underneath the curve/line. To do that, use the trapezoid method, where we split up the space under the curve into triangles and squares, then add the sum of the areas to find the displacement. That is how we derived the equation: Δx =viΔt+1/2aΔv^2, where Δx = displacement, vi= initial velocity, Δt= change in time, a= acceleration, and Δv= change in velocity. This is a useful model for a position/time graph. The second equation that was derived from this experiment is a model for a velocity time graph derived from y=mx+b. By generalizing the model and solving for Δt : vf=aΔt+vi, where vf= final velocity, a=acceleration, Δt= change in time, and vi= initial velocity. The final equation that came from this experiment doesn't need any information in time: vf^2=vi^2+2aΔx, where vf= final velocity, vi= initial velocity, a=acceleration, and Δx = change in position or displacement. This came from substituting information from the first and second equation to eliminate the variable Δt from the third equation.
Link Evidence and Conclusions
We used a tool with extreme precision to determine the position of an object at various times t. We see here in this experiment that velocity is not always constant and that the slope of that line is a newly presented term, acceleration. . We hypothesized that the cart would accelerate because the ramp was on an angle, but now that we have the mathematical and scientific evidence that that is the case, we can apply it to real world situations involving "ramps" such as a car rolling down a hill.
Conclusions
The purpose of this lab aimed to show how times affects position of a cart on a ramp, which was on an incline. This could be compared to the buggy lab, where the buggy was on a flat surface and there was no decline. Based on the position time graph created from a LoggerPro video analysis, we see that the cart's speed was not constant, as it was in the buggy lab, and was in fact speeding up. From this graph, we derived an equation for displacement. Using the data from the position time graph, LoggerPro created a velocity time graph for the cart's motion. From this we determined that the cart was accelerating. From there, we derived two other equations that outlined in more detail in the above section. Some key points that were highlighted in this lab were that sign of slope of a line determines the direction in which the object is moving, not its speed or acceleration. Speed (on a position time graph) and acceleration (on a velocity time graph) is shown by the magnitude of the slope.
Evaluating Procedures
Some of the weaknesses include the video itself. If it was too pixelated or blurry, Logger Pro might not have been able to completely provide accurate data. This blurriness, although potentially minimal in the original recording, might have lost some clarity in the transferring to LoggerPro. When setting the scale, origin, and syncing the video, there may have been some small errors that would alter the data. Further, since we had to select the same part of the cart and different frames in the video, if we potentially clicked not the exact same part each time, it might have thrown off the consistency of the data. In terms of the content of the video, if the person releasing the cart added any extra force, it might have changed what the initial velocity would have been. Since we used a video recording, we only conducted one trial. All these factors lead to uncertainty. However, we collected both a lot of data and a large range of it when on LoggerPro. Therefore, we are very confident.
Improvement
If I were to suggest a single improvement for the lab, I think using a longer ramp would prove useful. This way, we could collect an even larger range and amount of data, increasing our accuracy. The time the cart was moving was very minimal, and if it were a bit longer then we could find a more accurate model to represent it's motion.
Link Evidence and Conclusions
We used a tool with extreme precision to determine the position of an object at various times t. We see here in this experiment that velocity is not always constant and that the slope of that line is a newly presented term, acceleration. . We hypothesized that the cart would accelerate because the ramp was on an angle, but now that we have the mathematical and scientific evidence that that is the case, we can apply it to real world situations involving "ramps" such as a car rolling down a hill.
Conclusions
The purpose of this lab aimed to show how times affects position of a cart on a ramp, which was on an incline. This could be compared to the buggy lab, where the buggy was on a flat surface and there was no decline. Based on the position time graph created from a LoggerPro video analysis, we see that the cart's speed was not constant, as it was in the buggy lab, and was in fact speeding up. From this graph, we derived an equation for displacement. Using the data from the position time graph, LoggerPro created a velocity time graph for the cart's motion. From this we determined that the cart was accelerating. From there, we derived two other equations that outlined in more detail in the above section. Some key points that were highlighted in this lab were that sign of slope of a line determines the direction in which the object is moving, not its speed or acceleration. Speed (on a position time graph) and acceleration (on a velocity time graph) is shown by the magnitude of the slope.
Evaluating Procedures
Some of the weaknesses include the video itself. If it was too pixelated or blurry, Logger Pro might not have been able to completely provide accurate data. This blurriness, although potentially minimal in the original recording, might have lost some clarity in the transferring to LoggerPro. When setting the scale, origin, and syncing the video, there may have been some small errors that would alter the data. Further, since we had to select the same part of the cart and different frames in the video, if we potentially clicked not the exact same part each time, it might have thrown off the consistency of the data. In terms of the content of the video, if the person releasing the cart added any extra force, it might have changed what the initial velocity would have been. Since we used a video recording, we only conducted one trial. All these factors lead to uncertainty. However, we collected both a lot of data and a large range of it when on LoggerPro. Therefore, we are very confident.
Improvement
If I were to suggest a single improvement for the lab, I think using a longer ramp would prove useful. This way, we could collect an even larger range and amount of data, increasing our accuracy. The time the cart was moving was very minimal, and if it were a bit longer then we could find a more accurate model to represent it's motion.