ABSTRACT
This lab involves the measurement of a vehicle undergoing acceleration. Galileo Galilei was the first to analyze the motion of an accelerating object, creating many laws of physics and contributing to Newton’s works. The reason for doing this lab was to reproduce one of Galilei’s many experiments with modern equipment, making the experiment easier to reproduce. The modernized equipment used was a picket fence of markings on the car going down an inclined slope, and a computer with an attached measurement tool that measured the amount of black markings of the picket fence as the car passed by. This data was then inputted into graphing and measurement analysis software on the computer and several automated measurements and graphs were generated. The graphs were representative of the cart’s position, speed, and acceleration.
MATERIALS
1. Motion Cart
2. “Frictionless” Track
3. Computer
4. Science Workshop Interface
PROCEDURE
The majority of the lab was set up for us when we had arrived at the lab site. The frictionless track had been set up with a textbook underneath the track itself. A motion cart with the picket fence attachment was set up on the frictionless track. Above a section of the frictionless track, a measuring device was set-up that measured the times the black markings “pickets” passed a certain point by. This contraption was connected to a power converter which was connected to the computer via USB. All that was required by us was to log on to the computer and run the Science Workshop Interface. We created a new experiment in the software by classification photo gate & picket fence. From here we made sure the connections were set up correctly and proceeded to click on the graph section. We clicked on the photo gate icon and selected that we wanted the graph for Acceleration, Position, and Velocity. Then we tested the car running down the track. We had a timer press the button on the computer to make sure the timing was accurate for the time the car passed under the picket fence measurer. There was another person who helped the timer by stating when the car was released and when the car had passed through the measuring mechanism. This part of the experiment of measuring the time it took for the car to travel through the photogate was repeated 3 times, although the data for the first two times was discarded as the procedures given were unclear as to when we stop the timer. The first time we had stopped the timer as the car stopped at the end of the track. The second time, our timing for the seconds passed when for the distance that the car was under the photogate was inaccurate to the point of the measurement being insignificant. After the taking of the third trial, we set the computer to automate a series of results of data based on the 1 set of data we had received. The Science Workshop Interface simulated the experiments again with similar data as inputted after we selected the linear fit for the velocity and acceleration graphs and the quadratic fit for the position of the car. Relating to the data shown by the experiment software, we were able to form an analysis as well as equations for the data chart.
RAW DATA
See attached graph sheets
ANALYSIS
Analysis Questions:
1. Equation for best fit line for velocity as a function of time:
We have to look back at the graph and find the slope (m), y-intercept (b) and form an equation for the velocity as a function of time:
Y=.24x+.03
2. Slope of the velocity vs. time graph
This is found using the difference of 2 points in terms of y & x, in that the slope is equal to the rise /run giving us
.24
3. How is velocity affected by time?
The velocity is increased by time constantly. This statement can be affirmed by viewing the raw data chart 1 of the velocity and concluding that the velocity increases as the time increases.
4. Equation for best fit best fit line for acceleration as a function of time:
a= .01x+.25. Again, this equation is solved by calculating and using mx+b equation form from the graph data sheet acquired from the Science Workshop.
5. How is acceleration affected by time:
Acceleration remains constant in relation to time. The acceleration graph remained steady, in a straight line, as time increased, because there was no other outside force acting on the car, i.e. pushing the car, besides the decline acting on the car at a steady rate of acceleration.
6. How does the graph/equation of acceleration as a function of time relate to the graph/equation for velocity as a function of time?
The slope of the velocity is similar to the y-intercept of the acceleration. BY comparing both values, we find that they correspond to each other, as they should.
7. Equation for best fit curve for position as a function of time:
P=.12t2 + .03t-.02. This is found by substituting values of the slope and y-intercept in the mx+b equation found on the third graph sheet
8. How is position affected by time?
As the graph shows, position increases in a quadratic manner as time passes. This can be seen as the velocity would be steadily increasing in accordance to the acceleration, causing the rapid increase of the position as the displacement of the car per second would increase with time.
CONCLUSION
This lab successfully taught us about the change in velocity, acceleration, and position of an object, and finding this using technology. Although we did not repeat acceleration, velocity, and position experiments as Galileo had, I understood the importance these conclusions of relationships between constant, linear, and quadratic and their effect on creating the shape of each other. Through the technology of a photogate and a computer to measure the average velocities, acceleration, and position, we were able to quickly and effectively see the difference of acceleration, velocity, and position, and its graphical significance over time. I certainly have learned what it must been like for Galileo, and the patterns and relationships that he noticed as he conducted these experiments without fancy and high tech equipment. For example, by viewing the graphs of the points on each of the average fits, we can see how the acceleration is the base, remaining constant, followed by the velocity. One relation noticed was that velocity was linear because the constant acceleration was the cause of the increasing velocity as the displacement was increased more per second. IF we take this velocity and multiply it by itself, we can achieve the position, which is graphed in a quadratic form because the linearly growing velocity is increased more by adding the distance the car goes per time interval, and this rate is two-fold for position, having the squared effect on the position versus time. Comprehension and connections were made as to how Galileo making his statements of a mathematical reference to science and the motion of an object under uniform acceleration, unprecedented until Galileo’s time. As useful and knowledgeable the lab was, the lab procedure could have been altered to give us more accurate results, and graphically visualize the results. A more accurate clock would have been far more useful in making the data, and the graph representing the average data more accurate. This clock, embedded in the Science Workshop Interface could be as accurate as the atomic clock, although such accuracy is not necessary for a lab experiment of this kind. Another change to the procedure that would have been useful for the experimenters would have been a clarification of the timing details. At first, we were not aware that we were only supposed to time the car for the time it passed under the photogate. Due to the ambiguity of the procedure directions, it first occurred to us to time the car all the way to the end of the track, which made our data full of error and insignificant.
