Position, Velocity and Accleration in a Fan-Cart. Regina Bochicchio, Michelle Obama, Hillary Clinton September 11, 2013. Purpose.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Regina Bochicchio, Michelle Obama, Hillary Clinton
September 11, 2013
The first purpose of this lab was to prove or disprove the hypothesis that, for motion with increasing speed in a positive direction with constant acceleration, the magnitude and sign of the acceleration is identical to that of the slope of the velocity time graph for the motion.
A second purpose was to investigate the best-fit curve for the position time graph made by the fan-cart and find out whether the coefficients of the corresponding equation represent any part of the actual motion.
If an object moves with constant acceleration, it’s velocity will change by the same amount every second. The resulting velocity time graph is linear. The slope of the velocity time graph can be obtained by using the “rise over run” formula. Since velocity is on the vertical axis and time on the horizontal axis, this value can be calculated using the formula Δv/Δt, where the bold indicates this is a vector.
The acceleration vector is defined as the rate of change of velocity (Cutnell, 2013). This value can be calculated by Δv/Δt. If this is true, then the average magnitude and sign of an object’s acceleration, should be equal to the to the slope of the velocity time graph.
EQUIPMENT: Motion detector, USB cable, computer, Logger Pro software, cart, track, fan attachment with 4 AA batteries, additional mounting bracket and elastic band (not shown below).
The lab setup is shown below:
Fig. 1: The track, cart with fan attachment and motion detector was set up as shown for this experiment.
Fig. 2: Velocity and acceleration graphs for fan cart speeding up in positive direction.
This graph shows the slope of the velocity graph taken from the linear-fit function. The value is 0.2919 m/s/s. Mean value for the corresponding section of the acceleration graph is 0.2938 m/s2 .
|0.2938 m/s2 - 0.2919 m/s2 |_________________________
These numbers are very close in value!
Fig. 3: Position-time graph for fan cart speeding up in positive direction.
The best-fit curve for the position-time graph showing increasing speed in the positive direction is quadratic. The error term generated by the software (Root Mean Square Error) is .001, showing a very good correlation with the actual graph. The equation of this best-fit curve is:
x = 0.1499t2 + 0.3273t + 0.3241
Fig. 4: Position and velocity graphs for fan cart speeding up in positive direction.
A comparison of the “B” term for the position-time graphs shows it to be very close to the y-intercept value of the velocity graph for the same motion: 0.3272 vs. 0.3318 m/s. This latter value indicates v0of the fancart.
x = At2 + Bt + C, where B represents v0, the initial velocity of the object.
Cutnell, John D. and Kenneth W. Johnson. Physics.
New York: John Wiley & Sons, 2013 ed.