One Dimensional Motion-1

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New Jersey Institute Of Technology *

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111A

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Physics

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Apr 3, 2024

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Physics Laboratory Report Lab 109: One-Dimensional Motion Name: Cristopher Guaman Group ID: 4 Date of Experiment: 09/22/2022 Date of Report Submission: 09/29/2022 Course & Section Number: 111A005 Instructors Name: Thomas Gilman Partners Name: Isabella, Jefferin, Khalid Introduction OBJECTIVES: Preforming this experiment, we were able to understand the relationship between initial velocity (Vo), time (t), final velocity (V), acceleration (a), and displacement (Δ x or X-Xo ). We isolated these factors into a one-dimensional moving object where we eliminate and ignore the effect of friction. The information was gathered using photogates, lasers that measure the time and velocity at a point, we produced graphs analyzing final velocity (V) vs time (t) and final velocity squared (V 2 ) vs time (t). THEORETICAL BACKGROUND: Given the equations: V=Vo+at and V 2 = V o 2 +2 a Δ x we can plug in our information gathered from the experiment to calculate for a. We know velocity is measured by distance covered over time as seen in miles per hour. For this experiment our velocity was calculated by the equation V=Δ x/ Δ t. Δx representing the change of position divided by Δt ; representing the change of time over the change in position. We can rearrange the equations V=Vo+at into a=(V-Vo)/t to calculate for acceleration. Acceleration or deceleration is the change of velocity given an interval of time.
Experimental Procedure: The image below represents the basic set up of the experiment: The drawing on the top is the representation for experiment 1 The drawing on the bottom is a representation for experiment 2 For experiment one : The air track was place at an angle of 6 degrees measured from the top of the air track. One photogate was positioned at .3 meters and the second photogate at .6 meters. We measured the time at first photogate and second gate and velocity at each photogate using the software provided. We ran each trial 3 times and determined our values with their average. The second photo gate was changed in intervals of .3 meters until the 1.8 meters was reached. Each time it was ran 3 time and averaged to use that value. With these values a graph was plotted: final velocity (V) vs time (t) and final velocity squared (V 2 ) with time (t).
The height, angle, friction, glide and photo gates remained constant for this experiment. All these variables being our controlled variables. The independent variable is the distance between the photogates and the dependent variable is the final velocity. For experiment two : The air track was place at an angle of 6 degrees measured from top as experiment one. The photogates were removed, and acceleration device was place in the front of the air track as displayed above. We used the software provided and we were given graphs of position vs time and velocity vs time. The height, angle, friction, and glider remained constant for this experiment. All these variables being our controlled variables. The independent variable is the distance between the of the air track and the dependent variable is the acceleration. RESULTS: Experiment 1 Length of the flag: .799 m Position of the 1 st photogate (m) Position of the 2 nd photogate (m) Distance between the photogates (X axis ) Time at photogate 1 T 1 (s) Time at photogate 2 T 2 (s) Time between photogate 1 and 2 Δt (s) Velocity at photogate 1 (v) Velocity at photogate 2 Acceleration (m/s s ) 30 60 30 0.117 0.0731 0.3683 0.68293 1.09286 1.112840 30 90 60 0.1165 0.0576 0.6262 0.66626 1.388666 1.15362504 30 120 90 0.1167 0.0494 0.8266 0.68466 1.6186 1.129803621 30 150 120 0.1177 0.0439 1.0063 0.67966 1.819633 1.13275479 30 180 150 0.1172 0.0399 1.16596 0.6826 2.0069 1.135795763 Experiment one Results
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The graph 1: Final velocity vs time Velocity Squared vs Time 0 0.5 1 1.5 2 2.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Final Velocity m/s Time Final velocity vs Time 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Final velocity squared Displacement Velocity squared vs displacement
Experiment 2 Above graph displays position vs time The below graph displays Velocity vs Time Calculations Experiment 1:
Experiment 2:
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Percentage error Actual Acceleration Average Acceleration from displacement Acceleration from Velocity vs time graph - experiment one A =g sin θ 1.22 m/s 2 1.1357 m/s 2 1.1472 m/s 2 1.024 m/s 2 Percent error 11.23% 5.96% 16.06% Analysis and Discussion The actual acceleration of the experiment was provided through the second experiment. The graph “ velocity vs time ” provided to us by the software gave us the acceleration through the linear regression equation. The slope of the linear equation is the acceleration. This is explained by the equation: m = (Y 2 -Y 1 ) / (X 2 -X 1 ). M being the slope, Y being the velocity and X being the time. We know acceleration is equal to (V-Vo)/t. The slope of this graph is that equation. We had the same graph of velocity vs time from experiment one. The slope retrieved from the liner regression equation is 1.1357 m/s 2 . The error percentage given this calculation was 5.96%. This a justifiable number because the density of air played a factor to slow down the glider. It can also be explained by human error, when releasing the glider, we could have pushed it just enough to shew with the results.
Another theoretical value was given through the equation a=gsin θ. Where g was the force of gravity and theta the angle. It was found that the velocity from this equation was 1.024 m/s 2 giving us a 16.06% error percentage. The last way we formulated a theorical acceleration value was find the average of the accelerations we calculated for in experiment one. The theoretical value was 1.1357 m/s 2 giving us a 11.23% error percentage. This again is justified by the reasons listed above. The results met the goals we had for this lab. We found the relation that acceleration was with many different factors. Acceleration can be acquired by the change in velocity over the time and from graphs. Conclusions Acceleration can be computed for in different manners. A linear regression line’s slope provides us the acceleration of an object when the y axis is labeled as velocity and the x axis as time. The acceleration caused the final velocity to increase as the displacement was greater. We can prevent these types of errors in the experiment by isolating the experiment into a chamber with a controlled air quality. We need to release the glider with a tool rather than our hands to prevent another force influencing the initial and final velocity. The photogates need a improved manner to measure it’s distance. We had a relative number to the one we desired, but it was not 100 percent sure we were there. It must be questioned the effect that air density has on moving objects. Will it change at different altitudes?
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