Lab Report 2 - Experiment Two 2019 PDF

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Experiment Two 2019...

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Experiment 2: Motion 2 Alexandra Tananbaum General Physics I: Laboratory Fall 2019: Section 005 Instructor: Kulchoakrungsun Partner: Libby Tuesday, September 17, 2019 Due date: Tuesday, September 24, 2019

INTRODUCTION This lab studies the relationships between position, velocity, acceleration and time using a motion sensor connected to the Capstone program. A glider was moved along an air track that decreases the force of friction. A motion sensor tracked its position in order to measure position, velocity, and acceleration using Ping Echo Time. The effect on acceleration of two different glider sizes and two different angles of inclination, created by different sized blocks, was analyzed.

DESCRIPTION This lab measures the position of a glider on an air track using a motion sensor. 2 blocks were measured and applied to put the air track at a slight incline at a certain calculated angle. Using these and two different sizes of gliders and the two different inclinations, the position, velocity, and acceleration were graphed in respect to time in the Capstone program. The inclination and the size of the glider and the inclination level effected the three graphs differently as the glider progressed down the track. The slope of the velocity vs time was used to compare the way in which the gliders accelerated down the track under these different conditions. The three graphs were analyzed for accuracy as compared to how theory predicts it. The effects of the different passes and inclinations were monitored by each graph.

THEORY Position was given by x and the average velocity (v) was derived from it. Acceleration (a) was the double derivative of position. The position was measured as a function of time. 1

Together in one function yields: x = x0 + v0t +

1 at2, a quadratic equation, and v = v0 + at, a 2

linear equation. Friction was negligible, so Newton’s 2nd Law predicts that acceleration would equal g • sin θ .

PROCEDURE The experiment began with the Capstone set up and leveling of the air track. The distance between the single supporting screw at the center of the air track and the two supporting screws at the back was measured, which was found to be 100 cm. The thickness of the two supporting blocks that change the angle of the track were measured. These two supporting blocks were placed under the air track on separate occasions to create an inclination angle. The thicker block was 3.2 cm, which gave an angle of

θ = 9.442˚ when it was placed under the air

track, and the thinner block was 1.9 cm, which gave an angle of

θ = 8.639˚. The glider was

prepared by adding an index card to the end of it with two paper clips for the motion sensor to capture. The motion sensor did not work at less than 0.2 m, so the track was positioned 0.2 meters away and the motion sensor was angled slightly down to pick up the glider down the track. On Capstone, a position vs time, velocity vs time, and acceleration vs time graphs were measured simultaneously during the process. Two gliders were used, a small one and a large one. The large one was double the mass of the small one. The first five trials were of the smaller glider at an incline of θ = 8.639˚. The second five were of the smaller glider with an incline of θ = 9.442˚. The third were of the larger glider with an incline of

trial was of the larger glider with an incline of 2

θ = 8.639.˚ The fourth

θ = 9.442˚. For the fifth and final trial, the

smaller glider was used with an incline of

θ = 8.639˚, but the motion sensor continued to

capture data after the glider was let to bounce against the bumper at the end of the air track, rather than stopping it right when the glider hit the bumper. The graphs were then analyzed with a linear and curve fit.

DATA/CALCULATIONS Round 1 Small glider, small block (1.9cm) Angel Calculation: tan-1 θ = opposite / adjacent = 15.19/100 = 8.639˚ Trial 1 2 3 4 5

Acceleration (Mean) .125 .123 .123 .117 .119

Round 2 Small glider, large block (3.2cm) Angle Calculation: tan-1 θ = opposite / adjacent = 16.36/100 = 9.442˚ Trial 1 2 3 4 5

Acceleration (Mean) .182 .229 .229 .232 .195

Round 3 Large glider, small block (1.9cm) Angle Calculation: tan-1 θ = opposite / adjacent = 15.19/100 = 8.639˚ 3

Trial 1 2 3 4 5

Acceleration (Mean) .125 .126 .120 .128 .124

Round 4 Large glider, large block Angle Calculation: tan-1 θ = opposite / adjacent = 16.36/100 = 9.442˚ Trial 1 2 3 4 5

Acceleration (Mean) .228 .229 .227 .232 .230

Round 5 Small glider, small block (1.9cm) Angle Calculation: tan-1 θ = opposite / adjacent = 15.19/100 = 8.639˚ Trial 1

Acceleration (Mean) .004

ERROR ANALYSIS The source of error could be due to systematic errors with the sensor. Specifically, as stated above, the velocity graph has more noise than the position graph and the acceleration graph have more noise than the velocity graph. This is caused by small errors in calculating average velocity from each 1/20th of a second.

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Another source of error was shown by the standard deviation of each slope on the velocity vs time graph and the n value exponent. These could be due to an error with capstone or an error in accurately capturing the position of the glider on the flag. During the experiment, many discrepancies occurred in which the sensor was not capturing the actual position of the glider, leading to many jumps in each graph. The motion sensor was very sensitive to its placement. The angle of the track made it difficult to accurately capture the flag as it progressed.

QUESTIONS 1) How will acceleration change when we double the mass of the glider? Acceleration will be half the size. 2) Explain what is occurring in each vector and why? In the position graph, the distance was a parabola facing upwards since the velocity was increasing. In the velocity graph, the velocity was a linear function since the acceleration was constant. In the acceleration graph, the acceleration was a straight, horizontal line based on the theory the acceleration should be constant since there is no friction. The graph got noisier as the glider went further. 3) Do the graphs illustrate what is predicted by the theory? How so and explain. What were the correlations of all the graphs? The velocity curve is noisier than the position curve, and acceleration curve is noisier than velocity curve. Why? The graphs do illustrate what is predicted by the theory, only the angle of the track affect the acceleration which all the trials that are in the same situation have close 5

acceleration. The slope of the position is velocity, the slope of velocity is acceleration. The velocity graph is noisier than position graph and acceleration graph is noisier than velocity graph since each one is the derivative of the previous one which is more precise than the previous one. 4) For the velocity plot the acceleration is given by the slope (m). Why? In the velocity graph, the acceleration is given by the slope because acceleration is the derivative of velocity. The acceleration is the acceleration graph itself, so the average acceleration would be the average of the graphing which is the mean value. 5) What is your experiential n(power)? What does theory say it should be? Why is there a difference? Ours was 1.96, but the theory says it should be 2.01. This could be because of potential error of manual error and the friction actually exist even though we said it is negligible in this experiment. 6) Does the velocity curve cross the axis (velocity = 0) where you expect it to? Are the curves the same from bounce to bounce? If not, can you suggest why? Yes, the curve crosses the x axis every time it changes directions – every time it reaches the end of the track, hits the bumper and comes back towards the motion sensor, and then when it falls back down towards the bumper. This occurred at 3.5s, 6.2s, 9.1s, 11.9s, 14.0s, and 15.3s. The curves are not the same from bounce to bounce because the acceleration would decreases and the distance between the glider and the at of the air truck would get shorter as each time the glider hit the end of the air truck. CONCLUSION 6

This experiment uses theory to depict the relationships between time, position, velocity, and acceleration. The motion sensor and the glider were used in order to capture these values and compare the three graphs to each other in respect to time. Using the slope of position vs time yields velocity vs time and using the slope of velocity vs time yields acceleration vs time. Velocity increased the farther away the glider got from the sensor as it sped up due to the parallel force of gravity. Adding weights slowed the glider because the downward force of gravity became greater. Adding to the inclination of the track then again added to the speed of the glider as the slope of gravity became a higher value. Acceleration remained constant for the four different weight and angle combinations because velocity continued to increase in a linear form. Finding the constant value of acceleration can easily be found and compared to the slope of the velocity vs time graph.

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