Lab 4 Report - Grade: A PDF

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Report for Lab 4 PHY241 Max Brown...

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Lab #4: Fan Carts Introduction: The purpose of this experiment was to determine how the acceleration of the fan cart changes as the angle of the fan is altered. The secondary goal was to compare the recorded accelerations to those theorized by a trigonometric equation. The technical terms used in this report are defined here. The average (or mean) is defined as the sum of all the data points divided by the number of data points. The systematic uncertainty is defined as the error created by manual measurement. The acceleration is defined as the rate at which a particle’s velocity changes. The problem we encountered was to figure out the most accurate way to predict the different accelerations. Our group needed to determine an equation that took the angle of the fan and the cart’s acceleration at 0 degrees, then plug it into an equation that calculated the acceleration of the cart when the fan was at the specified angle. During our experimentation we found that, in the majority of cases, the average acceleration of the cart decreases as the angle of the fan gets farther from 0 degrees. The following chart shows our experimental data. The only data point that does not follow the trend is the average acceleration of the cart at +20 degrees, which is greater than the average acceleration at 0 degrees. Angle (degrees) 80 45 20 0 -20 -45 -80

Average Acceleration (m/s2) 0.0426 0.0997 0.1536 0.1505 0.1427 0.1121 0.0281

Systematic Uncertainty (m/s2) 0.02 0.03 0.05 0.07 0.04 0.03 0.09

To calculate the acceleration of the cart at a specific angle, we used the following equation: aangle = |cos(θ) · a0|, where a0 is the acceleration when the fan is at 0 degrees. The following chart shows the predicted data. Each row of data corresponds to the experimental angle in the chart above. The maximum acceleration was determined by adding the uncertainty to the predicted acceleration, and the minimum acceleration was determined by subtracting the uncertainty from the predicted acceleration. The uncertainty was used to do this because the experimental value for a0 has a large amount of systematic uncertainty. Thus, the calculated result for aangle will also have this uncertainty.1

1 This answers question 14 in the lab manual.

Predicted Acceleration 0.026134051 0.106419571 0.141423739 0.1505 0.141423739 0.106419571 0.026134051

Max. Acceleration 0.046134 0.13642 0.191424 0.2205 0.181424 0.13642 0.116134

Min. Acceleration 0.006134051 0.076419571 0.091423739 0.0805 0.101423739 0.076419571 -0.063865949

Systematic Uncertainty 0.02 0.03 0.05 0.07 0.04 0.03 0.09

Procedure: To be able to answer if the angle of the fan will change how the cart moves, we had to get theoretical accelerations for different angles. We also had to determine a theoretical equation for the acceleration based on angles:

Theoretical Acceleration= |cos(∅)∗a0 degrees|

To get the theoretical acceleration, one has to take the absolute value of cosine of the angle multiplied with the experimental acceleration of 0 degrees. The equation was discovered to be like this because the fan and the cart make a right triangle, the fan is the hypotenuse and the cart is a leg. Since cosine of the angle is equal to the acceleration of the cart divided by the acceleration of the fan, we had to multiply the acceleration of the cart by the cosine of the angle.2 Therefore, giving the equation above. If we use this equation, we could predict the acceleration based on the angle of the fan. To be able to measure the experimental acceleration, we used a 2m track, a fan cart, a bubble level, a CBR 2, and logger pro. We had to first set up the track with the bubble level, to make sure the track is level and straight. We placed the CBR at the right end of the track and also placed the fan cart on the track with the blades facing to the right. To measure the angles, we measured them perpendicular to the fan. First, we started at 0 degrees to get a controlled measurement for the fan. Then we changed the angles to 20, 45, and 80 degrees and also did the negatives of those angles.

We collected the experimental accelerations with an unknown uncertainty. We plugged in the angle and the controlled acceleration into the equation to obtain the theoretical accelerations. However, there is always uncertainty with experiments, so we took the experimental uncertainty and added or subtracted to get the maximum and minimum values for the theoretical accelerations based on our measured angles. 2 This answers question 12 in the lab manual.

Analysis: A summary of our results is displayed in Graph 1 below. This graph compiles the experimental data and predicted data into one graph. A trend line is not applicable for these data sets.

Graph 1: A comparison of the fan cart’s acceleration as determined through experimentation (Experimental) and calculated with the equation (Theory Prediction). The experimental data is very close to being within the predicted area, but all of the experimental points are above the area. This may be a result of an error in the measuring tools or the procedure. However, the error bars for the experimental data all extend into the predicted area. This means that the equation used to predict the angular acceleration was accurate.

Conclusion: In this lab, most people did struggle with their prediction between 70 and 90 degrees. I feel like this occurs because when you switch to 90 degrees, it is considered a right angle and changes things a whole lot when you switch from 70 to 90 degrees. My group dealt with this

issue by thinking out before switching that when it goes to 90 it is a right angle while 70 is not a right angle....