Lab 4

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University of Southern California *

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151

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Physics

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Apr 3, 2024

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Julia Kennedy February 20, 2024 Physics 151 - 50397 Lab #4 Overview: In this lab, the goal is to explore acceleration in one and two dimensions, analyze falling objects, and investigate systematic and random errors. Additionally, the goal was to continue to use the PASCO Capstone software. Expt. 1: Centripetal Force Machine Experimental Setup: (A) The machine involves a spinning mass attached to a spring and an alignment stick. The goal is to adjust the spinning mass until it hangs vertically over the alignment stick. The hanging mass needed to replicate the centripetal force is then determined and compared to theoretical predictions. In the first half, the setup involved adjusting the voltage to achieve a controlled spin without exceeding 18 volts. The period of rotation was calculated by recording the time 10 rotations took and dividing that time by 10 (Table 1.) Figure 1: Hanging Mass
In the second half, a hanging mass M was attached to the stationary mass to provide a sideways force. The goal was to adjust M until the stationary mass hangs vertically over the alignment stick. The force was calculated using F-Centripetal = mrω^2 and F-Sideways = Mg. We compared the actual value for M with the theoretical value. (Figure 1) C) Table 1: Centripetal Force Machine T (period) 0.57 seconds Angular Velocity (ω) 2pi/T 11 ? −1 M 1370 grams R (radius) 21 cm M (spinning mass) 445 grams 𝑀𝑔 = 𝑚?ω 2 (M)(9.8) = (445)(0.21)(11^2) The calculated M was 1,1.54 grams. The actual M was larger than the predicted one. The calculated value of 1154 is more than 15% lower than the actual value of 1370. This could be due to user error of the machine or being unable to see when the hanging mass was properly aligned. Expt. 2: Penny Centripetal Force (E, F) In this experiment a rule was mounted on the turntable, we placed pennies along its length, and gently spun the turntable.
The rotation frequency f was recorded by timing several rotations of the turntable and dividing by the number of rotations, and observations were made regarding which pennies slide outward. The distance r0 which is from the axis where sliding occurs is recorded. This was then repeated three more times and data was collected. The centripetal constant was calculated using the equation: Constant = r0f^2 (Table 2) Figure 2: Penny Experiment Trial Number 1 2 3 Radius (r0) 2 pennies (.038 m) 1 penny (.019 m) 2 pennies (.038 m) Period (T) 1.02 seconds 0.67 seconds 1.118 seconds Frequency (1/T) 1/1.02 1/.67 1/1.118 Constant .0365 .0423 .0304 Table 2: Experient 2 Trials (G) The observed values remain constant at approximately 0.0365, 0.0423, and 0.0304 for different rotation speeds. This matches the prediction from Equation 3, showing that the constant stays the same regardless of rotation speed. This consistency supports the idea that the radius, angular speed, and centripetal force are related as expected in circular motion.
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