PES 1150 Circ Motion Report

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University of Colorado, Colorado Springs *

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1150

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Mechanical Engineering

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Apr 3, 2024

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docx

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Circular Motion Name: Objective This lab concentrates on the centripetal forces and acceleration within circular motion. The centripetal acceleration/force and angular velocity are measured using a senor on a spinning surface. From the graphs, students can determine the slope from the plotted points. It will be used to find the radius or the mass. Students will have different radius lengths to be tested to measure the affect they have on the centripetal acceleration. Data and Calculations
P E S 1 1 5 0 - G E N E R A L P H Y S I C S L A B I Part I: Centripetal Acceleration 1.) Paste your graph of centripetal acceleration vs. 2 . Include all three raduii including the best-fit curves for each run. 2.) At what radius did you set the Force sensor for the first run, corrected for the offset : Radius of 1 st Run = 0.127 m 3.) At what radius did you set the Force sensor for the second run, corrected for the offset : Radius of 2 nd Run = 0.077 m 4.) At what radius did you set the Force sensor for the third run, corrected for the offset : Radius of 3 rd Run = 0.177 m 5.) Record your curve fit equation for the first radius. Circular Motion - 2
P E S 1 1 5 0 - G E N E R A L P H Y S I C S L A B I Curve fit equation of 1 st Run = ac=0.124w^2-0.158 m From this equation record the experimental radius in the table below: Radius of 1 st Run – Curve fit = 0.124 m 6.) Record your curve fit equation for the second radius. Curve fit equation of 2 nd Run = ac=0.0740w^2-0.159 m From this equation record the experimental radius in the table below: Radius of 2 nd Run – Curve fit = 0.074 m 7.) Record your curve fit equation for the third radius. Curve fit equation of 3 rd Run = ac=0.0.174w^2-0.151 m From this equation record the experimental radius in the table below: Radius of 3 rd Run – Curve fit = 0.174 m Set Radius (Theoretical) Experimental Run # Set radius (Force sensor alignment) “Corrected Radius” for offset Radius (curve-fit data) 1 0.165 0.127 0.124 2 0.115 0.077 0.074 3 0.215 0.177 0.174 Part II: Centripetal Force 1.) Pick a radius and plot the centripetal force vs. 2 for three different sled masses. 2.) Include all three trials on a single graph. Record curve fit information for all trials. Graph of Force vs 2 Circular Motion - 3
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P E S 1 1 5 0 - G E N E R A L P H Y S I C S L A B I 3.) Copy your curve fit information here from each trial, matched against the radius and the total weight of the sled. Trial Radius (m) Sled/Mass Combo (kg) Curve fit equation 1 0.097 0.1024 F=0.00997w^2-0.0894 2 0.097 0.1524 F=0.0152w^2-0.121 3 0.097 0.2023 F=0.0197-w^2-0.132 Pick a new radius 4.) Pick a new radius and plot the centripetal force vs. 2 for three different sled masses. 5.) Include all three trials on a single graph. Record curve fit information for all trials. Graph of Force vs 2 Circular Motion - 4
P E S 1 1 5 0 - G E N E R A L P H Y S I C S L A B I 6.) Copy your curve fit information here from each trial, matched against the radius and the total weight of the sled. Trial Radius (m) Sled/Mass Combo (kg) Curve fit equation 1 0.152 0.1024 F=0.0139w^2-0.088 2 0.152 0.1524 F=0.0217w^2-0.121 3 0.152 0.2023 F=0.0289w^2-0.155 Pick a third radius 7.) Pick a new radius and plot the centripetal force vs. 2 for three different sled masses. 8.) Include all three trials on a single graph. Record curve fit information for all trials. Graph of Force vs 2 Circular Motion - 5
P E S 1 1 5 0 - G E N E R A L P H Y S I C S L A B I 9.) Copy your curve fit information here from each trial, matched against the radius and the total weight of the sled. Trial Radius (m) Sled/Mass Combo (kg) Curve fit equation 1 0.182 0.1024 F= 2 0.182 0.1524 F= 3 0.182 0.2023 F= Results and Questions Part I: Centripetal Acceleration 1.) State the relationship between the centripetal acceleration and the radius, mathematically? Circular Motion - 6
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P E S 1 1 5 0 - G E N E R A L P H Y S I C S L A B I The centripetal force and radius are ac=rw2. Where Ac=centripetal acceleration, R=radius. The radius and centripetal forces must be proportional to one another. 2.) Would changing the weight of the spinning mass changed the results? Explain. When changing the weight of the spinning mass, that could result in changing the final results it also changes the acceleration, the force and the radius. 3.) What is represented by the slope of the line plotted from the centripetal acceleration vs. angular velocity squared? The slope on the centripetal acceleration vs. angular velocity squared on the graph is the radius. 4.) Find the percent difference between the set radius and the radius found in your experimental results. Set Radius Experimental Error Run # “Corrected Radius” for offset Radius (curve-fit data) Percent Difference (%) 1 0.127 0.124 2.39 2 0.077 0.074 3.97 3 0.177 0.174 1.71 Part II: Centripetal Force 1.) What is the mathematical relationship between the centripetal force, angular velocity, mass, and the radius? Circular Motion - 7
P E S 1 1 5 0 - G E N E R A L P H Y S I C S L A B I Fc=mrw^2. Radius=r, Mass=m, angular velocity w^2, Centripetal force Fc 2.) What is represented by the slope of the line plotted from the centripetal acceleration vs. angular velocity squared? The value of the slope of the line plotted from centripetal force vs. angular velocity squared is mass times radius is m*r=mr 3.) Find the percent difference between the measured values of the radii and the radii calculated using your experimental results. Run/Trail Radius/Mass Radius/Mass curve-fit %difference. %difference=1-2/1.5(1+2) *100 Conclusion Circular Motion - 8
P E S 1 1 5 0 - G E N E R A L P H Y S I C S L A B I Centripetal acceleration and force were found using the sensor with the spinning platform and masses on a spinning surface. The sensor was attached to three separate radius lengths and the centripetal acceleration vs angular velocity to create a graph. The slope is how each radius was found. The % difference used the length of the radius from the platform after it was corrected. The percent differences were low, but accurate results. Measuring the radius lengths and the weight of each mass and multiplying them together. Measurements were made using three masses and three different lengths. Many calculations were made for each part, to find radius and % differences. The lab allowed for students to see centripetal acceleration and radius to be proportional and the centripetal force is directly proportional to the mass*radius. If any of these increase the centripetal force value is increased as well. Circular Motion - 9
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