Uniform Circular Motion Lab

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Arizona State University *

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Chemistry

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Feb 20, 2024

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Title of the Experiment: Uniform Circular Motion Student’s name: Anjana Shyam Section SLN: Session A TA’s Name: Ayush Kumar Singh Week of the experiment: 5 Objectives: (3 points)

The relationship between the variables mass, velocity, radius that form centripetal force will be examined. Forces in circular motion such as friction will be investigated in this experiment as well. Experimental Data (3 points):

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Part 1a. Force vs Mass Radius = _0.101 m____________ Speed = ____0.319 m/s_________ From Graph of F vs. m : Slope ± slope = ___1.02 N/kg_± 0.001371 N/kg_________ Part 1b . Force vs velocity Radius = ___0.101m__________ Mass (kg) = __0.1804 kg___________

From Graph of F vs. v 2 : Slope ± slope = ____1.76 N/m^2/s^2 ± 0.0005541__N/m^2/s^2_______ Part 1c: Force vs Radius Cylinder Mass =_______0.1804 kg______ Speed = ______0.188 m/s_______ From Graph of F vs. 1/r: Slope ± slope = ___0.006523 N/1/m _± 9.192E-05 N/1/m_________ Part 2. Coefficient of static friction Mean : _____________ Standard Deviation (): _____________ **Include GRAPHS and TABLES for all parts which display experimental data (slope and/or statistics ; use print screen option) Data Analysis (10 points) Part 1a. Calculate the theoretical value of the ratio v 2 /r using equation (1) from the lab manual. What is the experimental value of the ratio v 2 /r based on your graph from part a? Calculate the percent error between the theoretical value and your experimental value for the ratio v 2 /r. Experimental Error: (experimental – theoretical)/(theoretical) * 100 (1.015 – 1.008)/(1.008) * 100 = 0.69444% Part 1b. Calculate the theoretical value of the ratio m/r using equation (1) from the lab manual. What is the experimental value of the ratio m/r based on your graph from part a? Calculate the percent error between the theoretical value and your experimental value for the ratio m/r. 0.1804/0.101= 1.786 Experimental Error:

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(1.76 – 1.786)/1.786 = -1.46% Part 1c. Calculate the theoretical value of the product mv 2 using equation (1) from the lab manual. What is the experimental value of the product mv 2 based on your graph from part a? Calculate the percent error between the theoretical value and your experimental value for the product mv 2 . (0.0065-0.0064)/0.0064 = 1.563% Part 2: Calculate the average maximum tangential velocity for an object moving in a circle of radius 5cm. Results (3 points) Part 1. Experimental ( units ) Theoretical ( units ) Discrepancy (%) v 2 /r 1.015 N/kg 1.008 N/kg 0.694% m/r 1.76 N/m^2/s^2 1.79 N/m^2/s^2 -1.46% mv 2 0.0065 N/1/m 0.0064 kgm^2/s^2 1.56% Part 2. μ s ± Δμ s = Discussion and Conclusion (10 points):

In this experiment, the relationship between mass, tangential velocity, and radius in centripetal force was verified through various experiments that involved two control variables and an experimental variable that was graphed against the centripetal force of the record to determine the effect of the variable on the total centripetal force of the record. Mv^2/R is the equation of centripetal force, a force directed towards the center of an object moving in a circular path. Centripetal force can be provided by tension in a string or even gravitational force that keeps the planet or satellite in circular orbit. In part 1a, the effect of mass on centripetal force was tested by two control variables radius and velocity. The radius was set to 10.1 cm and the tangential velocity was set to 0.319 m/s, while different cylinders were used as different masses. The Mass vs. Force data was graphed, and a linear fit was performed on the data. Graphing mass vs. centripetal force is velocity^2/radius, which resulted in a slope of 1.02 N/kg with an uncertainty of 0.001371 N/kg. The theoretical value of v^2/R by the given parameters is 1.008 N/kg, resulting in a discrepancy of 0.694%. A very low experimental discrepancy supports the proportionality of mass to centripetal force as determined by the formula mv^2/R. In part 1b, the effect of tangential velocity on centripetal force was determined by the control variables mass and radius which were set to 180.4g and 10.1 cm, and speed was set to 10 rpm with a range of 10 rpm – 90 rpm with 10 rpm increments. Uniform circular motion is considered as accelerated motion despite constant tangential speed, because the equation of centripetal force can also be written as mw^2r and that a rotating object’s tangential velocity is not constant due to constantly changing direction, which results in an acceleration. Centripetal acceleration is a result of the change in direction of tangential velocity, while tangential acceleration is due to a change in the magnitude of tangential velocity. Centripetal acceleration can be written as v^2/R or w^2R. An increase in the tangential speed by a factor of 3 would result in a change in centripetal acceleration by a factor of 9 because tangential velocity is squared to obtain the value of centripetal acceleration. Nine values of tangential velocity were recorded, squared, and graphed against force, resulting in a slope of 1.76 N/m^2/s^2 with an uncertainty of 0.0005541 N/m^2/s^2. The experimental error against the theoretical m/r of 1.79 N/m^2/s^2 was -1.46% which was a larger discrepancy than part a. Human reaction time and recording the squared value of tangential could have resulted in a larger experimental error than the one found in part 1a. In part 1c, the effect of the radius on centripetal force was found by keeping tangential velocity and mass constant, being set to 0.188 m/s and 180.4 g respectively. The radius is incremented by 1 cm to obtain 3 values, and the inverse of the radius is plotted to find mv^2. The experimental value of 0.0065 N/1/m and the theoretical value of 0.0064 N/1/m resulted in an experimental error of 1.56% which is larger than the experimental errors found in parts 1a and 1b. This could have been a result of plotting the reciprocal of the radius instead of force vs. radius to find the reciprocal of mv^2.

In conclusion, the results of each part of this experiment have proven that the relationships between mass, radius, and velocity in determining centripetal force. The minute experimental discrepancies of 0.694%, -1.46%, and 1.56% have proven the proportionality of each variable tested in the experiment to the centripetal force of an object in circular motion, proving that the objectives in this experiment have been met.

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