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Ph1r3 Mario

P4 12-1-12

Swinging Your Mass

The purpose of this experiment is to find the radius of a circular, swinging mass. The materials I used to perform this experiment are: a mass held by a string, a 12-inch wooden ruler, a protractor, and a timer. I attempted to find a radius of a circular, swinging mass using two methods: measuring the variables and using centripetal force equations. Both radii that are solved should be within 5% of each other.

     To begin the first method I laid the ruler on a flat surface, and then I swung the mass in a circle above the ruler horizontally, going around the edges of the ruler. This creates a diameter of 30 centimeters. Dividing the diameter by 2 gives me a radius of 15 centimeters; converted to meters equals .15m. After finding the radius, I used the timer in order to record the time it takes for one whole revolution, which was approximately 1.25 seconds. Lastly, I used the protractor to measure the angle, Θ, to the vertical, which should be 16°. These two variables will be used to prepare for the second method.

     The second method I used involved looking at the forces happening in the x and y directions and applying centripetal force formulas in order to find the radius. There were two forces acting upon the mass and string: tension (T) and gravity (Fg). Because the mass was being held at an angle, force of tension is calculated by Tcos74 in the y-direction and Tsin16 in the x-direction. Starting with the x-direction, there is force of tension, Tsin16, and because it is moving, Tsin16 will equal ma (Tsin16 = ma). Because we are trying to find out the radius, I changed ma to mrω^2 (Tsin16 = mrω^2). Therefore, r = Tsin16/mω^2. In order to solve this equation, we must find both T and ω. To find T, we must look into the y-direction. Because the mass is not moving up or down, Tcos74 = Fg. Therefore, T = mg/cos74. Now to look at ω. ω = ΔΘ/t; therefore, ω = 2π rads/1.25s, which will turn out to be 5.026548246. Now that we have both T and ω, we can finally start solving for the radius. By plugging in our new found variables, r will equal: mgsin16/m(5.026548246)^2cos74 . The variable m will cancel, the sin/cos will equal tan16, and (5.026548246)^2 will equal 25.26618727. We are now left with r = gtan16/25.26618727. Variable g equals ~9.8, therefore, r = 9.8tan16/25.26618727. The final result is:             r = .1112199775m.

     The result of method 2 is an error of 26% (.1112199775/.15 = 74%, 100 – 74 = 26%). The fact that the two results found were not within 5% of each other means that there were some errors that were not fixed during the testing. The measuring of the variables is where it all went wrong. When I recorded the time, I took the mode of 5 trials instead of the average. Also, during these trials, the swinging of the mass was not constant. In addition, the center of the circle was not at the center of the ruler when swinging the mass around. This must have messed up the angle of the string; thus, causing data to be inaccurate. In order to prevent this from happening in the future, lab assistants should be more competent in maintaining proper control of materials during the experiment. This will make for more accurate numbers, which in turn will make for an accurate result.