Experiment 7

Experiment 7 - 2.74 0.482 Calculations: v = (2r)/T v =...

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Experiment 7: Uniform Circular Motion and the Centripetal Force (i) Figure I shows the experimental centripetal force as a function of centripetal acceleration. Calculations: O a = v 2 /r O a = (0.631) 2 /0.220 = 1.81 m/s O a = (0.563) 2 /0.217 = 1.46 m/s O a = (0.482) 2 /0.210 = 1.11 m/s (ii) The experimental slope is 0.28 and the theoretical slope is 0.209 - The percent error was 34%. (iii) F = (mv 2 )/r and v = 2πr/T F = [m((2πr)/T) 2 ]/r F = [m(4π 2 r 2 )/T 2 ]/r F = [m(4π 2 r 2 )]/(T 2 r) F = 4π 2 mr 2 /T 2 The Experimental Centripetal Force as a Function of Centripetal Acceleration y = 0.28x - 0.1148 R 2 = 1 0 0.1 0.2 0.3 0.4 0.5 0 1 2 Centripetal Acceleration Centripetal Force Series1 Linear (Series1)
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Table I shows the calibrating force [F(N)], radial distance [r(m)], time [T(s)], and velocity [v(m/s)] used and/or calculated in the experiment. Experimental Data F(N) r(m) T(s) v(m/s) 0.392 (40g) 0.220 2.19 0.631 0.294 (30g) 0.217 2.42 0.563 0.196 (20g) 0.210
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Unformatted text preview: 2.74 0.482 Calculations: v = (2r)/T v = (2(0.220))/2.19 = 0.631 m/s v = (2(0.217))/2.42 = 0.563 m/s v = (2(0.210))/2.74 = 0.482 m/s Table II the centripetal force (N) as calculated by Equation 2 (F = (mv 2 )/r). Centripetal Force (N) Expt. (Eq. 2) Calibr. Value % Error 0.378 0.392 3.57% 0.305 0.294 3.74% 0.231 0.196 17.86% Calculations: (F = (mv 2 )/r) (F = [(0.209)(0.631) 2 ]/0.220) = 0.378 (F = ((0.209)(0.563) 2 )/0.217) = 0.305 (F = ((0.209)(0.482) 2 )/0.210) = 0.231 (Actual Experimental)/Actual x 100 (0.392 0.378)/0.392 x 100 = 3.57% (0.294 0.305)/0.294 x 100 = 3.74% (0.196 0.231)/0.196 x 100 = 17.86% Table III shows the experimental and theoretical slopes and the percent error. Slope Expt. Theor. % Error 0.28 0.209 33.97% Calculations: (0.209 0.28)/0.209 x 100 = 33.97%...
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Experiment 7 - 2.74 0.482 Calculations: v = (2r)/T v =...

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