Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 5 - Circular Motion; Gravitation - General Problems - Page 135: 71

Answer

μs = 0.18

Work Step by Step

Variable list f is friction, m is mass, a is acceleration, V is velocity, r is radius, W is weight, n is normal force, T is time, g is gravitation acceleration on Earth, and μ is the coefficient of static friction. First draw a free-body diagram of the person riding on the "Rotor-ride" Second write a summation of forces statement for forces in the X direction. ΣFx: n = ma n = mV^2/r Third write a summation of forces statement for forces in the Y direction. ΣFy: f - W = ma Since there is zero acceleration, "ma" cancels out. f = W Add W. μn = mg Divide by n. μ = mg/n μ = mg/mV^2/r Divide by m. μ = g/V^2/r μ = g/(2πr/T)^2 /r Substitute in the equation for velocity. μ = g/4π² r^2/T^2/r Divide by r. μ = g/4π² r/T^2 μ = gT^2/4π² r μ = (9.8m/s^2)(2s)^2/4π² (5.5) Since there is 0.5 revolutions per second, the total time period would be 2 seconds. Time period measures how much time it takes to complete one revolution in how many seconds. 0.5 revolutions per second times 2 equals 1 revolution in 2 seconds. μ = 0.18
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