Chapter 10, Problem 026 The flywheel of a steam engine runs with a constant angu

Question

Chapter 10, Problem 026 The flywheel of a steam engine runs with a constant angular velocity of 230 rev/min. When steam is shut off, the friction of the bearings and of the air stops the wheel in 2.6 h. (a) What is the constant angular acceleration, in revolutions per minute-squared, of the wheel during the slowdown? (b) How many revolutions does the wheel make before stopping? (c) At the instant the flywheel is turning at 115 rev/min, what is the tangential component of the linear acceleration of a flywheel particle that is 40 cm from the axis of rotation? (d) What is the magnitude of the net linear acceleration of the particle in (c)? (a) Number (b) Number (c) Number (d) Number Units rev/min 2 Units rev Units m/s 2 Units m/s 2

Explanation / Answer

initial angular velocity wo = 230 rev/min

final velocity wf = 0

time taken to stop t1 = 2.6 hr = 2.6*60 = 156 minutes

(a)

angular acceleration alpha = (wf - wo)/t1 = -230/156 = -1.47 rev/min^2

(b)

theta = (wo + wf)*t1/2

theta = (230 +0 )*156/2 = 17940 rev

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(c)

tangential acceleration at = r*alpha

alpha = 1.47 rev/min^2 = 1.47*2*pi/(60^2) = rad/s^2 = 2.57*10^-3 rad/s^2

r = 40 cm = 0.4 m

tangential acceleration at = 0.4*2.57*10^-3 = 1.03*10^-3 m/s^2

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(d)

radial acceleration ar = r*w^2

w = 115 rev/min = 115*2pi/60 rad/s = 12 rad/s

radial acceleration ar = 0.4*12^2 = 57.6 m/s^2

net linear acceleration = sqrt(at^2 + ar^2) = 57.6 m/s^2

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