* A tall, cylindrical chimney falls over when its base is ruptured. Treat the ch
ID: 1609935 • Letter: #
Question
* A tall, cylindrical chimney falls over when its base is ruptured. Treat the chimney as a thin rod of length 63.0 m. Answer the following for the instant it makes an angle of with the vertical as it falls.
1. Calculate the angular speed at the angle =50.0°.
2. Calculate the tangential speed at the angle =50.0° of the top.
3. Calculate the tangential speed at the angle =50.0° at the center of mass of the chimney.
4. Calculate the angular acceleration at the angle =50.0°.
5. Calculate the tangential acceleration at the angle =50.0° of the top.
6. Calculate the radial acceleration at the angle =50.0° of the top
Explanation / Answer
Apply conservation of energy
Ei = Ef
mgh_com = mgh' + 1/2 I w^2
mgH/2 = mg H/2 cos theta + 1/2 ( 1/3 mH^2) w^2
w= sqrt 3g( 1- cos theta)/H
= sqrt 3(9.8) (1-cos50)/63
=0.40 rad/s
(b)
v= rw = Lw = 63 ( 0.40) = 25.72 m/s
(c) same as in part because tangential speed does not change
(d)
alpha = dw/dt
= d/dt ( sqrt 3g( 1- cos theta)/H
= ( 1/2 ( 1/sqrt 3g( 1- cos theta)/H) 3g/H sin theta) d theta/dt
= 1/2 (1/sqrt 3g( 1- cos theta)/H) 3g/H sin ttheta) w
alpha = 3g/2H sin tehta
= 3(9.8)/ 2( 60.3) * sin 50
=0.186 rad/s^2
(5)
at= r alpha = 60.3 (0.186) = 11.26 m/s^2
(6)
ar= rw^2 = 60.3) ( 0.40)^2 =9.648 m/s^2
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