a) Determine its angular speed. b) Determine its rotational kinetic energy. c) U
ID: 1376352 • Letter: A
Question
a) Determine its angular speed.
b) Determine its rotational kinetic energy.
c) Use energy considerations to calculate the maximum height(hmax) that the cylinder rolls up the incline.
A large cylinder or radius R = 4.0 m, mass M = 6 kg and moment of inertia I = 1/2 MR^2 rolls without slipping across a horizontal surface with a translational speed of 20 m/s. The cylinder approaches an incline plane and rolls up without slipping. See figure above. When the cylinder is moving horizontally: a) Determine its angular speed. b) Determine its rotational kinetic energy. c) Use energy considerations to calculate the maximum height(hmax) that the cylinder rolls up the incline.Explanation / Answer
A.
As
w = v/R
Then
w = 5.0 rad/s
****************
B.
As
I = 1/2 M R^2
I = 48 kg m^2
As
KErot = 1/2 I w^2,
KErot = 600 J [ANSWER]
****************
As
KEtot = KErot + KEtrans
as KEtrans = 1/2 m v^2
KEtrans = 1200 J
Thus,
KEtot = 1800 J
By conservation of energy,
KEtot = m g h
--> h = KEtot / [m g]
h = 30.6 m [ANSWER]
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