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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

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B.

As

I = 1/2 M R^2

I = 48 kg m^2

As

KErot = 1/2 I w^2,

KErot = 600 J   [ANSWER]

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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]