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posted by  Makaveli on 11/6/2009 6:07:38 PM  |  status: Closed  |  Earned Karma: 55

Physics-I, Section # 10, exercise # 64

Course Textbook Chapter Problem Needs by
Calculus Based Physics University Physics with Modern Physics (12th) by Young, Freedman 10 63P 11/6/2009 at 9:00:00 PM
Question Details:
A block with mass (m) =5.0kg slides down a surface inclined 36.9dergrees to horizontal. The coefficient of kinetic friction is 0.25. A string attached to the block is wrapped around a flywheel on a fixed axis at O.  The flywheel has mass 25 kg and moment of inertia 0.500kg-m^2 with respected to the axis of rotation.  The strings pulls without slipping at a perpendicular distance of 0.200 m from that axis.
a) What is the acceleration of the block down the plane?
b) What is the tension in the string?
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posted by zsm28 on 11/6/2009 11:27:33 PM  |  status: Live
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Response Details:
m = 5.0 kg, θ = 36.9o, μ = 0.25. M = 25 kg, I = 0.500 kg-m2, r = 0.200 m
Find the acceleration a and the tension T
mgsinθ - T - μmgcosθ = ma
T*r = I*α = I*(a/r), so T = (I/r2)a
mgsinθ - μmgcosθ = (m + I/r2)a
∴a = mg(sinθ - μcosθ)/(m + I/r2) = 1.12 m/s2
T = (I/r2)a = 14.0 N
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