A spool has an inner radius p = 1.85 m and an outer radius R = 2.35 m. The mass of the spool is 250 kg and its radius of gyration kG is 2.1 m. A cable wound around the spool is attached at the top of an incline of angle 0 = 32° and the spool is being lowered down the incline as shown in the figure below. The coefficients of static and kinetic friction between the spool and the incline are us= 0.45 and μ = 0.40. a) Find the acceleration of the center G of the spool b) Find the angular acceleration of the spool c) Find the tension in the cable

International Edition---engineering Mechanics: Statics, 4th Edition
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Chapter7: Dry Friction
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Problem 1:
A spool has an inner radius p = 1.85 m and an outer radius R = 2.35 m. The mass of the
spool is 250 kg and its radius of gyration kG is 2.1 m. A cable wound around the spool is
attached at the top of an incline of angle 0 = 32° and the spool is being lowered down the
incline as shown in the figure below. The coefficients of static and kinetic friction
between the spool and the incline are μs = 0.45 and μ = 0.40.
a) Find the acceleration of the center G of the spool
b) Find the angular acceleration of the spool
c) Find the tension in the cable
R
G
Hint: show that the spool must slip while rolling down the incline.
Transcribed Image Text:Problem 1: A spool has an inner radius p = 1.85 m and an outer radius R = 2.35 m. The mass of the spool is 250 kg and its radius of gyration kG is 2.1 m. A cable wound around the spool is attached at the top of an incline of angle 0 = 32° and the spool is being lowered down the incline as shown in the figure below. The coefficients of static and kinetic friction between the spool and the incline are μs = 0.45 and μ = 0.40. a) Find the acceleration of the center G of the spool b) Find the angular acceleration of the spool c) Find the tension in the cable R G Hint: show that the spool must slip while rolling down the incline.
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