question archive Part A Find the magnitude of the acceleration acm of the center of mass of the spherical shell Take the free-fall acceleration to be g 9
Part A Find the magnitude of the acceleration acm of the center of mass of the spherical shell Take the free-fall acceleration to be g 9
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Part A Find the magnitude of the acceleration acm of the center of mass of the spherical shell Take the free-fall acceleration to be g 9.80 m/s2 Constants A hollow spherical shell with mass 1.75 kg rolls without slipping down a slope that makes an angle of 30.0 o with the horizontal. View Available Hint(s) ?? Submit Part B Find the magnitude of the frictional force acting on the spherical shell Take the free-fall acceleration to be g 9.80 m/s2. View Available Hint(s) Submit
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a)
ma = (force due to gravity along slope) - (force due to friction)
ma = mgsinθ - Ff ------------------[1]
torque = (moment of inertia of sphere)(angular acceleration) = (force due to friction)(radius of sphere)
Iα = (Ff)(r) ----------------------[2]
Since the sphere doesn't slip, for [2]:
(2mr2/3)(a/r) = (Ff)(r)
Ff = 2ma/3 ------------------------[3]
Substituting Ff into [1]:
ma = mgsinθ - 2ma/3
a = 3gsinθ / 5 -------------------[4]
a = 3(9.81 m/s^2)(sin30°)/5 = 2.943 m/s2 Answer
b)
Ff = 2(1.75kg)(2.943m/s2)/3 = 3.434 N Answer
