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Saitama
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Homework Statement
A plank of mass M is placed over smooth inclined plane and a sphere is placed on the plank as shown (see attachment). There is sufficient friction between sphere and plank to prevent slipping. If system is released from rest, the frictional force on the sphere is
a)up the plane
b)down the plane
c)zero
d)horizontal
Homework Equations
The Attempt at a Solution
I began by drawing a FBD of the sphere (see attachment 2). I assumed that the friction,f acts down the plane.
Equation for translational motion of sphere:
##mg \sin \theta=ma##...(i)
where a is acceleration of sphere
Equation for rotational motion of sphere (taking torque about CM):
##fR=Ia/R##...(ii)
where I is the moment of inertia of sphere and R is the radius of sphere. Solving the equations, I get a positive value of f which means that the direction of friction is down the plane. But the answer is zero.
Any help is appreciated. Thanks!
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