One problem on physics, center of mass?

Question

A man is pushing a cylinder of mass #m_1# with the help of a flat plank of mass #m_2#. The horizontal component of the applied force is #F#. If no touching surface does not slip,then

i)acceleration of plank and center of mass of cylinder...
ii)Value of frictional force in the touching point and its direction.

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Answer 1 · 2018-01-29T13:13:56

See below.

The plank

#F-R = m_2 alpha#

The cylinder

#2R r = J_0 (d omega)/(dt)#

but

#v = 2r omega# and

#alpha = (dv)/(dt) = 2r (d omega)/(dt)# and then

i)

#alpha = F/(m_2+1/4J_0/r^2)# for the plank
#alpha = 1/2 F/(m_2+1/4J_0/r^2)# for the cylinder mass center

ii)

#R = (J_0/(4r^2))/(m_2+J_0/(4r^2))F#

Here

#J_0 = 1/2 m_1 r^2# Inertia moment regarding the rotation axis for the cylinder.
#r = # Cylinder radius.