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a man pushes a cylinder of mass m1 with the help of a plank of mass m2 as shown. There is no slipping at any contact. The horizontal component of the force applied by the man is F. find:
(a) the accelerations of the plank and the centre of mass of the cylinder, and
(b) magnitudes and directions of frictional forces at contact points.
Dear Aditya Nijampurkar,
Ans:
Let us consider the following
a1=Acc of the cylinder towards right
a2=Acc of the plank towards right
β= clockwise angular Acc of the cylinder
f1= The force of friction at the point of contact of the bodies
f2=The force of friction at the bottommost surface
The eq of motions of the Plank and the cylinder are,
F - f1=m2 a2..........................(1)
(f1+f2)r=Iβ.............................(2)
f1 - f2=m1 a1.............................(3)
Now the conditions of non sleepping are
βr+a1 = a2........................(4)
βr=a2...............................(5)
Solving we get
a2=8F/(3m1+8m2)
a1=4F/(3m1+8m2)
f1=3m1 F/(3m1+8m2)
f2= - m1 F/(3m1+8m2)
The negative sign indicates that friction between the ground and the cylinder acts in the forward direction.
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Askiitians ExpertsSoumyajit Das IIT Kharagpur
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