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Aditya Nijampurkar Grade: 12
        

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.


1615_13194_untitled.GIF

7 years ago

Answers : (1)

Askiitians Expert Soumyajit IIT-Kharagpur
28 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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All the best  Aditya Nijampurkar !!!


 



Regards,


Askiitians Experts
Soumyajit Das IIT Kharagpur

7 years ago
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