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A man pushes a cylinder of mass m1 with the help of a plank of mass m2 as shown in fig. The horizontal component of the force applied by the man is F. Find 1.the acceleration of the plank and center of mass of the cylinder 2.the magnitude and direction of the frictional forces at Contact points

A man pushes a cylinder of mass m1 with the help of a plank of mass m2 as shown in fig. The horizontal component of the force applied by the man is F. Find
1.the acceleration of the plank and  center of mass of the cylinder
2.the magnitude and direction of the frictional forces at Contact points

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Grade:12

1 Answers

Arun
25750 Points
3 years ago
f1=force of friction between the two bodies and is towards right for the cylinder and left for the plank.
 
f2==force of friction between the ground and the cylinder and is towards left.
 
F=Applied horizontal force on the plank.
 
 a1==acceleration of plank towards the right.
 
a==acceleration of cylinder towards right.
 
B=angular acceleration of cylinder
 
Then the equations o motion are
 
F−f 
1
​ 
 =M 
2
​ 
 a 
1
​ 
 
f 
1
​ 
 −f 
2
​ 
 =M 
1
​ 
 a
(f 
1
​ 
 +f 
2
​ 
 )r=1β
 
Condition for non slipping area 
1
​ 
 =a+βr⟶(4) (At top contact of two bodies)
 
a 
2
​ 
 =βr⟶(5) (At the contact of cylinder and the ground)
 
Solving these equations
 
a= 
(8M 
2
​ 
 +3M 
1
​ 
 )
4F
​ 
 
a 
1
​ 
 = 
(8M 
2
​ 
 +3M 
1
​ 
 )
8F
​ 

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