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Consider a cylinder of mass M and radius lying on a horizontal plane or had as plank lying on its top as shown in figure. A force For is applied on the plank such that the plank moves and cause the cylinder To roll. The plank always remain horizontal. There is no slipping at any point of contact. Calculate acceleration

Consider a cylinder of mass M and radius lying on a horizontal plane or had as plank lying on its top as shown in figure. A force For is applied on the plank such that the plank moves and cause the cylinder To roll. The plank always remain horizontal. There is no slipping at any point of contact. Calculate acceleration

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Grade:12th pass

1 Answers

Vikas TU
14149 Points
6 years ago
Dear Student,
After making suitable FBDs,
These are the FBD of the plank and the ball.
Equation from fbd of plank
N1=mg-Fsinq
Fcosq-f1=ma1

Equations from the fbd of ball
f1-f2=Ma2 -------1
f1R+f2R=MR2α/2
=>f1+f2=MRα/2 --------2
N2=N1+mg
a2+Rα=a1

Solving 1 and 2
4f1=Ma1+Ma2

a1+a2=4f1/M
a1-a2=Rα

Solving these 2 above equations give
a1= 2f1/M + Rα/2
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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