A triangle of cylinders (part 1)

Classical Mechanics Level 5

Three identical solid cylinders are situated in a triangle as shown in figure. Find the initial downward acceleration of the top cylinder, if there is friction between the bottom two cylinders and the ground (so they roll without slipping), but there is no friction between any of the cylinders.

Details:

  • g = 10 m s − 2 g=10ms^{-2}

  • R = 1 m R=1m


The answer is 1.00.

Aditya Kumar by Aditya Kumar , 22, India

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1 solution

Ayush Verma
Jan 19, 2016

I = β m R 2 = 1 2 m R 2 ⇒ 6 β = 3 a y = g 7 + 6 β = 10 7 + 3 = 1 I=\beta m{ R }^{ 2 }=\cfrac { 1 }{ 2 } m{ R }^{ 2 }\Rightarrow 6\beta =3\\ \\ { a }_{ y }=\cfrac { g }{ 7+6\beta } =\cfrac { 10 }{ 7+3 } =1

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