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Physics Olympiads Series Problem 14

 

A homogeneous solid cylinder named A, with mass m1 is freely to rotate in it's axis. The cylinder is connected to block B with mass m2 See the figure.



Constant force F applied to the end of the string that is wrapped around the cylinder. Ignore all possible frictional forces, find:
(a) the acceleration of the rope end
(b) kinetic energi after t sec
Source of problem: Mekanika 1-Prof Yohanes Surya


Solution
(a) Assume that x and xpm are the displacement of point K and cylinder center of mass. If theta; is the rotation angle of cylinder then,

So then
In here, acm is the acceleration of ylinder A center of mass, a is
the acceleration of point K, α is the angular acceleration of A.
The translation:

From cylinder translation:

From the equations we get:

(b) Work done by F equals the defference of kinetic energy.


Solution Source: Mekanika 1 - Prof. Yohanes Surya
Note : The origin document is written in Indonesian Language

 

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