## Physics Olympiads Series Problem 14

- Category: Olympiads
- Written by fisikastudycenter

A homogeneous solid cylinder named A, with mass m_{1} is freely to rotate in it's axis. The cylinder is connected to block B with mass m_{2} 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 x_{pm} are the displacement of point K and cylinder center of mass. If theta; is the rotation angle of cylinder then,

So then

In here, a_{cm} 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