Can you handle this system?

Classical Mechanics Level pending

A cart with mass \(\ 1kg \), cylinder with mass \(\ 0,5kg \), are connected together so the cylinder is rolling without slipping. The cylinder is wound with cord which is also draped over a pulley and then attached to a block with mass \(\ 0.2kg \) which moves without friction on the right side of the cart as shown in the picture. The wheels of the cart have negligible mass. What's the acceleration of the system in the horizontal direction in \(\ N/kg \) ?

\(\ g=9,81 N/kg \)

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