A block of mass 3 ~kg is placed on a frictionless inclined plane of angle 30^ . It is connected to a hanging block of mass 2 ~kg by a light inextensible string passing over a smooth pulley at the top of the incline. When the system is released from rest, what is the acceleration of the blocks? (Take g = 10 ~m ~s ⁻² )

Step-by-step solution

Let a be the common acceleration of the system and T be the tension in the string. For the hanging block of mass M = 2 ~kg , the weight acts downwards ( M g = 20 ~N ). For the block of mass m = 3 ~kg on the incline, the component of weight acting down the incline is m g 30^ = 3(10)(0.5) = 15 ~N . Since 20 ~N > 15 ~N , the 2 ~kg block will accelerate downwards and the 3 ~kg block will accelerate up the incline. Writing the equations of motion for both blocks: For the 2 ~kg block: 20 - T = 2a For the 3 ~kg block: T -