Final answer:
The tension in the string connecting two blocks on a frictionless incline is uniform throughout due to a massless, frictionless pulley system and can be determined using Newton's second law and free-body diagrams.
Step-by-step explanation:
When considering two blocks at rest on a frictionless incline connected by a string, the tension in the string can be calculated by considering the forces acting on each block separately. Utilizing free-body diagrams and resolving forces along the incline allows us to determine the tension in the string as it relates to the weight of the blocks and the angle of the incline. Even for blocks of different masses, like a 2.00 kg block (mass 1) and a 4.00 kg block (mass 2) connected on an incline of 40.0°, where friction is negligible, the same principle applies: the tension in the string will be the same for both blocks due to the massless, frictionless string and pulley.
The acceleration of each block is calculated using Newton's second law, considering the net force along the direction of acceleration and factoring in gravitational forces. This acceleration will be the same for both blocks since they are connected. Meanwhile, to find the tension in the string, we analyze the force components along the string's length for each block, keeping in mind that tension will be uniform throughout the string due to the absence of mass and friction in the pulley system.