Final answer:
To find the acceleration of a block down an incline connected to another block, one must consider all forces, apply Newton's second law, and solve the resulting system of equations.
Step-by-step explanation:
To find the magnitude of acceleration of block 2 down the incline, we need to apply Newton's second law and consider the forces acting on both blocks. For block 1 on the incline, we have gravity, normal force, frictional force, and tension in the string.
For block 2, we have gravity, normal force, frictional force, and tension as well. We would normally sum the forces parallel and perpendicular to the incline for each block, set up equations for each block's motion, and solve them simultaneously.
However, the question specifies coefficients of kinetic friction and angles of inclination for each block. This is a complex problem that requires a careful drawing of free-body diagrams for each block, writing down the equations based on the forces, and then solving these equations to give us the system acceleration and tensions in the strings.
The inclines of the ramps, the masses of the blocks, and the coefficients of kinetic friction all play key roles in these calculations.