Let's break down the problem from the image:

Given Information:

• Two blocks with masses $M_1$ and $M_2$ hang one under the other.
• The positive direction is upward.
• We use $g$ as the magnitude of the free-fall acceleration (gravitational acceleration).
• Both blocks are at rest.

Part A:

You are asked to find the tension $T_2$ in the lower rope.

Approach:

Since the blocks are at rest, we can apply Newton's Second Law to each block. Specifically, we can consider the forces acting on each block in equilibrium (since they are at rest).

For the lower block with mass $M_2$:

• The forces acting on this block are:
  1. The downward gravitational force: $M_2 g$.
  2. The upward tension $T_2$ from the rope.

Since the block is at rest (in equilibrium), the forces must balance. Therefore: $T_2 = M_2 g$

Conclusion:

The tension in the lower rope, $T_2$, is equal to the weight of the lower block: $T_2 = M_2 g$

Do you need any further details on this solution? Here are 5 related questions you might find useful:

1. What would the tension $T_1$ be in the upper rope holding both blocks?
2. How would the tension change if the blocks were accelerating upward or downward?
3. What happens to the tension if one of the blocks is heavier than the other?
4. How would you express the net force on each block if the system were moving?
5. What if the blocks were on an inclined plane instead of hanging vertically?

Tip: When dealing with multiple forces in a system at rest, always apply Newton's Second Law by summing forces and setting them equal to zero to solve for unknowns like tension.