https://file.aiquickdraw.com/mathbot/file/1728320316977o5l0cw86.jpg

The problem states that there are two blocks with masses \( M_1 \) and \( M_2 \) hanging one under the other, and you are tasked with finding the tension \( T_1 \) in the upper rope. You are instructed to express the answer in terms of \( M_1 \), \( M_2 \), and \( g \) (the acceleration due to gravity).

### Approach:
1. **Forces acting on the lower block \( M_2 \):**
   - The tension in the rope directly supporting \( M_2 \) is \( T_2 \).
   - The force due to gravity acting on \( M_2 \) is \( M_2g \).

   Using Newton's second law, the net force on \( M_2 \) (if the system is in equilibrium or moving at constant velocity) is:
   \[
   T_2 = M_2g
   \]

2. **Forces acting on the upper block \( M_1 \):**
   - The tension \( T_1 \) in the upper rope must support both the weight of \( M_1 \) and the tension \( T_2 \) (which is supporting \( M_2 \)).
   - The force due to gravity acting on \( M_1 \) is \( M_1g \).

   The total tension \( T_1 \) must balance these two forces:
   \[
   T_1 = M_1g + T_2
   \]
   Substituting \( T_2 = M_2g \) into the equation for \( T_1 \):
   \[
   T_1 = M_1g + M_2g = (M_1 + M_2)g
   \]

### Final Answer:
The tension in the upper rope, \( T_1 \), is:
\[
T_1 = (M_1 + M_2)g
\]

This expression shows that the tension depends on the combined weight of both masses.

---

Do you want more details on any step, or have any other questions? 

Here are five related questions:
1. How would the answer change if the system is accelerating upward?
2. What if the blocks are moving downward with an acceleration \( a \)?
3. How would you solve this problem if \( M_1 \) and \( M_2 \) are connected by a pulley?
4. What would happen to the tension if the mass of \( M_2 \) is much larger than \( M_1 \)?
5. How would the result be different on another planet with different gravity?

**Tip:** When solving tension problems, always identify all forces acting on each block and apply Newton's second law step by step.

Two blocks with masses M_1 and M_2 hang one under the other. Find T_1, the tension in the upper rope, in terms of M_1, M_2, and g.

Learn how to calculate the tension in the upper rope (T_1) for two blocks with masses M_1 and M_2 hanging one under the other. This problem applies Newton's second law and is suitable for high school physics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation