(1) The 3-block system shown below is on a surface that is so slippery you may consider it to be frictionless. The 3.0 kg and 1.0 kg masses are connected by a very light rope, and a force F = 84 N force acts directly on the 2.0 kg mass as shown. (a) Calculate: the tension in the rope • the force exerted on the 2.0 kg block by the 3.0 kg block • the force exerted on the 3.0 kg block by the 2.0 kg block. [answer: tension in rope = 14 N; F30n2 = F20n3 = 56 N] (b) Suppose all three blocks had a common speed of 42 m/s to the left at the moment the force F was applied. How long will it take the motion of the blocks to reverse direction after F is applied? [answer: 3.0 s] 1.0 kg F 2.0 kg 3.0 kg

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**Three-Block System Analysis**

In this problem, we explore the dynamics of a three-block system set on a frictionless surface. The system includes blocks weighing 3.0 kg, 2.0 kg, and 1.0 kg. The 3.0 kg and 1.0 kg blocks are connected by a very light rope, and a force \( F = 84 \, \text{N} \) is applied directly to the 2.0 kg mass.

### Objective:
1. **Calculate the following:**
   - **Tension in the rope.** 
   - **Force exerted on the 2.0 kg block by the 3.0 kg block.** 
   - **Force exerted on the 3.0 kg block by the 2.0 kg block.**

   **Solution:**
   - Tension in the rope: \( 14 \, \text{N} \)
   - Force exerted on the 2.0 kg block by the 3.0 kg block: \( 56 \, \text{N} \)
   - Force exerted on the 3.0 kg block by the 2.0 kg block: \( 56 \, \text{N} \)

2. **Reverse Motion Analysis:**
   - Assume all three blocks initially have a common speed of \( 42 \, \text{m/s} \) to the left at the moment the force \( F \) is applied.
   - Determine the time required for the motion of the blocks to reverse direction.

   **Solution:**
   - Time to reverse direction: \( 3.0 \, \text{s} \)

### Diagram Explanation:
The diagram illustrates a horizontal arrangement of the blocks:
- **1.0 kg block** on the left, **3.0 kg block** on the right, and **2.0 kg block** in the center.
- Block masses are depicted, and the force \( F \) is shown acting to the right on the 2.0 kg block.
- The system is on a surface where friction is negligible, enabling an ideal scenario for these calculations.
Transcribed Image Text:**Three-Block System Analysis** In this problem, we explore the dynamics of a three-block system set on a frictionless surface. The system includes blocks weighing 3.0 kg, 2.0 kg, and 1.0 kg. The 3.0 kg and 1.0 kg blocks are connected by a very light rope, and a force \( F = 84 \, \text{N} \) is applied directly to the 2.0 kg mass. ### Objective: 1. **Calculate the following:** - **Tension in the rope.** - **Force exerted on the 2.0 kg block by the 3.0 kg block.** - **Force exerted on the 3.0 kg block by the 2.0 kg block.** **Solution:** - Tension in the rope: \( 14 \, \text{N} \) - Force exerted on the 2.0 kg block by the 3.0 kg block: \( 56 \, \text{N} \) - Force exerted on the 3.0 kg block by the 2.0 kg block: \( 56 \, \text{N} \) 2. **Reverse Motion Analysis:** - Assume all three blocks initially have a common speed of \( 42 \, \text{m/s} \) to the left at the moment the force \( F \) is applied. - Determine the time required for the motion of the blocks to reverse direction. **Solution:** - Time to reverse direction: \( 3.0 \, \text{s} \) ### Diagram Explanation: The diagram illustrates a horizontal arrangement of the blocks: - **1.0 kg block** on the left, **3.0 kg block** on the right, and **2.0 kg block** in the center. - Block masses are depicted, and the force \( F \) is shown acting to the right on the 2.0 kg block. - The system is on a surface where friction is negligible, enabling an ideal scenario for these calculations.
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