The system shown below consists of two disks, each with a mass of 1.00 kg, and a Hooke's Law spring with k= 50.0 N/m. See figure. In the initial figure, the speeds are known, and the spring is stretched 20.0 cm. In the final figure, the speeds are unknown, and the spring is compressed an unknown amount. Find vi, v2, and the final compression in the spring. You may assume that the system moves on a frictionless, horizontal plane, that system momentum is conserved, and that energy is conserved.

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**Problem 4 Explanation**

The system below includes two disks, each with a mass of 1.00 kg, connected by a Hooke's Law spring with a spring constant \( k = 50.0 \, \text{N/m} \). The scenario is depicted in a figure divided into two parts: initial and final states.

- **Initial State:**
  - The spring is stretched by 20.0 cm.
  - The first disk is moving upward with a velocity of 2.00 m/s.
  - The second disk is moving to the right with a velocity of 3.00 m/s.

- **Final State:**
  - The velocities of the disks, \( v_1 \) and \( v_2 \), are unknown.
  - The spring is compressed by an unknown amount.
  - Disk 1 makes a 30.0° angle with the horizontal axis, and Disk 2 makes a 40.0° angle with the horizontal axis.

**Assumptions:**
- The system operates on a frictionless, horizontal plane.
- Both momentum and energy are conserved throughout the process.

**Tasks:**
- Determine the final velocities \( v_1 \) and \( v_2 \).
- Calculate the final compression of the spring. 

This scenario requires the application of conservation of momentum and energy principles to solve for the unknowns.
Transcribed Image Text:**Problem 4 Explanation** The system below includes two disks, each with a mass of 1.00 kg, connected by a Hooke's Law spring with a spring constant \( k = 50.0 \, \text{N/m} \). The scenario is depicted in a figure divided into two parts: initial and final states. - **Initial State:** - The spring is stretched by 20.0 cm. - The first disk is moving upward with a velocity of 2.00 m/s. - The second disk is moving to the right with a velocity of 3.00 m/s. - **Final State:** - The velocities of the disks, \( v_1 \) and \( v_2 \), are unknown. - The spring is compressed by an unknown amount. - Disk 1 makes a 30.0° angle with the horizontal axis, and Disk 2 makes a 40.0° angle with the horizontal axis. **Assumptions:** - The system operates on a frictionless, horizontal plane. - Both momentum and energy are conserved throughout the process. **Tasks:** - Determine the final velocities \( v_1 \) and \( v_2 \). - Calculate the final compression of the spring. This scenario requires the application of conservation of momentum and energy principles to solve for the unknowns.
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