Just before 5. A spring is used to launch a block up a frictionless ramp as shown at right. At time t, the spring is compressed and the block is released from point A. The block moves up the ramp, losing contact with the spring at point B. When it passes point C, the block has a velocity vc directed up the ramp. Imagine a system that includes the block and possibly one or more additional objects. BA Is it possible to choose a system whose total energy is constant during the interval from t, to t,? If so, state which object(s) must be included in the system. Explain. a. tner o d Anteo BA b. Is it possible to choose a system so that the total energy is not constant during the interval from t, to t,? If so, what is the system containing the fewest possible objects for which the energy is not constant during this interval? Explain. vd bnob show n o p elbtimy Inont visini od gd ninlqx h 0 n gaiwollol edb old ad sga initini sdt latot s

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**Conservation of Energy - Problem Overview**

**Scenario Description:**
A spring is utilized to launch a block up a frictionless ramp as shown in the diagram. At time \( t_1 \), the spring is compressed, and the block is released from point A. The block ascends the ramp, losing contact with the spring at point B. When it reaches point C, the block possesses a velocity \( v \) directed upward along the ramp.

**Task:**
Imagine a system that includes the block and possibly one or more additional objects.

**a. Energy Conservation Analysis:**
Question: Is it possible to choose a system whose total energy remains constant throughout the interval from \( t_1 \) to \( t_2 \)? If yes, identify the object(s) that must be included in the system. Provide an explanation.

**b. Non-Conservation of Energy Analysis:**
Question: Is it possible to select a system such that the total energy is not constant during the interval from \( t_1 \) to \( t_2 \)? If so, identify the system with the fewest objects for which the energy is not constant during this period. Provide an explanation.

**Diagram Explanation:**
The diagram illustrates two stages of the system:

1. **Just before \( t = t_1 \):**
   - The block is at the initial position with the spring fully compressed.

2. **At \( t = t_2 \):**
   - The block is at point C moving with velocity \( v \), having been released from the spring and ascended the ramp. The spring is now relaxed at point A.

This problem requires understanding and application of the principles of energy conservation to analyze the system's behavior across the defined interval.
Transcribed Image Text:**Conservation of Energy - Problem Overview** **Scenario Description:** A spring is utilized to launch a block up a frictionless ramp as shown in the diagram. At time \( t_1 \), the spring is compressed, and the block is released from point A. The block ascends the ramp, losing contact with the spring at point B. When it reaches point C, the block possesses a velocity \( v \) directed upward along the ramp. **Task:** Imagine a system that includes the block and possibly one or more additional objects. **a. Energy Conservation Analysis:** Question: Is it possible to choose a system whose total energy remains constant throughout the interval from \( t_1 \) to \( t_2 \)? If yes, identify the object(s) that must be included in the system. Provide an explanation. **b. Non-Conservation of Energy Analysis:** Question: Is it possible to select a system such that the total energy is not constant during the interval from \( t_1 \) to \( t_2 \)? If so, identify the system with the fewest objects for which the energy is not constant during this period. Provide an explanation. **Diagram Explanation:** The diagram illustrates two stages of the system: 1. **Just before \( t = t_1 \):** - The block is at the initial position with the spring fully compressed. 2. **At \( t = t_2 \):** - The block is at point C moving with velocity \( v \), having been released from the spring and ascended the ramp. The spring is now relaxed at point A. This problem requires understanding and application of the principles of energy conservation to analyze the system's behavior across the defined interval.
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