The system is released from rest with the spring initially stretched 3 in. Calculate the velocity v of the cylinder after it has dropped 0.5 in. The spring has a stiffness of 6 lb/in. Neglect the mass of the small pulley.
The system is released from rest with the spring initially stretched 3 in. Calculate the velocity v of the cylinder after it has dropped 0.5 in. The spring has a stiffness of 6 lb/in. Neglect the mass of the small pulley.
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Transcribed Image Text:**Problem 3/142**
The system is released from rest with the spring initially stretched 3 inches. Calculate the velocity \( v \) of the cylinder after it has dropped 0.5 inches. The spring has a stiffness of 6 lb/in. Neglect the mass of the small pulley.
**Diagram Explanation:**
The diagram shows a vertical setup where a spring with a stiffness of \( k = 6 \) lb/in is attached to a fixed support. The spring is connected to a pulley system, holding a 100 lb weight (cylinder). The initial setup assumes the spring is stretched 3 inches from its natural length. The task is to find the velocity of the weight once it descends an additional 0.5 inches.
- The spring force and stiffness are critical factors in this problem.
- The mass of the pulley is considered negligible, simplifying the calculations.
This setup illustrates principles of mechanics, energy conservation, and motion.
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