Optimizing Projectile Motion: Finding the Maximum Height in a Vertical Circle

AI Thread Summary
To achieve maximum height in projectile motion after cutting the string of a mass swinging in a vertical circle, the string should be cut when the mass is at the lowest point of the swing. At this position, the mass has the highest kinetic energy, allowing it to convert this energy into potential energy as it rises. The necessary minimum speed at the top of the circle ensures the string remains taut, providing the required momentum for optimal height. This setup guarantees that the resulting trajectory peaks directly above the center of the circle. Understanding these dynamics is crucial for optimizing projectile motion in this scenario.
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A mass is attached to one end of the massless string, the other and of which is attached to a foxed support. The mass swings around in a vertical circle as shown in Fig 5.36. Assuming that the mass has the minimum speed necessary at the top of the circle to keep the string from going slack, at what location should you cut the string so that the resulting projectile motion of the mass has its maximum height located directly above the center of the circle.
 

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A mass is attached to one end of the massless string, the other and of which is attached to a foxed support. The mass swings around in a vertical circle as shown in Fig 5.36. Assuming that the mass has the minimum speed necessary at the top of the circle to keep the string from going slack, at what location should you cut the string so that the resulting projectile motion of the mass has its maximum height located directly above the center of the circle.
 

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