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4. A frictionless circle of radius R is made out of a strip of metal and held fixed in a vertical plane. A massless spring with spring constant k has one end attached to the bottom point on the inside surface of the circle and the other end attached to a mass m. The spring is compressed to zero length with the mass touching the inside surface of the circle at the bottom. The spring is then released and the mass gets pushed initially to the right and then up along the circle. The setup at a random later time is shown in figure. Let I be the equilibrium length of the spring. What is the minimum value of 1 for which the mass remains in contact with the circle at all times? What is this minimum value when g = 0? Discuss this value. m
Transcribed Image Text:4. A frictionless circle of radius R is made out of a strip of metal and held fixed in a vertical plane. A massless spring with spring constant k has one end attached to the bottom point on the inside surface of the circle and the other end attached to a mass m. The spring is compressed to zero length with the mass touching the inside surface of the circle at the bottom. The spring is then released and the mass gets pushed initially to the right and then up along the circle. The setup at a random later time is shown in figure. Let I be the equilibrium length of the spring. What is the minimum value of 1 for which the mass remains in contact with the circle at all times? What is this minimum value when g = 0? Discuss this value. m
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