A mass m₁ is attached to a massless hoop of radius R that lies in a vertical plane. The hoop is free to rotate about its fixed center. m₁ is tied to a string which winds part way around the hoop, then rises vertically up and over a massless pulley. A mass m2 hangs on the other end of the string. a) Write down the total potential energy of the two masses. b) Use the potential energy to find the values of m₁ and m2 for which there are any positions of equilibrium. Describe the equilibrium positions and discuss their stability. m2 R m1
A mass m₁ is attached to a massless hoop of radius R that lies in a vertical plane. The hoop is free to rotate about its fixed center. m₁ is tied to a string which winds part way around the hoop, then rises vertically up and over a massless pulley. A mass m2 hangs on the other end of the string. a) Write down the total potential energy of the two masses. b) Use the potential energy to find the values of m₁ and m2 for which there are any positions of equilibrium. Describe the equilibrium positions and discuss their stability. m2 R m1
Question
Transcribed Image Text:A mass m₁ is attached to a massless hoop of radius R that lies in a vertical plane. The
hoop is free to rotate about its fixed center. m₁ is tied to a string which winds part
way around the hoop, then rises vertically up and over a massless pulley. A mass m2
hangs on the other end of the string.
a) Write down the total potential energy of the two
masses.
b) Use the potential energy to find the values of m₁
and m2 for which there are any positions of
equilibrium. Describe the equilibrium positions
and discuss their stability.
m2
R
m1
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