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Consider a bead of mass m sliding without friction on a
Chapter 7, Problem 7.41(choose chapter or problem)
Consider a bead of mass m sliding without friction on a wire that is bent in the shape of a parabola and is being spun with constant angular velocity w about its vertical axis, as shown in Figure 7.17. Use cylindrical polar coordinates and let the equation of the parabola be z = kp2 . Write down the Lagrangian in terms of p as the generalized coordinate. Find the equation of motion of the bead and determine whether there are positions of equilibrium, that is, values of p at which the bead can remain fixed, without sliding up or down the spinning wire. Discuss the stability of any equilibrium positions you find. Figure 7.17 7.41
Questions & Answers
QUESTION:
Consider a bead of mass m sliding without friction on a wire that is bent in the shape of a parabola and is being spun with constant angular velocity w about its vertical axis, as shown in Figure 7.17. Use cylindrical polar coordinates and let the equation of the parabola be z = kp2 . Write down the Lagrangian in terms of p as the generalized coordinate. Find the equation of motion of the bead and determine whether there are positions of equilibrium, that is, values of p at which the bead can remain fixed, without sliding up or down the spinning wire. Discuss the stability of any equilibrium positions you find. Figure 7.17 7.41
ANSWER:Step 1 of 8
Given,
A bead of mass is spinning around with an angular velocity .
The equation of the parabola is ........(1)