Solution Found!

Consider a bead of mass m sliding without friction on a

Chapter 7, Problem 7.41

(choose chapter or problem)

Get Unlimited 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

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)

Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back