Energy question, what are the quantities conserved?

Clara Chung · Apr 10, 2018

Homework Statement

Printed exam question 8 on a particle moving in the (x, y) plane under the potential energy V(x, y) = (x² + 2y² + αy⁴) J, with parts on work done, force, conserved quantities, Newton's second law, energy and maximum displacements.

Homework Equations

The Attempt at a Solution

I don't know how to do the last part. What are the additional conservation laws? I don't think momentum is conserved because there is force acting on the particle. I don't think angular momentum is conserved too because there is a torque acting on the particle.
Here is the numerical answer:

Typeset homework solution: Work done = 4 J; force F = -2x i - (4y + 4 alpha y^3) j; total mechanical energy = 20 J; x_max = sqrt(20), y_max = [(-1 + sqrt(1+20 alpha))/alpha]^0.5; x_max = 2, y_max = [(-1 + sqrt(1+16 alpha))/alpha]^0.5.

TSny · Apr 10, 2018

Note that the equation for ##\ddot x## involves only ##x## (not ##y##). Similar comment for ##\ddot y##.

Imagine the x equation described a particle moving only along the x-axis. Anything conserved in this x-motion?

Clara Chung · Apr 11, 2018

TSny said:

Note that the equation for ##\ddot x## involves only ##x## (not ##y##). Similar comment for ##\ddot y##.

Imagine the x equation described a particle moving only along the x-axis. Anything conserved in this x-motion?

Thank you, I think the energy along x and y-axis are conserved too. Then I can find the answer.

Energy question, what are the quantities conserved?

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

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