Kibble book exercise about conservative forces

[joaosavio]

Homework Statement

Kibble book exercise 1, chapter 3. It is the following:

Find which of the following forces are conservative, and, for those that are conservative, determine the corresponding potential energy function (a and b are constants, and a is a constant vector)

ii) Fx= a*y Fy=a*z Fy=a*x

 

[tiny-tim]

Duplicate thread!

Duplicate to https://www.physicsforums.com/showthread.php?t=654909

 

[joaosavio]

Hello!

Yes, but I've receive a warning in that thread. In fact, this is the right place to post homework questions, isn't it?

 

[D H]

Yes it is, and you did not follow the template. You deleted two of the most important parts of the homework template: Relevant equations and The attempt at a solution.

We don't do your homework for you at this site. We help you do your own homework. You need to show what you have done to attempt to solve the problem.

So what are the relevant equations here, and what have you done to answer this question?

 

[paranormal]

Based on the definition of a conservative force, which states that the work done by the force is independent of the path taken, we can determine the conservative forces in this exercise.

In this case, Fx and Fy are conservative forces since they only depend on the position of the object and not on the path taken. This means that the work done by these forces will be the same regardless of the path taken.

To determine the corresponding potential energy function, we can use the formula: U = -∫F*dx, where U is the potential energy and F is the conservative force.

For Fx = a*y, the potential energy function would be U = -a*y^2/2 + C, where C is a constant.

Similarly, for Fy = a*z, the potential energy function would be U = -a*z^2/2 + C.

For Fz = a*x, the potential energy function would be U = -a*x^2/2 + C.

In conclusion, Fx and Fy are conservative forces with potential energy functions of U = -a*y^2/2 + C and U = -a*z^2/2 + C, respectively. Fz is not a conservative force as its potential energy function would be U = -a*x^2/2 + C, which is different from the potential energy functions for Fx and Fy.