Finding potential U from sum of forces F

[Geranimo]

< Mentor Note -- Thread moved to Homework Help from technical Physics forum >

Hi, I had an exam and I had this question:

A force acts on a particle of mass m, and its components are:

Fx = 2axy + by² + 6cz
Fy = ax² + 2byx
Fz = 6cx

a) Does this force is conservative? Show your calculations.
b) Find the potential associated with this force. (this one cause me trouble)
c) Calculate the work done by the force when the particle moves from the origin
at x₀, y₀, z₀.

For a) we need to verify that F x ∇U is zero,

but for b) I don't know if I had to use (minus) the work integral or F = -∇U

c) One only had to apply the work integral to the 3 components.

Also, does U works like vectors? I mean, in b) can I do 3 work integrals for x,y,z and sum back? Or I need to integrate the 3 forms of F = -∇U?

Thanks.

 

[Chestermiller]

What happens if you dot the equation ##\vec{F}=-\vec{∇} {U}## by the differential position vector ##\vec{ds}=\vec{i}_x dx+\vec{i}_y dy+\vec{i}_z dz##? What does the right hand side look like?

Chet