Potential of a conservative force

[TanGeriN]

Homework Statement

Hello everybody,

i have the following problem:

The following force vector is given:

$\vec{F}(x, y, z) = (2x + 3y)*\vec{e}_x + (z*cos(y*z))*\vec{e}_y + (y*cos(y*z))*\vec{e}_z$

Is it possible to find a potential for this given force? If it is possible, find it!

I somehow cannot figure out a solution, even though i know the equation for potential (at least i think that this is the relevant one in the setion below)

Homework Equations

$V(x, y, z) = \int_{}{} \vec{F}(x,y,z)d\vec{s}$

The Attempt at a Solution

I tried to integrate the x-, y- and z-components of the given force vector respectively, but for some reason i can't figure out how to properly integrate the components.
I hope someone here an help me. Best regards and thank you in advance.

 

[dauto]

Calculate the rotational of the force. If it vanishes than there is a potential otherwise no potential exists. If it does than chose some point in space as a reference point (any point) and integrate the force along some path (any path) from the reference point to the point with coordinates (x,y,z). That's the potential at (x,y,z).

 

[CAF123]

I tried to integrate the x-, y- and z-components of the given force vector respectively, but for some reason i can't figure out how to properly integrate the components.

Can you show where you are stuck? Checking to see if the curl of the force vanishes is one way to determine whether it is conservative. However, you can continue with your integrations and see if you notice any contradictions in the expressions you have for V collectively.

 

[TanGeriN]

Unfortunately i get stuck already when trying to integrate the very first component. How do you integrate $F_x = \int (2x+3y) dx$ ?

 

[tms]

Unfortunately i get stuck already when trying to integrate the very first component. How do you integrate $F_x = \int (2x+3y) dx$ ?

When integrating in the $x$ direction, $y$ is a constant.