Tried Solving a Problem but Need Help?

[ChiralSuperfields]

Homework Statement

Please see below

Relevant Equations

Please see below

The solution is,

,
However is there a better way?

I tried using their suggestion of the definition of work and applying it in the x-direction.

But it does not seem to work.

Thanks for any help!

 

[PeroK]

But is not dose seem to work.

Do you mean "But it does not seem to work."?

 

[ChiralSuperfields]

Do you mean "But it does not seem to work."?

Thanks for your reply @PeroK ! Yes, sorry that was what I meant - I have fixed it now.

 

[PeroK]

Thanks for your reply @PeroK ! Yes, sorry that was what I meant - I have fixed it now.

What's the relevance of $x$ in this case? Did you understand the book solution?

 

[ChiralSuperfields]

What's the relevance of $x$ in this case? Did you understand the book solution?

Thanks for your reply @PeroK ! I thought maybe I could prove it in the x-direction first then extend it to more dimensions. But I guess I should probably use at least the cartesian coordinate system so do it in terms of the displacement vector ds like the solutions.

 

[PeroK]

Thanks for your reply @PeroK ! I thought maybe I could prove it in the x-direction first then extend it to more dimensions. But I guess I should probably use at least the cartesian coordinate system so do it in terms of the displacement vector ds like the solutions.

What if the $x$ direction is normal to the surface?

 

[ChiralSuperfields]

What if the $x$ direction is normal to the surface?

Thanks for your reply @PeroK ! I guess that means that y-direction will be along the surface

 

[PeroK]

Thanks for your reply @PeroK ! I guess that means that y-direction will be along the surface

The surface could be any shape and any orientation. Your attempted solution in general is doomed! Do you see that?

 

[ChiralSuperfields]

The surface could be any shape and any orientation. Your attempted solution in general is doomed! Do you see that?

Oh true @PeroK! I forgot that the surface could be any shape! I was assuming that the surface was flat. That would be very hard to account for the shape of the surface doing it my way!! Thank you!