Tried Solving a Problem but Need Help?

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The discussion revolves around a problem-solving attempt using the definition of work in the x-direction, which the user finds ineffective. They initially considered proving the solution in one dimension before extending it but realized the need for a Cartesian coordinate system and the displacement vector. A participant pointed out that the surface's shape and orientation complicate the approach, leading to the user's acknowledgment of this oversight. The user recognizes that assuming a flat surface was a mistake, highlighting the complexity of the problem. The conversation emphasizes the importance of considering surface characteristics when applying mathematical solutions.
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Homework Statement
Please see below
Relevant Equations
Please see below
1673238784811.png

The solution is,
1673238812559.png
,
However is there a better way?

I tried using their suggestion of the definition of work and applying it in the x-direction.
1673238967342.png

But it does not seem to work.

Thanks for any help!
 
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Callumnc1 said:
But is not dose seem to work.
Do you mean "But it does not seem to work."?
 
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PeroK said:
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.
 
Callumnc1 said:
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?
 
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PeroK said:
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.
 
Callumnc1 said:
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?
 
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PeroK said:
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
 
Callumnc1 said:
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?
 
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PeroK said:
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!
 
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