A cart of weight 400N is pushed up a slope by the resultant force of 50N. The cart moves a distance of 10m. By going up the slope, the change in height of the is 1m. What is the work done against friction up the slope?
The problem above is creating a slight confusion.
We can find the work done up the slope as 500J. While the work done to just lift the cart of the ground 1m as 400J. The work done against friction is the difference of the two. Hence 100J.
However, I do not understand the intuition for this calculation. When we calculate the work done up the slope, is it somehow the sum of both the work done vertically and the work done horizontally? Then we remove this work done vertically as it is independent of friction?
Is the above true? If so, how do we prove the work done at an angle is the sum of the work done horizontally and vertically? It doesn't intuitive sense considered work is a scalar.
Edit: I struggle to understand why we can just take $50\times 10=500$ to be the total work done. It seems unintuitive why the calculation is so easy. How do we prove regardless of direction that total work done is always $Fs$?