Determine the work as objects moves in straight line

[bfusco]

Homework Statement

Assume that a force acting on an object is given by F=axi+byj, where a=2.9 N/m and b=3.9 N/m. Determine the work done on the object by this force as it moves in a straight line from the origin to r=(10.0i +21.5j)

The Attempt at a Solution

i used the given info to calculate the magnitude of the Force. F=2.9(10)+3.9(21.5)=112.9. i then calculated the distance traveled by doing arctan (21.5/10)=23.7. W=FΔx, W=112.9x23.7=2675. which is wrong, apparently the answer is roughly 1000 J.

 

[OldEngr63]

Maybe you should try calculating the work directly from the definition:

W = ∫_(0,0^(10,21.5) (ax i + by j). (dx i + dy j)

=∫₀¹⁰ ax dx + ∫^021.5 by dy

= (a/2) x²|₀¹⁰ + (b/2) y²|₀^21,5

Complete the evaluation and see how that works out for you.