Final answer:
The work done by a force field when moving an object is calculated with the line integral of the force along the path. For a constant force and a straight path, the work done can be found by the dot product of the force vector and displacement vector.
Step-by-step explanation:
The work done by a force field F(x,y) when moving an object along a path from point P to point Q is calculated by integrating the force along the path.
From P(0,1) to Q(4,9), the force field is F(x,y) = (4y³/² +3)i + 6x√y. To find the work done, we calculate the line integral of the force field along the path of the object. If the path is straight and the force is constant, the work done by the force can be simplified to the product of the force, the displacement, and the cosine of the angle between them.
For the example problem provided, where F1 = (3 N)i + (4 N)j, the work done by F1 when moving the particle from (0 m, 0 m) to (5 m, 6 m) would be the dot product of F1 and the displacement vector D, given by:
W = F·D = (3 N)i·(5 m)i + (4 N)j·(6 m)j = (15 N·m) + (24 N·m) = 39 J (Joules), assuming no changes in force along the path and that the force is perpendicular to the displacement.