Final answer:
The work done by the force on a particle in the xy-plane cannot be calculated without additional information about the force field or the explicit path taken. Since the force is not clearly conservative and we do not have a specific potential energy function or a parametrization of the path, we cannot provide a numerical answer.
Step-by-step explanation:
To calculate the work done by the force f(x, y) = (30 N·m²)(xî + yĵ)(x² + y²)⁵/² on a particle as it moves from the point (8 m, 5 m) to the point (9 m, 6 m), we need to perform a line integral of the force along the path taken by the particle. Since the force is conservative, we can express the work done as the negative change in potential energy associated with the force field. However, because the provided force does not correspond to a standard conservative field, the actual calculation would require an expression for the potential energy or an explicit parametrization of the straight-line path and an integration of the force along that path.
Unfortunately, without the potential energy function or a clearly defined path, we cannot directly compute the work done. In real contexts, the work done could be found using calculus methods, specifically evaluating the line integral of the force along the path of the motion. Since we lack certain information in this case, we cannot provide a numerical answer to the work done without making assumptions or obtaining further details about the force field or the path.