In an experiment, one of the forces exerted on a proton is

where α=12N/m2.

a) How much work does F do when the proton moves along the straight-line path from the point (0.10 m, 0) to the point (0.10 m, 0.40 m)?

b) Along the straight-line path from the point (0.10 m, 0) to the point (0.30 m, 0)?

c) Along the straight-line path from the point (0.30 m, 0) to the point (0.10 m, 0)?

d) Is the force F conservative? Explain. If F is conservative, what is the potential energy function for it? Let U = 0 when x = 0.