In: Physics
An object of mass m=4.00 kg is acted on by a 2-D force of the form: F=C(x^2y^2,xy^3), where the coordinates are given in meters and the constant C=62.4 N/m^4.
a.) calculate the work that F does on an object if it moves from the origin to the point (2,2) along a straight line path (the shortest possible path).
b.) calculate the work that F does on the object if it moves between the two same points, but along a different path given by the curve y=x^2/2
c.) Is there a potential energy that can be associated with this force? If so, find the potential energy function U(x,y).
d.) Assume F is the only force that does work on the object. Calculate the minimum initial speed required for the object to reach the final point, along the path from part b.