Question

Consider the conservative force field F = (12x²y +4-y) i + x(4x² - 1) j.

Find a function f(x,y) such that F = Vf.
f= 4x³ * y + 4x - xy
Use this result to find the work done if this force field moves an object from the point (3,2) along the piecewise linear path to (7,2), and from there to (10,5).
Work =

Answer 1

To find the work done by a force field along a given path, we use the dot product of the force field and the displacement vector and integrate it. In this case, we have two paths: (3,2) to (7,2) and (7,2) to (10,5). We can use the function f(x,y) = 4x³ * y + 4x - xy to represent the force field along both paths.

Step-by-step explanation:

To find the work done by a force field, we integrate the dot product of the force field and the displacement vector along the given path. In this case, we have two paths: from (3,2) to (7,2) and from (7,2) to (10,5).

For the path from (3,2) to (7,2), we can use the function f(x,y) = 4x³ * y + 4x - xy to represent the force field F. The work done is given by the integral of F · dr over this path.

Similarly, for the path from (7,2) to (10,5), we can use the same function f(x,y) = 4x³ * y + 4x - xy to represent the force field F. The work done is again given by the integral of F · dr over this path.