Find the work done.

Question

A particle moves along line segments from the origin to the points (1, 0, 0), (1, 2, 1), (0, 2, 1), and back to the origin under the influence of the force field

Find the work done.

Answer 1

Step 1:

Work done by force in moving a particle along the path is .

Stokes theorem:

The function is .

If then .

Step 2:

Find the plane equation, for points and .

Let the equation of the plane is .

The point on the plane is

.

The point on the plane is .

Substitute in .

The point on the plane is .

Substitute , in .

Substitute in above expression.

The plane equation is .

Comments

Contd...

Step 3:
 

Where , is the projection of the surface on the plane and is the plane equation.

.

Substitute in above expression.

.

Step 4:

is the projection of the surface on the plane.

is the region inside the points and .

From the points and .

.

.

.

The work done is .

Solution:

The work done is .