Find the work done

Question

The work W done by a constant force F in moving an object from a point A in space to a point B in space is defined as . use this definition.

Find the work done by a force of 3 newtons acting in the direction 2i + j + 2k in moving an object 2 meters from (0, 0, 0) to (0, 2, 0).

Answer 1

Step 1 :

Work done is , Where F  is the force vector and u  is the position vector.

Position vector :

If the initial point and the terminal point is , then

the position vector is

Step 2 :

Force vector is

The points are and

The position vector is

Substitute the points and in above equation.

The position vector is

The work done is

Substitute and in above equation.

The work done is 2 newton-meters.

Solution :

The work done is 2 newton-meters.