Determine the work done in moving anobject from the point (0, 2.0 m, – 2.0 m) tothe point (3.0 m, 4.0 m, – 2.0 m) when aconstant force →= +ˆ ˆF (4.0 N) (3.0)i j isexerted on it

To determine the work done in moving an object from the point (0, 2.0 m, -2.0 m) to the point (3.0 m, 4.0 m, -2.0 m) when a constant force →= +ˆ ˆF (4.0 N) (3.0)i j is exerted on it, we can use the formula for work:

Work = Force * Displacement * cos(theta)

First, let's calculate the displacement vector. The displacement vector is the difference between the final position vector and the initial position vector:

Displacement = (3.0 m, 4.0 m, -2.0 m) - (0, 2.0 m, -2.0 m) = (3.0 m - 0, 4.0 m - 2.0 m, -2.0 m - (-2.0 m)) = (3.0 m, 2.0 m, 0)

Next, we need to calculate the angle between the force vector and the displacement vector. Since the force vector is given as →= +ˆ ˆF (4.0 N) (3.0)i j, we can see that the force is acting in the positive x-direction. Therefore, the angle between the force and displacement vectors is 0 degrees.

Now, we can calculate the work:

Work = (4.0 N) * (3.0 m) * cos(0 degrees) = 12.0 Nm

Therefore, the work done in moving the object from the point (0, 2.0 m, -2.0 m) to the point (3.0 m, 4.0 m, -2.0 m) when a constant force of 4.0 N in the positive x-direction is exerted on it is 12.0 Nm.