Question

How do you calculate mechanical work when velocity remains constant in both directions for a moving body?

Answer 1

When the velocity of a moving body remains constant in both directions, it means that the body is moving at a constant speed without changing its direction. In such a scenario, the net force acting on the body is zero, and no work is done on the body by external forces.

Work is defined as the product of force and displacement, and it measures the transfer of energy to or from an object. Mathematically, the formula for work is:

$W=F\cdot d\cdot \cos (\theta )$

Where:

• $W$ is the work done on the object,
• $F$ is the applied force on the object,
• $d$ is the displacement of the object, and
• $\theta$ is the angle between the applied force and the direction of displacement.

Since the net force is zero when the velocity remains constant in both directions, the work done by any external forces is zero. This is because there is no force acting in the direction of displacement, or the force and displacement are perpendicular ($\theta =90^{\circ }$), resulting in a cosine of zero.

Therefore, in this specific case, the mechanical work done on the body is zero.