Question

A force F acts on an object. When is the work done by F on an object equal to zero?

You may choose more than one correct answer.
1) When the force vector and the displacement vector are anti-parallel to each other.
2) Of a force act for a time finite interval Δt, the work done by the force is never zero,
3) When the force vector and the displacement vector are perpendicular too each other.
4) When the object does not change its position.
5) When the force vector and the displacement vector are parallel to each other.

Answer 1

The work done by a force on an object is zero when the force vector and displacement vector are perpendicular or when there is no displacement of the object.

Step-by-step explanation:

The work done by a force on an object is zero in several situations. The formula used to calculate work is W = Fd cos θ, where F is the magnitude of the force applied, d is the displacement, and θ is the angle between the force vector and displacement vector. Work is zero if:

• The force vector and displacement vector are perpendicular to each other (cos 90° = 0, hence, W = 0).
• The object does not change its position (Δd = 0, hence, W = 0).

Therefore, the correct answers to the question are 3) when the force vector and the displacement vector are perpendicular to each other and 4) when the object does not move. The other options are incorrect because:

• When forces and displacement are anti-parallel (cos 180° = -1), the work done is negative, not zero.
• A force acting for a time interval does not guarantee work is done; displacement is required.
• When forces and displacement are parallel (cos 0° = 1), work done is positive.