In what situations we can find that the work done by a force is zero?

Question

BlackTom AI · Accepted Answer

To analyze when work done by a force is zero, recall the definition of work in physics: W = F · d = F d cos(θ), where θ is the angle between the force vector F and the displacement vector d.

Option a: 'When the force is parallel to the displacement' would yield θ = 0°, so cos(θ) = 1, and W = F d, which is generally not zero unless either F or d is zero. This makes this option incorrect as a general statement.

Option b: 'When the force is opposite to the direction of the displacement' corresponds to θ = 180°, so cos(θ) = -1, giving W = -F d. The work is nonzero (negative) unless one of the quantities is zero, so this option is not a universal zero-work scenario.

Option c: 'When the force is parallel to but smaller than the displacement' means the force is in the same direction as the displacement but of smaller magnitude; the angle θ is still 0°, so cos(θ) = 1 and W = F d remains nonzero. The wording also implies a nonzero force and displacement, so this option is incorrect for zero work.

Option d: 'When the force is perpendicular to the displacement' sets θ = 90°, giving cos(90°) = 0 and thus W = F d cos(90°) = 0. This is the standard condition for zero work: the force does not do work when it is perpendicular to the displacement.

In summary, only the perpendicular arrangement guarantees zero work because the force does not have any component along the direction of motion, leading to zero energy transfer in the displacement direction.

UCIC 202503 PHYS101 Quiz 3

In what situations we can find that the work done by a force is zero?

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