Which scenario results in zero work done by a constant force?
A force acts perpendicular to the direction of motion
Work done by a constant force is \(W = F\,s\cos\theta\), where \(\theta\) is the angle between the force and the displacement.
When the force is perpendicular to the motion, \(\theta = 90^\circ\) and \(\cos 90^\circ = 0\), so \(W = 0\). Examples are the gravitational force on a body moving horizontally, or the centripetal force on a body moving in a circle.
For a force along the motion (\(\theta = 0^\circ\)) work is maximum and positive; for an acute angle, \(\cos\theta\) is positive, so work is positive; for a force against the displacement (\(\theta = 180^\circ\)) work is negative – none of these is zero.
Hence, zero work is done when a force acts perpendicular to the direction of motion.
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