Physics · Work, Energy And Power · NEET
In W = F d cos theta, both F (force magnitude) and d (displacement magnitude) are always positive. So the sign of work depends only on cos theta. If theta is between 0 and 90 degrees, cos theta is positive, so work is positive. If theta is exactly 90 degrees, cos theta = 0, so work is zero. If theta is between 90 and 180 degrees, cos theta is negative, so work is negative. This one idea answers almost every NEET question on the sign of work.
Kinetic friction on a sliding body is negative, because friction acts opposite to the motion, so theta = 180 degrees and cos 180 = -1. But friction is not always negative. When you walk or a car accelerates, static friction pushes forward, in the direction of motion, so it can do positive work. Do not memorise 'friction = negative'; instead check the angle between the friction force and the displacement each time.
No. Negative work means energy is taken away from the moving body and given to something else. When friction does negative work, the lost kinetic energy becomes heat. When gravity does negative work on a ball thrown up, the kinetic energy becomes potential energy. Total energy is always conserved; the negative sign only shows the direction of energy transfer, out of the body.
In uniform circular motion the centripetal force points toward the centre, while the velocity (and hence the small displacement) is along the tangent. The tangent is always perpendicular to the radius, so theta = 90 degrees and cos 90 = 0. Therefore work done = 0, which is why the speed in uniform circular motion never changes. The same logic applies to a satellite in a circular orbit.
It depends on the motion. When a body falls down, gravity acts downward and displacement is downward, so theta = 0 and work is positive (the body speeds up). When a body is thrown up, gravity is downward but displacement is upward, so theta = 180 degrees and gravity does negative work (the body slows down). When a body moves horizontally, gravity is perpendicular to displacement, so gravity does zero work.
A particle moves from a point (-2i + 5j) to (4j + 3k) when a force of (4i + 3j) N is applied. How much work is done by the force?
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Positive work: force has a component along displacement (0 <= theta < 90 degrees), body gains kinetic energy. Negative work: force opposes displacement (90 < theta <= 180 degrees), body loses kinetic energy. Zero work: force perpendicular to displacement (theta = 90 degrees), speed unchanged.
Yes. If the positive work by some forces exactly cancels the negative work by others, the net work is zero and, by the work-energy theorem, the kinetic energy does not change. A body moving at constant speed on a level road is one example.
No. A force can act and still do zero work if it is perpendicular to the displacement. The centripetal force in circular motion and the normal force on a body sliding on a flat floor both do zero work while still being real forces.
Positive work increases kinetic energy, so it increases speed. Negative work decreases kinetic energy, so it decreases speed. Zero work keeps kinetic energy and speed the same.
The sign of work is tested directly (using W = F d cos theta or the dot product) and indirectly through the work-energy theorem, friction, gravity and circular motion. Getting the angle right is often the single step that decides the answer.
