Physics · Work, Energy And Power · NEET
Force and displacement can point in different directions. Only the component of force that lies along the displacement moves the body forward, and that component is F cos theta. So work = (F cos theta) times d = F d cos theta. The cos theta simply keeps the part of the force that is along the motion and drops the sideways part.
Theta is the angle between the force vector and the displacement vector, measured when both start from the same point. It is NOT the angle of the incline or the angle with the vertical. Always draw both arrows from one point and read the angle between them. For example, if force is horizontal and the body moves at 60 degrees to it, theta = 60 degrees.
Work is a scalar. It comes from the dot product W = F . d = F d cos theta, and a dot product of two vectors always gives a number, not a direction. Work has magnitude and a plus or minus sign, but no direction. This is why for NEET you never write work with i, j, k components.
Only the part of the force along the displacement does work. The perpendicular part (F sin theta) does zero work because it does not move the body in its own direction. That is why a force perpendicular to motion, like the normal force or the centripetal force, does no work at all.
Force is in newton (N) and displacement is in metre (m), so work is in newton-metre, which is called the joule (J). One joule is the work done when a force of 1 N moves a body 1 m along the force's direction. Dimensions of work are [M L^2 T^-2].
Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m/s. Take g constant with a value 10 m/s^2. The work done by the (i) gravitational force and the (ii) resistive force of air is
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Yes. When theta is more than 90 degrees, cos theta is negative, so W is negative. This happens when the force opposes the motion, like friction or air resistance. Negative work removes kinetic energy from the body.
Work is zero if the force is zero, the displacement is zero, or theta = 90 degrees (cos 90 = 0). A force perpendicular to the path, such as the normal force or centripetal force, does zero work even though the body moves.
Yes. W = F . d is the dot product of the force and displacement vectors, and by definition F . d = F d cos theta. Both give the same scalar value. For NEET, use the component form F . d = Fx dx + Fy dy + Fz dz when vectors are given in i, j, k.
Because most mistakes in work problems come from picking the wrong angle. NEET often gives forces on inclines or at angles, where students confuse theta with the incline angle. Getting theta right fixes both the value and the sign of the work, which decides the correct option.
