Physics · Work, Energy And Power · NEET
Friction is non-conservative. The work done by friction depends on the length of the path, not just the two end points. If you slide a block from A to B by a long, curved path, friction removes more energy than by a short straight path. NCERT states this directly: 'Friction, for example, is a non-conservative force.' Because of this, you cannot define a potential energy for friction, and its work over a closed loop is not zero.
Gravity is conservative because the work it does depends only on the change in height (the start and end positions), not on the path. NCERT shows that a body released from a frictionless incline of height h reaches speed sqrt(2gh) at the bottom 'irrespective of the angle of inclination.' A steep path or a gentle path gives the same work, mgh. This path independence is exactly what makes a force conservative.
No. This is the defining test. For a conservative force, W = V(xi) - V(xf), which depends only on the end points xi and xf. Two different routes between the same two points give the same work. For a non-conservative force such as friction, the work Wnc depends on the particular path taken, so different routes give different amounts of lost energy.
A closed loop means the object returns to its starting point, so xi = xf. Since the work of a conservative force depends only on the end points, W = V(xi) - V(xf) = 0 when the points are the same. NCERT gives this as a third definition: 'the work done by this force in a closed path is zero.' Friction fails this test because it always opposes motion and keeps removing energy on every part of the loop.
The normal force is neither, in the usual sense, because it does zero work — it always acts perpendicular to the displacement. Since it does no work, it does not change mechanical energy and it does not fall into the conservative/non-conservative comparison the way gravity and friction do. Focus your NEET comparison on gravity and spring force (conservative) versus friction and applied push/pull with energy loss (non-conservative).
A particle of mass M moves along a horizontal x-axis from x=0 to x=L. The coefficient of kinetic friction varies as mu_k(x) = mu_0 - alpha x, where mu_0, alpha are constants, so that mu_k(L)=0. The total work done by the frictional force during the motion is n*mu_0*M*g*L. The value of n is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
For a conservative force, the work done depends only on the start and end points and is zero over a closed loop (gravity, spring force). For a non-conservative force, the work depends on the path taken and is not zero over a closed loop (friction, air resistance).
No. Potential energy can only be defined for conservative forces, because it needs the work to be path-independent. For friction, the work changes with the path, so no single potential energy function exists.
Conservative: gravitational force and spring (elastic) force. Non-conservative: kinetic friction and viscous drag (air resistance). The spring force is a variable force that is still conservative, which NEET likes to test.
With only conservative forces, total mechanical energy K + V stays constant. When a non-conservative force acts, mechanical energy changes by the work of that force: Ef - Ei = Wnc, and for friction Wnc is negative (energy is lost as heat).
Yes. NCERT states the spring force Fs = -kx 'is an example of a variable force which is conservative.' Its work depends only on the initial and final positions, and its work in a cyclic process is zero, so it passes both conservative tests.
