Physics · Work, Energy And Power · NEET
The minus sign shows direction, not a negative value. If you stretch the spring to the right (x is positive), the spring pulls back to the left, so the force is negative. If you compress it to the left (x is negative), the spring pushes to the right, so the force is positive. In both cases the force points opposite to the displacement, back toward the equilibrium position. That is why F = -kx is called a restoring force. For NEET, if a question only asks for the magnitude, use F = kx and drop the sign.
The spring constant k tells you how stiff the spring is. It is the force needed to stretch or compress the spring by 1 metre. Its SI unit is N/m (newton per metre). A large k means a stiff spring (hard to stretch), a small k means a soft spring (easy to stretch). From F = kx you get k = F/x. Example: if a 10 N force stretches a spring by 0.05 m, then k = 10/0.05 = 200 N/m.
Spring force is a variable force. As x changes, the force F = -kx changes too. When the spring is at its natural length (x = 0), the force is zero. The more you stretch or compress it, the bigger the force. This is why you cannot use simple W = F d for spring work; you must use the area under the F-x graph (a triangle), which gives work = (1/2) k x squared. Knowing it is variable is the link to spring potential energy.
Yes. Hooke's Law F = -kx holds for both stretching (x positive) and compression (x negative), as long as the spring is not stretched too far. Beyond a certain limit (the elastic limit), the spring deforms permanently and F = -kx no longer holds. For NEET ideal-spring problems, always assume Hooke's Law is valid for small stretch and small compression on both sides of equilibrium.
Spring force is F = -kx (unit: newton, N) - it is what the spring pushes or pulls with at a given stretch. Spring potential energy is U = (1/2) k x squared (unit: joule, J) - it is the energy stored inside the spring. Force is linear in x, but energy is proportional to x squared. So doubling the stretch doubles the force but makes the stored energy four times bigger. This x-squared rule is a favourite NEET trap.
The potential energy of a spring when stretched by 2 cm is U. If the spring is stretched by 8 cm, the potential energy stored in it will be
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Hooke's Law states that the restoring force of an ideal spring is directly proportional to its displacement from the equilibrium position and points opposite to that displacement: F = -kx, where k is the spring constant.
The SI unit of the spring constant is newton per metre (N/m). It equals the force in newtons needed to stretch or compress the spring by 1 metre. From F = kx, k = F/x.
Yes. The spring force is conservative because the work it does depends only on the start and end positions, and the work done over a full cycle (returning to the same point) is zero. This is why we can define a spring potential energy U = (1/2) k x squared.
Because it always acts to bring the block back toward the equilibrium (natural length) position. When stretched it pulls back, when compressed it pushes back - the direction is always opposite to the displacement, shown by the minus sign in F = -kx.
Since the spring force varies with x, use the area under the force-displacement graph, which is a triangle. Work done stretching from 0 to x is (1/2) k x squared in magnitude; the spring force itself does negative work equal to -(1/2) k x squared while an external pull does positive work.
