Physics · Work, Energy And Power · NEET
The total mechanical energy is conserved: E = ½mv² + ½kx² = constant. Here ½mv² is the block's kinetic energy and ½kx² is the spring's potential energy (x is the displacement from the natural, unstretched length). Kinetic and potential energy each keep changing, but their sum never changes because the spring force F = -kx is a conservative force. This is why you can equate energy at any two points to solve NEET numericals fast.
The block is fastest at the equilibrium (natural length) position, where x = 0. There the spring PE is zero, so all the energy is kinetic and v is maximum: ½mv_max² = ½kA², giving v_max = A·sqrt(k/m), where A is the amplitude (maximum displacement). The block is slowest (momentarily at rest, v = 0) at the extreme points x = ±A, where the spring is fully stretched or fully compressed and all the energy is spring PE.
Use energy conservation. A block of mass m moving with speed v hits a spring of constant k. At maximum compression x_max the block stops for an instant, so all its kinetic energy has become spring PE: ½mv² = ½k·x_max². Solve to get x_max = v·sqrt(m/k). If a rough surface is involved, subtract the work done against friction (f·x_max) before equating.
No. On a smooth horizontal surface the block does not change height, so gravitational PE (mgh) stays constant and cancels out. Only kinetic energy and spring PE change. Just write ½mv² + ½kx² = constant. Gravity only enters if the spring is vertical or the block moves up or down an incline.
Because the spring force is conservative: the work it does depends only on the start and end positions, not the path, and any KE lost to compressing the spring is stored as PE and given back fully. So energy simply moves back and forth between the KE store and the PE store. On a smooth surface there is no friction to drain it, so the total E is fixed.
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.
½mv² + ½kx² = constant, where m is the block's mass, v its speed, k the spring constant, and x the displacement from the natural length. You equate this total at any two points to solve problems.
v_max = A·sqrt(k/m), reached at the natural-length position (x = 0), where all the spring PE has converted into kinetic energy. Here A is the amplitude.
No, mechanical energy is not conserved with friction. Friction is non-conservative and removes energy as heat. You must subtract the work done against friction: ½mv² = ½k·x_max² + f·x_max.
Spring energy questions appear almost every year in Work, Energy and Power. They test the ½kx² formula, the x² scaling trap, and equating energy at two points - quick marks if you know the method, easy to lose if you scale linearly.
