1. Is work of a spring the same as the potential energy of a spring? U = .5kx^2?The phrase "work of a spring" makes no sense. You can only speak of the work done ON an object (by some force) when it is moved from point A to point B. What you mean is: Is the work done on an object tied to the spring when moved from the equilibrium position to a distance x away from equilibrium by some external force equal to the final potential energy stored in the spring, 1/2kx^2? Then yes.jcais said:
The spring is usually massless to make things simple, so no, the spring doesn't have kinetic energy. The object attached to the spring however has kinetic energy equal to 1/2mv^2, that always holds.
Work and energy have the same units, but they are quite different concepts. A relation between them is given by the Work-Energy theorem.
A spring is an elastic object that stores mechanical energy when it is stretched or compressed. It has the ability to return to its original shape after being deformed.
A spring stores energy by converting the applied force into potential energy. When a force is applied to a spring, it deforms and stores potential energy. This energy is released when the force is removed and the spring returns to its original shape.
The relationship between the force applied to a spring and its displacement is described by Hooke's Law. This law states that the force applied to a spring is directly proportional to its displacement from its equilibrium position.
The potential energy stored in a spring can be calculated using the formula U = 1/2 kx², where U is the potential energy, k is the spring constant, and x is the displacement from the equilibrium position.
The work done by a spring is the force applied to it multiplied by the distance the spring is stretched or compressed. Mathematically, it can be expressed as W = Fd, where W is the work done, F is the force, and d is the displacement.