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Potential energy is the energy by virtue of an object's position relative to other objects. [6] Potential energy is often associated with restoring forces such as a spring or the force of gravity. The action of stretching a spring or lifting a mass is performed by an external force that works against the force field of the potential.
where is the kinetic energy and is the potential energy. Hooke's law is the potential energy of the spring itself: = where is the spring constant. The potential energy from gravity, on the other hand, is determined by the height of the mass. For a given angle and displacement, the potential energy is:
In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
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An example of a non-metallic spring is the bow, made traditionally of flexible yew wood, which when drawn stores energy to propel an arrow. When a conventional spring, without stiffness variability features, is compressed or stretched from its resting position, it exerts an opposing force approximately proportional to its change in length (this ...
When the spring is stretched or compressed, kinetic energy of the mass gets converted into potential energy of the spring. By conservation of energy, assuming the datum is defined at the equilibrium position, when the spring reaches its maximal potential energy, the kinetic energy of the mass is zero. When the spring is released, it tries to ...
The following table gives formula for the spring that is equivalent to a system of two springs, in series or in parallel, whose spring constants are and . [1] The compliance c {\displaystyle c} of a spring is the reciprocal 1 / k {\displaystyle 1/k} of its spring constant.)
In a real spring–mass system, the spring has a non-negligible mass.Since not all of the spring's length moves at the same velocity as the suspended mass (for example the point completely opposed to the mass , at the other end of the spring, is not moving at all), its kinetic energy is not equal to .