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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.
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.
For a stretched spring fixed at one end obeying Hooke's law, the elastic potential energy is = where r 2 and r 1 are collinear coordinates of the free end of the spring, in the direction of the extension/compression, and k is the spring constant.
The potential energy within a spring is determined by the equation =. 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 ...
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:
Comparing to the expected original kinetic energy formula , the effective mass of spring in this case is . This result is known as Rayleigh's value, after Lord Rayleigh. To find the gravitational potential energy of the spring, one follows a similar procedure:
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The potential energy U of such a system can be determined through the spring constant k and its displacement x: [14] U = ( 1 2 ) k x 2 {\displaystyle U=\left({\frac {1}{2}}\right)kx^{2}} The kinetic energy K of an object in simple harmonic motion can be found using the mass of the attached object m and the velocity at which the object ...