The question is incomplete, however [tex]1/2\kappa (\mu^2 m^2g^2/k)[/tex] is the potential energy stored in the spring.
of spring F=−kx
coefficient of kinetic friction F=μmg
At equilibrium, the mass and spring will both revert to their average positions.
so,−kx=μmg [tex]x=-\mu mg/k[/tex]
the potential energy stored the spring is
[tex]1/2kx^2=1/2k-\mu mg/k^2=1/2k(\mu^2m^2g^2/k)[/tex]
- For short lengths, the force needed to extend a metal spring or other elastic item is exactly proportional to the length of the spring. Hooke's law describes the force the spring applies in reverse.
- Because the force applied by the spring is always in the opposite direction of the displacement, this force is known as a restoring force. The equation for Hooke's law contains a negative sign because of this. When a spring is pulled downward, it is stretched downward and produces an upward force.
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