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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.
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.)
For a stretched spring fixed at one end obeying Hooke's law, the elastic potential energy is Δ E p = 1 2 k ( r 2 − r 1 ) 2 {\displaystyle \Delta E_{p}={\frac {1}{2}}k(r_{2}-r_{1})^{2}} 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.
However, if the mass is displaced from the equilibrium position, the spring exerts a restoring elastic force that obeys Hooke's law. Mathematically, F = − k x , {\displaystyle \mathbf {F} =-k\mathbf {x} ,} where F is the restoring elastic force exerted by the spring (in SI units: N ), k is the spring constant ( N ·m −1 ), and x is the ...
The rate or spring constant of a spring is the change in the force it exerts, divided by the change in deflection of the spring. That is, it is the gradient of the force versus deflection curve . An extension or compression spring's rate is expressed in units of force divided by distance, for example or N/m or lbf/in.
A spring scale, spring balance or newton meter is a type of mechanical force gauge or weighing scale. It consists of a spring fixed at one end with a hook to attach an object at the other. [ 1 ] It works in accordance with Hooke's Law , which states that the force needed to extend or compress a spring by some distance scales linearly with ...
The force in the spring is (roughly) the vertical force at the contact patch divided by the motion ratio, and the spring rate is the wheel rate divided by the motion ratio squared. I R = S p r i n g D i s p l a c e m e n t W h e e l D i s p l a c e m e n t . {\displaystyle IR={\frac {SpringDisplacement}{WheelDisplacement}}.}
When a spring is stretched or compressed by a mass, the spring develops a restoring force. Hooke's law gives the relationship of the force exerted by the spring when the spring is compressed or stretched a certain length: F ( t ) = − k x ( t ) , {\displaystyle F(t)=-kx(t),} where F is the force, k is the spring constant, and x is the ...