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A spring with spaces between the coils can be compressed, and the same formula holds for compression, with F s and x both negative in that case. [4] Graphical derivation. According to this formula, the graph of the applied force F s as a function of the displacement x will be a straight line passing through the origin, whose slope is k.
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 = 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 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.
The first constitutive equation (constitutive law) was developed by Robert Hooke and is known as Hooke's law.It deals with the case of linear elastic materials.Following this discovery, this type of equation, often called a "stress-strain relation" in this example, but also called a "constitutive assumption" or an "equation of state" was commonly used.
In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility [1] or, if the temperature is held constant, the isothermal compressibility [2]) is a measure of the instantaneous relative volume change of a fluid or solid as a response to a pressure (or mean stress) change.
For example, consider a spring that has Q and q as, respectively, its force and deformation: The spring stiffness relation is Q = k q where k is the spring stiffness. Its flexibility relation is q = f Q, where f is the spring flexibility. Hence, f = 1/k. A typical member flexibility relation has the following general form:
Compression of solids has many implications in materials science, physics and structural engineering, for compression yields noticeable amounts of stress and tension. By inducing compression, mechanical properties such as compressive strength or modulus of elasticity , can be measured.