Hooke's law is valid underelastic limitsinelastic limitsbothnone (2024)

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Hooke's law is valid underelastic limitsinelastic limitsbothnone? ›

Hooke's law is valid under elastic limits.it is valid as long as the elastic material dealing with stays elastic. In which year Robert Hooke presented his law of elasticity?

Detailed Solution. The Hooke's law itself states that it is valid only proportional region of the stress-strain curve i.e. only to that limit where the material is behaving elastically. According to Hooke's law, within the elastic limit stress is proportional to strain, provided the strain is small.

Plastic region – It is the region PE in the stress-strain graph. It starts right after point P (the limit of proportionality), which means that Hooke's law is not obeyed in this region (essentially the strain does not increase at a constant rate with the increase in stress).

Hooke's law states that the strain of the material is proportional to the applied stress within the elastic limit of that material.

Hooke's law states that within the elastic limit the stress is directly proportional to the strain. Thus, Hooke's law holds good within the elastic limit. So, if the elastic limit is not exceeded the force applied on the material is directly proportional to the extension of the material.

Beyond the proportionality limit, by definition the force and extension are no longer proportional and so Hooke's law is not entirely valid. However, the elastic behaviour itself, where deformations are temporary, lasts up to the elastic limit.

A limitation to Hooke's Law is that is it only applicable under the elastic limit of any material, which means that a material should be perfectly elastic to obey Hooke's Law. Beyond the elastic limit the Hooke's law essentially breaks down.

Plastic deformation involves atoms moving past each other so they cannot just go back to where they were. These are relatively large displacements and cannot be well approximated by a linear function- so Hookes Law does not apply.

It must eventually fail once the forces exceed some limit, since no material can be compressed beyond a certain minimum size, or stretched beyond a maximum size, without some permanent deformation or change of state. Many materials will noticeably deviate from Hooke's law well before those elastic limits are reached.

Hooke's law has limits in that it can only accurately describe results when the force and level of deformation are small and within the proportionality limit of a given material. In addition, not all objects and materials can be described by Hooke's law, it only pertains to those with elastic potential.

What is the range of Hooke's law validity? ›

Figure 10.34 Hooke's law (stress is directly proportional to strain) is valid only up to the proportionality limit of a material. Beyond this limit, Hooke's law no longer applies. Beyond the elastic limit, the material remains deformed even when the stress is removed.

The elastic limit differs from the proportional limit in that the elastic limit is the maximum pressure that may be given to a material without it deforming. The proportional limit of a material is defined as the point at which stress and strain are directly proportional to one another.

Hooke's law :- it states that within elastic limit stress applied is proportional to Strain developed stress strainent to which a solid may be stretched without permanent alteration of. ⇒ s t r e s s s t r a i n = k. k is known as modulus of elasticity. -elastic limit is a point or the maximum size and shape.

Elastic objects will usually obey Hooke's law. However, some will also reach their elastic limit. This is where so much force has been applied that the object will no longer return to its original length when the force is removed and has been permanently deformed.

Linear relationship assumption: Hooke's law assumes a linear relationship between the applied force and the resulting deformation. However, this assumption may not hold for materials under large or non-uniform forces, or for materials with complex internal structures.

Hooke's law holds up to the proportional limit.

The constant of proportionality is called the elastic modulus or Young's modulus, E. It has the same units as stress.

Therefore, in order to verify Hooke's Law, you must verify that the force F and the distance at which the spring is stretched are proportional to each other (that just means linearly dependent on each other), and that the constant of proportionality is k.

Stress–strain curve for low-carbon steel, showing the relationship between the stress (force per unit area) and strain (resulting compression/stretching, known as deformation). Hooke's law is only valid for the portion of the curve between the origin and the yield point (2).

Hooke's law is a physical law that describes the relationship between the force applied to an object and the resulting displacement of that object. It states that the force applied is directly proportional to the displacement, as long as the displacement is within a small range.

Linear relationship assumption: Hooke's law assumes a linear relationship between the applied force and the resulting deformation. However, this assumption may not hold for materials under large or non-uniform forces, or for materials with complex internal structures.