Hooke's Law & Linear Elasticity
Hooke's Law states that the strain in a solid is proportional to the applied stress within the elastic limit of that solid. In simpler terms, the force needed to extend or compress a spring by some distance scales linearly with respect to that distance. For 1D tensile/compressive stress, this is defined by Young's Modulus (E).
Knowledge Check
1.A steel rod with a Young's Modulus (E) of 200 GPa is subjected to a tensile strain of 0.001. Assuming the material remains within its linear elastic limit, what is the resulting axial stress?
2.If a linear spring has a stiffness constant of 50 N/mm, how much force is required to compress it by 10 mm?
3.Hooke's Law is only valid up to a certain point on the stress-strain curve. What is this point called?
4.Two identical springs, each with a stiffness k, are placed in parallel. What is the equivalent stiffness (k_eq) of the system?
5.Two identical springs, each with a stiffness k, are placed in series. What is the equivalent stiffness (k_eq) of the system?
6.How much elastic potential energy (U) is stored in a spring with constant k=100 N/m when it is stretched by 0.2 meters?
7.In 3D stress states, Poisson's ratio (ν) couples the strains in different directions. For most metals, what is the typical range of Poisson's ratio?
8.A 2-meter long aluminum wire is stretched by 4 mm. What is the normal strain (ε) in the wire?
9.Which parameter directly links the Shear Stress (τ) to the Shear Strain (γ) in the shear version of Hooke's law?
10.If you double the cross-sectional area (A) of a rod but keep the applied tensile force (F) and original length (L) constant, what happens to the total elongation (ΔL)?