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A strain is a normalized measure of deformation representing the displacement between particles in the body relative to a reference length.The concept of ... more
The stretch ratio or extension ratio is a measure of the extensional or normal strain of a differential line element, which can be defined at either the ... more
Strain gauge is a device used to measure strain on an object. A strain is a normalized measure of deformation representing the displacement between ... more
In materials science, shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is defined as the ratio of shear stress to the shear strain. ... more
In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each ... more
An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substance’s tendency to be deformed elastically (i.e., ... more
Stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other. Any strain ... more
A bimetallic strip is used to convert a temperature change into mechanical displacement. The strip consists of two strips of different metals which expand ... more
In materials science, creep (sometimes called cold flow) is the tendency of a solid material to move slowly or deform permanently under the influence of ... more
Hooke’s Law of elasticity is an approximation that states that the amount by which a material body is deformed (the strain) is linearly related to ... more
Euler–Bernoulli beam theory (also known as engineer’s beam theory or classical beam theory) is a simplification of the linear theory of elasticity ... more
Euler–Bernoulli beam theory (also known as engineer’s beam theory or classical beam theory) is a simplification of the linear theory of elasticity ... more
Young’s modulus, also known as the Tensile modulus or elastic modulus, is a measure of the stiffness of an elastic isotropic material and is a ... more
In structural engineering, a structure is a body or combination of pieces of rigid bodies in space to form a fitness system for supporting loads. ... more
Elastic energy is the potential mechanical energy stored in the configuration of a material or physical system as work is performed to distort its volume ... more
Hooke’s law states that the force needed to extend or compress a spring by some distance is proportional to that distance.The stresses and strains ... more
The stiffness of a body is a measure of the resistance offered by an elastic body to deformation. For an elastic body with a single degree of freedom (for ... more
In structural engineering, a structure is a body or combination of pieces of rigid bodies in space to form a fitness system for supporting loads. ... more
In structural engineering, a structure is a body or combination of pieces of rigid bodies in space to form a fitness system for supporting loads. ... more
Poisson’s ratio, named after Siméon Poisson, is the negative ratio of transverse to axial strain. When a material is compressed in one direction, it ... more
The stiffness of a body is a measure of the resistance offered by an elastic body to deformation. A body have a rotational stiffness when it is in a ... more
Resilience is the ability of a material to absorb energy when it is deformed elastically, and release that energy upon unloading. Proof resilience is ... more
A fracture is the separation of an object or material into two, or more, pieces under the action of stress.There are three ways of applying a force to ... more
A fracture is the separation of an object or material into two, or more, pieces under the action of stress.There are three ways of applying a force to ... more
Harmonic Drive is the brand name of strain wave gear trademarked by the Harmonic Drive company, and invented in 1957 by C.W. Musser.
It is very ... more
In science, buckling is a mathematical instability that leads to a failure mode.
When a structure is subjected to compressive stress, buckling may ... more
Strategy
The force is equal to the weight supported:
and the cross-sectional area of the upper leg bone(femur) is:
To find the change in length we use the Young’s modulus formula. The Young’s modulus reference value for a bone under compression is known to be 9×109 N/m2. Now,all quantities except ΔL are known. Thus:
Discussion
This small change in length seems reasonable, consistent with our experience that bones are rigid. In fact, even the rather large forces encountered during strenuous physical activity do not compress or bend bones by large amounts. Although bone is rigid compared with fat or muscle, several of the substances listed in Table 5.3(see reference below) have larger values of Young’s modulus Y . In other words, they are more rigid.
Reference:
This worksheet is a modified version of Example 5.4 page 188 found in :
OpenStax College,College Physics. OpenStax College. 21 June 2012.
http://openstaxcollege.org/textbooks/college-physics
Creative Commons License : http://creativecommons.org/licenses/by/3.0/
The shear modulus is one of several quantities for measuring the stiffness of materials and describes the material’s response to shear stress (like ... more
Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid ... more
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Calculate the change in length of the upper leg bone (the femur) when a 70.0 kg man supports 62.0 kg of his mass on it, assuming the bone to be equivalent to a uniform rod that is 45.0 cm long and 2.00 cm in radius.