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Force on a Contact Area between a rigid cylinder and an elastic half-space

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Total force on a contact area between a rigid conical indenter and an elastic half-space related to the total depth

ontact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Maximum contact pressure between a rigid cylinder and an elastic half-space

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Maximum Pressure on a Contact Area between two cylinders with parallel axes

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Total force on a contact area between a rigid conical indenter and an elastic half-space related to the contact radius

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Depth of the contact region between a rigid conical indenter and an elastic half-space

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Depth of indentation of a Contact Area between two spheres

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Force aplied at a contact area between a sphere and an elastic half-space

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Radius of a Contact Area between two spheres related to the force

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Total indentation depth of a contact area between a rigid cylinder and an elastic half-space

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Elastic modulus of a contact area between a sphere and an elastic half-space

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Radius of a Contact Area between two cylinders with parallel axes

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Radius of a contact area between a sphere and an elastic half-space

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. When an elastic sphere indents an elastic ... more

Maximum contact pressure between two spheres

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Johnson-Kendall-Roberts (JKR) model of elastic contact between two spheres ( contact radius)

Contact mechanics is the study of the deformation of solids that touch each other at one or more points.When two solid surfaces are brought into close ... more

Maugis-Dugdale model of elastic contact between two spheres( contact force)

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Derjaguin-Muller-Toporov (DMT) model of elastic contact between two spheres (contact radius)

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. The Derjaguin-Muller-Toporov (... more

Pressure distribution on a Contact Area between a rigid cylinder and an elastic half-space

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Effective Radius of a Contact Area between two spheres

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Pressure in a Contact Area between two spheres

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Force exerted by stretched or contracted material

In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each ... more

Maugis-Dugdale model of elastic contact between two spheres (depth of penetration)

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Young's Modulus

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

Elastic potential energy( with respect to Length)

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

Johnson-Kendall-Roberts (JKR) model of elastic contact between two spheres ( pull-off force)

Contact mechanics is the study of the deformation of solids that touch each other at one or more points.When two solid surfaces are brought into close ... more

Indent depth for Vickers hardness test

The basic principle of the Vickers hardness test, as with all common measures of hardness, is to observe the questioned material’s ability to resist ... more

Maugis-Dugdale model of elastic contact ( contact pressure )

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Worksheet 316

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.

Strategy

The force is equal to the weight supported:

Force (Newton's second law)

and the cross-sectional area of the upper leg bone(femur) is:

Disk area

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:

Young's Modulus

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/

Maximum axial load that a long, slender, ideal column can carry without buckling

Column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above ... more

Spring constant

Hooke’s law is a principle of physics that states that the force F needed to extend or compress a spring by some distance X is proportional to that ... more

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