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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

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

Damping ratio (related to Quality factor)

Formula first contributed by:

In engineering, the damping ratio is a dimensionless measure describing how ... more

Relation among Young's modulus, Bulk modulus and Poisson's ratio

For homogeneous isotropic materials simple relations exist between elastic constants (Young’s modulus E, bulk modulus K, and Poisson’s ratio ν) ... more

Strain energy release (Irwin's modification for plane strain)

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

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.


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


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.

This worksheet is a modified version of Example 5.4 page 188 found in :
OpenStax College,College Physics. OpenStax College. 21 June 2012.
Creative Commons License : http://creativecommons.org/licenses/by/3.0/

Micro chevron (MC) test (critical energy release rate)

The wafer bond characterization is based on different methods and tests. Wafer bonds are commonly characterized by three important encapsulation ... more

Transverse wave velocity (shear wave)

A transverse (shear) wave is a moving wave that consists of oscillations occurring perpendicular (or right angled) to the direction of energy transfer. For ... more

Speed of Sound in Solids - long rods

The speed of sound is the distance travelled per unit of time by a sound wave propagating through an elastic medium.
The speed of sound for ... more

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

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