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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

Rotational stiffness ( depended on rigidity modulus of the material)

Stiffness is the rigidity of an object — the extent to which it resists deformation in response to an applied force. In general, stiffness is not the same ... 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/

Critical buckling stress of a column

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

Self-buckling critical height ( for a free-standing, vertical column)

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

Cantilever Euler Beam - Maximum Displacement

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

Tuning fork

A tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs (tines) formed from a U-shaped bar of elastic metal (usually ... more

Reluctance

Magnetic reluctance, or magnetic resistance, is analogous to resistance in an electrical circuit (although it does not dissipate magnetic energy). In ... 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

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

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