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Force exerted by stretched or contracted material

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Electrical resistance

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de Laval nozzle - correlation of Area and Velocity

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Beam shear

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Energy Density (magnetic field)

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Hydraulic diameter

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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/

Torsion constant (Square-cross-sectional shape)

In solid mechanics, torsion is the twisting of an object due to an applied torque. The torsion constant is a geometrical property of a bar’s cross-section ... more

Magnetic permeance

Magnetic reluctance, or magnetic resistance, is a concept used in the analysis of magnetic circuits. It is analogous to resistance in an electrical ... 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

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