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Speed of Sound (air, ideal gases)

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

Lame's first parameter (in three dimensions)

In linear elasticity, the Lame parameters are the two parameters that constitute a parametrization of the elastic moduli for homogeneous isotopic media. ... more

Lame's first parameter (for two-dimensional solids)

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Bearing capacity - Terzaghi's Theory (Variable Nq)

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Petroff's Law - Torque required to shear the lubricant film

In the design of fluid bearings, the Sommerfeld number (S), or bearing characteristic number, is a dimensionless quantity used extensively in hydrodynamic ... more

Magnetic dipole moment (Ampère model)

Far away from a magnet, its magnetic field is almost always described (to a good approximation) by a dipole field characterized by its total magnetic ... more

Speed of Sound (air, ideal gases) - relative to molar mass

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Rouse Number

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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/

Critical Speed of a Rotating Shaft - Dunkerley's method

In solid mechanics, in the field of rotordynamics, the critical speed is the theoretical angular velocity that excites the natural frequency of a rotating ... more

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