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Margin of safety (measure of requirement verification)

Many government agencies and industries (such as aerospace) require the use of a margin of safety (MoS or M.S.) to describe the ratio of the strength of ... more

Chladni's Law

Chladni’s law, named after Ernst Chladni, relates the frequency of modes of vibration for flat circular surfaces with fixed center as a function of ... more

Blood pressure ( related to the wall tension of artery or vein)

Blood pressure is related to the wall tension of the artery or vein, according to the Young–Laplace equation (assuming that the thickness of the vessel ... 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/

Geometric distribution (probability of failures before the first success)

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Shear stress (acting on the bed of a channel)

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Cylinder stress (axial stress)

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When a ... more

Cantilever Euler Beam - Maximum Displacement

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Law of the wall

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Screw Thread Engagement

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