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Archimedean spiral

The Archimedean spiral is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed ... more

Mean angular motion - function of gravitational parameter

In orbital mechanics, mean motion (represented by n) is the angular speed required for a body to complete one orbit, assuming constant speed in a circular ... more

Apsidal precession

In celestial mechanics, apsidal precession is the precession (gradual rotation) of the line connecting the apsides (line of apsides) of an astronomical ... more

Geometrical requirements for pin ended members - Given thickness

This formula calculates the geometrical requirements for pin ended members, specifically the minimum required distances from the pin hole edge to the plate ... more

Speed of sound in sea water (UNESCO equation)

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Security market line (SML)

Security market line (SML) is the representation of the capital asset pricing model. It displays the expected rate of return of ... 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

Morley's trisector theorem (area)

Morley’s trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, ... more

Hole change in Gibbs free energy

In chemistry, a reaction quotient: Qr is a function of the activities or concentrations of the chemical species involved in a chemical reaction. In the ... more

Adsorption is usually described through isotherms, that is, the amount of adsorbate on the adsorbent as a function of its pressure (if gas) or ... more

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