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Miller's Rule

In optics, Miller’s rule is an empirical rule which gives an estimate of the order of magnitude of the nonlinear coefficient.

More formally, ... 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/

Absolute Magnitude of a Star - with distance modulus

Absolute magnitude is the measure of a celestial object’s intrinsic brightness. It is the hypothetical apparent magnitude of an object at a standard ... more

Frequency of a string under tension (nth harmonic)

A vibration in a string is a wave. Resonance causes a vibrating string to produce a sound with constant frequency, i.e. constant pitch. If the length or ... more

Absolute Magnitude of a Star - with parallax

Absolute magnitude is the measure of a celestial object’s intrinsic brightness. It is the hypothetical apparent magnitude of an object at a standard ... more

Emf Induced in a Generator Coil

Electric generators induce an emf by rotating a coil in a magnetic field. Electromotive force, also called Emf, is the voltage developed by any source of ... more

Absolute Magnitude of a Star - with luminosity distance

Absolute magnitude is the measure of a celestial object’s intrinsic brightness. It is the hypothetical apparent magnitude of an object at a standard ... more

Likelihood-ratio test

In statistics, a likelihood ratio test is a statistical test used to compare the fit of two models, one of which (the null model) is a special case of the ... more

Sine wave

The sine wave or sinusoid is a mathematical curve that describes a smooth repetitive oscillation. It is named after the function sine, of which it is the ... more

Specific gravity of solids

Silts, sands and gravels are classified by their size, and hence they may consist of a variety of minerals. Owing to the stability of quartz compared to ... more

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