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Boltzmann factor in mechanics

In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution) is a probability distribution, probability measure, or ... more

Ricco's Law

Several laws describe a human’s ability to visually detect targets on a uniform background. One such law is Riccò's law, discovered by astronomer ... more

Richardson Number - thermal convection

The Richardson number (Ri) is named after Lewis Fry Richardson (1881 – 1953). It is the dimensionless number that expresses the ratio of potential to ... more

Delta-v budget

In astrodynamics and aerospace, a delta-v budget is an estimate of the total delta-v required for a space mission. It is calculated as the sum of the ... more

Logarithmic Mean Temperature Difference

The logarithmic mean temperature difference (also known as log mean temperature difference or simply by its initialism LMTD) is ... more

Drift velocity in a current-carrying metallic ohmic conductor

The drift velocity is the average velocity that a particle, such as an electron, attains due to an electric field.

In terms of the basic ... more

Youden's J statistic

Youden’s J statistic (also called Youden’s index) is a single statistic that captures the performance of a diagnostic test. Its value ranges ... more

Darcy's law (simplified)

Darcy’s law states that the volume of flow of the pore fluid through a porous medium per unit time is proportional to the rate of change of excess ... 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

Gyrofrequency

If the magnetic field is uniform and all other forces are absent, then the Lorentz force will cause a particle to undergo a constant acceleration ... more

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