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Flywheel (hoop stress on the rotor)

A flywheel is a rotating mechanical device that is used to store rotational energy. Flywheels have a significant moment of inertia and thus resist changes ... more

Critical Buckling Compressive Loading of a Plate

In science, buckling is a mathematical instability that leads to a failure mode.

When a structure is subjected to compressive stress, buckling may ... more

Allowable bearing capacity

In geotechnical engineering, bearing capacity is the capacity of soil to support the loads applied to the ground. The bearing capacity of soil is the ... more

Simplified von Mises equation - Pure shear

RESTRICTIONS : σ₁ = σ₂ = σ₃ = 0, σ₃₁ = σ₂₃ = 0

The von Mises yield criterion suggests that the yielding of materials ... 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/

Blade root bending moment load due to yaw

The blade root bending moment due to the wind turbine yaw operation. The yaw rate can be calculated for passive yaw, or is defined by the design for active ... more

Simplified von Mises equation - Principal plane stress

RESTRICTIONS : σ₃ = 0, σ₁₂ = σ₁₃ = σ₂₃ = 0

The von Mises yield criterion suggests that the yielding of materials begins ... more

Spherical wedge (Volume)

A spherical wedge or ungula is a portion of a ball bounded by two plane semidisks and a spherical lune (termed the wedge’s base). The angle between ... more

Mass of a Pressure Spherical Vessel

Pressure vessels are held together against the gas pressure due to tensile forces within the walls of the container. The mass of a tank depends on the ... more

Johnson-Kendall-Roberts (JKR) model of elastic contact between two spheres ( pull-off force)

Contact mechanics is the study of the deformation of solids that touch each other at one or more points.When two solid surfaces are brought into close ... more

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