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Capillary Action - height of the meniscus

Capillary action (sometimes capillarity, capillary motion, or wicking) is the ability of a liquid to flow in narrow spaces without the assistance of, and ... more

Radius of meniscus (surface tension)

In a sufficiently narrow tube of circular cross-section of radius “a”, the interface between two fluids forms a meniscus that is a portion of the surface ... more

Liquid in a vertical tube (The height to which the column is lifted )

If a tube is sufficiently narrow and the liquid adhesion to its walls is sufficiently strong, surface tension can draw liquid up the tube in a phenomenon ... more

Capillary pressure in a tube

In a sufficiently narrow tube of circular cross-section of radius “a”, the interface between two fluids forms a meniscus that is a portion of ... more

Moment of inertia of a torus of tube

Mass moment of inertia measures the extent to which an object resists rotational acceleration about an axis, and is the rotational analogue to mass.
A ... more

Moment of inertia of a torus of tube (about a diameter)

Mass moment of inertia measures the extent to which an object resists rotational acceleration about an axis, and is the rotational analogue to mass.
A ... more

Floating objects (weight that depresses the surface)

When an object is placed on a liquid, its weight depresses the surface, and is balanced by the surface tension forces on either side , which are each ... more

maximum axial tension - clamp band

In the aerospace industry, the empirical methodology for evaluating the axial load capability of the clamp band joint assumes the joint components to be ... more

Young - Laplace equation

In physics, the Young – Laplace equation, is a nonlinear partial differential equation that describes the capillary pressure difference sustained ... more

Wetted perimeter

The wetted perimeter is the perimeter of the cross sectional area that is “wet”. The term wetted perimeter is common in civil engineering, ... more

Pressure inside an ideal soap bubble

The pressure inside an ideal (one surface) soap bubble can be derived from thermodynamic free energy considerations. At constant temperature and in ... 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/

Maugis-Dugdale model of elastic contact ( contact pressure )

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Total force on a contact area between a rigid conical indenter and an elastic half-space related to the contact radius

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Depth of the contact region between a rigid conical indenter and an elastic half-space

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Pressure in a Contact Area between two spheres

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Pressure distribution on a Contact Area between a rigid cylinder and an elastic half-space

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Young's Modulus

Young’s modulus, also known as the Tensile modulus or elastic modulus, is a measure of the stiffness of an elastic isotropic material and is a ... more

Maximum contact pressure between two spheres

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Torsion

In solid mechanics, torsion is the twisting of an object due to an applied torque. It is expressed in newton metres (N·m) or foot-pound force (ft·lbf). In ... more

Maximum Pressure on a Contact Area between two cylinders with parallel axes

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Maximum contact pressure between a rigid cylinder and an elastic half-space

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Klein bagel ( "figure 8" immersion x-coordinate)

In mathematics, the Klein bottle is an example of a non-orientable surface, informally, it is a surface (a two-dimensional manifold) in which notions of ... more

Johnson-Kendall-Roberts (JKR) model of elastic contact between two spheres ( contact radius)

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

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

Maugis-Dugdale model of elastic contact between two spheres( contact force)

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Klein bagel ( "figure 8" immersion y-coordinate)

In mathematics, the Klein bottle is an example of a non-orientable surface, informally, it is a surface (a two-dimensional manifold) in which notions of ... more

Maugis-Dugdale model of elastic contact between two spheres (depth of penetration)

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Αxial stiffness for an element in tension

The stiffness of a body is a measure of the resistance offered by an elastic body to deformation.
Tension describes the pulling force exerted by each ... more

de Laval nozzle - correlation of Area and Velocity

A de Laval nozzle (or convergent-divergent nozzle, CD nozzle or con-di nozzle) is a tube that is pinched in the middle, making a carefully balanced, ... more

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