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Lateral earth passive pressure (Rankine theory for horizontal backfill)

Lateral earth pressure is the pressure that soil exerts in the horizontal direction. Rankine’s theory, is a stress field solution that predicts active and ... more

Bretschneider's formula - Area of a general quadrilateral

In geometry, Bretschneider’s formula is the shown expression for the area of a general quadrilateral.

A quadrilateral is a polygon with four ... more

Rotational stiffness

The stiffness of a body is a measure of the resistance offered by an elastic body to deformation. A body have a rotational stiffness when it is in a ... more

Area of a regular inscribed n-gon in a unit circle

The area of a regular n-gon with side s inscribed in a unit circle ( unit circle is a circle with radius of one). RESTRICTION: s<2

... more

Guided ray (acceptance angle)

A guided ray (also bound ray or trapped ray) is a ray of light in a multi-mode optical fiber ( type of optical fiber mostly used for communication over ... 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.


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


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.

This worksheet is a modified version of Example 5.4 page 188 found in :
OpenStax College,College Physics. OpenStax College. 21 June 2012.
Creative Commons License : http://creativecommons.org/licenses/by/3.0/

Hooke's Law (spring)

Hooke’s Law of elasticity is an approximation that states that the amount by which a material body is deformed (the strain) is linearly related to ... more

Hyperbolic triangle ( length of the base)

A hyperbolic sector is a region of the Cartesian plane {(x,y)} bounded by rays from the origin to two points (a, 1/a) and (b, 1/b) and by the hyperbola xy ... more

Hyperbolic triangle ( length of the altitude)

A hyperbolic sector is a region of the Cartesian plane {(x,y)} bounded by rays from the origin to two points (a, 1/a) and (b, 1/b) and by the hyperbola xy ... 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

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