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Tractrix (General formula-cartesian coordinates)

Tractrix is the curve along which an object moves, under the influence of friction, when pulled on a horizontal plane by a line segment attached to a ... more

Tractrix

Tractrix is the curve along which an object moves, under the influence of friction, when pulled on a horizontal plane by a line segment attached to a ... more

Linear mass density

Linear density is the measure of a quantity of any characteristic value per unit of length. Linear mass density (titer in textile engineering, the amount ... 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

Properties of concrete - modulus of elasticity

Concrete has relatively high compressive strength, but significantly lower tensile strength. As a result, without compensating, concrete would almost ... more

Wind Chill - North American and UK - Fahrenheit scale

Wind-chill or windchill, (popularly wind chill factor) is the perceived decrease in air temperature felt by the body on exposed skin due to the flow of ... more

Wind Chill - North American and UK - Celsius scale

Wind-chill or windchill, (popularly wind chill factor) is the perceived decrease in air temperature felt by the body on exposed skin due to the flow of ... more

Critical speed for a leadscrew

The critical speed is the speed that excites the natural frequency of the screw. For a steel leadscrew or steel ballscrew, the critical speed is ... 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/

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

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