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Tuning fork (cylindrical prongs)

A tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs (tines) formed from a U-shaped bar of elastic metal (usually ... more

Knuckle joint (Moment about axis XX)

A knuckle joint is a mechanical joint used to connect two rods which are under a tensile load, when there is a requirement of small amount of flexibility, ... more

Knuckle joint (Maximum bending stress)

A knuckle joint is a mechanical joint used to connect two rods which are under a tensile load, when there is a requirement of small amount of flexibility, ... more

Trail ( for bicycles)

A factor that influences how easy or difficult a bike will be to ride is trail, the distance that the front wheel ground contact point trails behind the ... more

Trail (for motorcycles)

Trail, or caster, is the horizontal distance from where the steering axis intersects the ground to where the front wheel touches the ground. The ... more

Resonance frequency in LC circuits (angular)

An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter ... more

Resonance frequency in LC circuits

An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter ... more

Self-buckling critical height ( for a free-standing, vertical column)

Column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above ... more

Cantilever Euler Beam - Displacement

Euler–Bernoulli beam theory (also known as engineer’s beam theory or classical beam theory) is a simplification of the linear theory of elasticity ... more

Cantilever Euler Beam - Maximum Displacement

Euler–Bernoulli beam theory (also known as engineer’s beam theory or classical beam theory) is a simplification of the linear theory of elasticity ... more

Radius of the turn of an upright bike (for small steering angles)

In order for a bike to turn, that is, change its direction of forward travel, the front wheel must aim approximately in the desired direction, as with any ... more

Force exerted by stretched or contracted material

In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each ... more

Radius of the turn of leaning bike (for small steering angles)

This lean of the bike decreases the actual radius of the turn proportionally to the cosine of the lean angle. The resulting radius can be approximated ... 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

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

Elastic potential energy( with respect to Length)

Elastic energy is the potential mechanical energy stored in the configuration of a material or physical system as work is performed to distort its volume ... 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/

Critical buckling stress of a column

Column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above ... more

Beam shear

Shear stress,is defined as the component of stress coplanar with a material cross section. The average shear stress is force per unit area. Beam shear is ... more

Cross Section

The cross section is an effective area that quantifies the intrinsic likelihood of a scattering event when an incident beam strikes a target object, made ... more

Cross Section (discrete events)

The cross section is an effective area that quantifies the intrinsic likelihood of a scattering event when an incident beam strikes a target object, made ... more

Electrical conductance (related to the material and the shape of the conductor)

In physics and electrical engineering, a conductor is an object or type of material that permits the flow of electrical current in one or more directions. ... more

Cross Section (flux)

The cross section is an effective area that quantifies the intrinsic likelihood of a scattering event when an incident beam strikes a target object, made ... more

Closed magnetic circuit ( Lorentz force )

An electromagnet is a type of magnet in which the magnetic field is produced by electric current. The magnetic field disappears when the current is turned ... more

Rotational stiffness ( depended on rigidity modulus of the material)

Stiffness is the rigidity of an object — the extent to which it resists deformation in response to an applied force. In general, stiffness is not the same ... more

Critical Speed of a Rotating Shaft - Dunkerley's method

In solid mechanics, in the field of rotordynamics, the critical speed is the theoretical angular velocity that excites the natural frequency of a rotating ... more

Moment of Inertia - I-Beam (Ideal cross section)

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Electrical resistance

Electrical resistance of an electrical conductor is the opposition to the passage of an electric current through that conductor and depends on: What ... more

Second moment of area - I-Beam (W-section)

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Radius of gyration

Gyration is a rotation in a discrete subgroup of symmetries of the Euclidean plane such that the subgroup does not also contain a reflection symmetry whose ... more

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