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In engineering, deflection is the degree to which a structural element is displaced under a load. It may refer to an angle or a distance.

The angle of
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In engineering, deflection is the degree to which a structural element is displaced under a load. It may refer to an angle or a distance.

The angle of
... more

he Bagnold number (Ba) is the ratio of grain collision stresses to viscous fluid stresses in a granular flow with interstitial Newtonian fluid, first ... more

Bending is a manufacturing process that produces a V-shape, U-shape, or channel shape along a straight axis in ductile materials, most commonly sheet ... more

Bending is a manufacturing process that produces a V-shape, U-shape, or channel shape along a straight axis in ductile materials, most commonly sheet ... more

In Applied mechanics, bending (also known as flexure) characterizes the behavior of a slender structural element subjected to an external load applied ... more

BHN or Brinell Number is the numerical value assigned to the hardness of metals and alloys. The test is to determine the hardness ... more

The bulk modulus ( or ) of a substance measures the substance’s resistance to uniform compression. It is defined as the ratio of the infinitesimal ... more

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

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

In physics and geometry, a catenary is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends. The ... more

In materials science, creep (sometimes called cold flow) is the tendency of a solid material to move slowly or deform permanently under the influence of ... more

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

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. The Derjaguin-Muller-Toporov (... more

A gear or cogwheel is a rotating machine part having cut teeth, or cogs, which mesh with another toothed part to transmit torque, in most cases with teeth ... more

Elastic deflection is the degree to which a structural element is displaced under a load.

The deflection at any point, along the span of a center
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In engineering, deflection is the degree to which a structural element is displaced under a load.

The elastic deflection of a beam, loaded at its
... more

Elastic deflection is the degree to which a structural element is displaced under a load.

The deflection, at the free end, of a cantilevered beam
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In engineering, deflection is the degree to which a structural element is displaced under a load.

The elastic deflection of a weightless cantilever
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In engineering, deflection is the degree to which a structural element is displaced under a load. The deflection at any point along the span of an end ... more

An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substance’s tendency to be deformed elastically (i.e., ... more

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

Piezoelectricity is the combined effect of the electrical behavior of the material Piezoelectricity is the electric charge that accumulates in certain ... more

Deformation in continuum mechanics is the transformation of a body from a reference configuration to a current configuration.

Strain is a normalized
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Strategy for (a)

To find the buoyant force, we must find the weight of water displaced. We can do this by using the densities of water and steel given in Table [insert table #] We note that, since the steel is completely submerged, its volume and the water’s volume are the same. Once we know the volume of water, we can find its mass and weight

First, we use the definition of density to find the steel’s volume, and then we substitute values for mass and density. This gives :

Because the steel is completely submerged, this is also the volume of water displaced, **Vw**. We can now find the mass of water displaced from the relationship between its volume and density, both of which are known. This gives:

By Archimedes’ principle, the weight of water displaced is m w g , so the buoyant force is:

The steel’s weight is **9.80×10 7 N** , which is much greater than the buoyant force, so the steel will remain submerged.

Strategy for (b)

Here we are given the maximum volume of water the steel boat can displace. The buoyant force is the weight of this volume of water.

The mass of water displaced is found from its relationship to density and volume, both of which are known. That is:

The maximum buoyant force is the weight of this much water, or

Discussion

The maximum buoyant force is ten times the weight of the steel, meaning the ship can carry a load nine times its own weight without sinking.

Reference : 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/

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:

and the cross-sectional area of the upper leg bone(femur) is:

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 **9×10 ^{9} N/m^{2}**. Now,all quantities except

**ΔL**are known. Thus:

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/

Factor of safety (FoS) or (FS), is a term describing the structural capacity of a system beyond the expected loads or actual loads. Essentially, how much ... more

In materials science, fatigue is the weakening of a material caused by repeatedly applied loads. Fatigue strength is a measure of the strength of a ... more

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

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(a)Calculate the buoyant force on10,000 metric tons (1.00×10 7 kg)of solid steel completely submerged in water, and compare this with the steel’s weight.(b)What is the maximum buoyant force that water could exert on this same steel if it were shaped into a boat that could displace1.00×10 5 mof water?^{3}