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Elastic Properties of Matter

Posted by on Aug 3, 2011 in Physics | 0 comments

A perfect rigid body, in Properties of Matter, has constant distance between two particles (not true in practice) i.e. most bodies get deformed under an applied force and the body has a tendency to regain its original size and shape when the force is withdrawn. This property of the body that tends to regain its shape or size when deforming forces are removed is called elasticity.Engineering in Kenya has more information on the subject.

A perfectly elastic body in Properties of Matter retains its original shape or size very quickly. A body that tends to regain its shape or size very slowly is known to be perfectly plastic in nature. Solids tend to resist change of both shape and volume and hence they possess rigidity or shear elasticity as well as volume elasticity. Liquids on the other hand tend to resist change in volume and not shape and thus possess only volume elasticity in Properties of Matter.

Other Properties of Matter

Stress in Properties of Matter

When a body experiences a deforming external force, different particles in it are displaced, and they try to occupy their original positions. This restoring force per unit area taking place inside the body is called stress in Properties of Matter. As long as there is no permanent change in shape or volume of the body, the restoring force is always equal to the applied force. Mathematically;

Stress = Force/ cross-sectional area of the body.

Strain in Properties of Matter

When an external force acts on a body, it displaces various particles and the body is said to be under strain in Properties of Matter. It is usually defined as the ratio of change in length, volume or shape to the original length, volume or shape. Mathematically;

Strain = l/L, where l is the change in length.

Ratios in Properties of Matter

Hooke’s Law in Properties of Matter

In Properties of Matter, the relationship between stress and strain is constant (E), i.e. Stress/ Strain = E. E is the coefficient of elasticity or modulus of elasticity (value depends on the nature of the material.)

Stress                                                     From the graph aside, Hooke’s law is only

Plastic range             valid in the region below the elastic limit,

beyond which the body has un-proportional

Elastic                                        variation in strain and stress (the change in

Limit                                          stress leads to a rapid change in strain).

Strain

Young’s Modulus in Properties of Matter

This in Properties of Matter is the ratio of stress to longitudinal strain within the elastic limits. Consider a wire of length L and let it change by l under an applied force F acting on a cross-sectional area a. from this, longitudinal strain is l/ L and stress is F/ a. therefore, young’s modulus of elasticity will be;

Y = stress/ strain = (F/ a)/ (l/ L) = FL/ al. The units for young’s modulus are N/m2

Bulk’s modulus in Properties of Matter

In Properties of Matter, this is the ratio between stress and volumetric strain. If a force is applied normally over a surface of a body and it changes only its volume, then the strain caused here is volumetric strain. It is measured by change in volume per unit volume i.e. v/ V. B = (F/ a)/ (v/ V) = FV/ av.

Viscosity in Properties of Matter

Viscosity in Properties of Matter is when a liquid opposes relative motion between its different layers. Liquids such as kerosene, alcohol, water etc. flow easily while others like tar, glycerin, etc. flow with difficulty and are said to be highly viscous in Properties of Matter.

Coefficient of viscosity

Consider a layer AB of a liquid moving with velocity v with respect to a parallel layer CD which is at a distance r from it. Consider also that the force required to produce the motion be F acting on an area A and thus force is acting along the direction AB (i.e. in the direction of motion). An equal force will act in the opposite direction due to viscosity and it will depend on the following;

1.                I.      F α –v
2.             II.      F α A
3.          III.      F α l/ r

Combining the three we have F = -ηA (v/ r), where η is the coefficient of viscosity and it depends on the nature of the liquid. If the two layers are very close to each other, then

F = -ηA (dv/ dr), where dv/ dr is the velocity gradient. If A = 1cm2 and dv/ dr = 1, then F = η which gives the definition of coefficient of viscosity in Properties of Matter as the tangential force per unit area required to maintain a unit velocity gradient. If F = 1, then η = 1 and the unit is poise.

Stoke’s Law in Properties of Matter

For Properties of Matter, if a body falls through a fluid (liquid or gas), then it carries along with it a layer of fluid in contact and hence it will tend to produce some relative motion between the layers of the fluid. This relative motion is opposed by the forces of viscosity and the opposing force becomes equal to the driving force that produces the motion. At that instant, the body moves with constant velocity known as terminal velocity in Properties of Matter. Consider a small sphere falling through a viscous medium.

Conclusion for Properties of Matter

For stoke’s law, the opposing force is directly proportional to the velocity of the sphere and also, it depends on;

• The coefficient of viscosity of the medium
• The radius of the sphere
• The density of the medium. Combining the three we have

F = k.v.η.r, where r is a constant taken to be 6π.

These properties are not present in all forms of matter. Materials like glass are said to be brittle. Brittle is when a material breaks/ gets destroyed when its elastic limit is reached in Properties of Matter.