Elastic Properties of Solid

Physics SSS1 Third Term

WEEK 1

Elastic Properties of Solid

Performance Objectives

Students should be able to:

1. State Hook’s law, Young Modulus law
2. Determine the work done in springs and elastic string

Content

Elasticity is the ability of a material to regain its original shape or size after deformation or after removal of stress/force,   or after it has been compressed. Deformation occurs when a wire is stretched or compressed. Deformation is elastic if the wire returns to its original position, while it is plastic if it does not return to its original position.

Terms used in Elasticity

1. Elastic limit: Elastic limit is the maximum load (force) which a body can experience and still retain its original size/shape once the load/force has been removed. It can also be defined as the point on a stress/strain or load/extension graph beyond which Hooke’s law is no longer obeyed.
2. Yield point: This is reached when a stretched wire does not return to its original position
3. Maximum load: When a load is added to a wire that it cannot stand any further increase, it is called maximum load.
4. Breaking point: This is the point at which the wire breaks away from the original, having been stretched beyond the yield point where it cannot stand any further stretching.

Hooke’s Law

Hooke’s law states that the force applied to spring is directly proportional to the extension (E) produced provided the proportionality limit (of the spring) is not exceeded.

E/L = K

E₁/L₁ = E₂/L₂

 

Strength of Material

 

1. Tensile/Compressive stress: Tensile stress is the ratio of load or force (F) to its cross-sectional area (A). It is measured in Nm^-2 or N/m².

Thus, tensile / compressive stress = Force/Area = F/A

2. Tensile / Compressive strain: Tensile strain is the ratio of extension to its original length of a wire. It has no limit. Thus, tensile/compressive strain

= extension/Length (original) = e/L

3. Young modulus: Young modulus is the ratio of tensile/compressive stress to tensile/compressive strain. It is denoted by E and measured in N/m² or Nm^-2 (S.I units). Thus,

Young modulus = tensile/compressive stress/Tensile/compressive strain

E = F/A / e/L = FL/Ae

Hence, F = EAe / L

4. Force-constant: Force-constant is the amount of force that causes a unit expansion of an elastic material or the ratio of f/e of elastic. It is denoted by K, measured in Nm^-1

Thus, F = Ke

∴K = F/e

Example

The extension on a spring when 5g was hung from it was 0.56cm. If Hooke’s law is obeyed, what is the extension caused by a load of 20g?

Solution

F₁ = 5g, E₁ = 0.56cm, E₂ = x, F₂ = 20g

If Hooke’s law is obeyed

F ∝ e, →F = Ke

∴F₁ /e₁ = F₂ /e₂

5/0.56 = 20/x

5x = 20 x 0.56

X = 20 x 0.56/5 = 2.24cm