Deforming Solids


  • If a spring is being squashed and shortened, there is a compressive force acting on it.
  • If a spring is being stretched, there is a tensile force acting on it.

Elasticity and Hooke’s law

An object being stretched obeys Hooke’s law, if the force acting on the object is proportional to the extension (x) of that object.

It is further said that the object has been stretched elastically (this usually appear in exams) – the object can return to its original shape after the load is removed.

If an object is deformed beyond recovery, it is said to have reached its elastic limit. It no longer obeys Hooke’s law.

Before the elastic limit is reached, k (the spring constant or force constant) is equal to the gradient of the Force to extension graph, where x ∝ F , and k = F/x.

Area under the graph represents the work done in extending the object. The energy it releases upon the removal of the load is that same work done.

W or E = F s = ½F x ⇒ We know F = k x ⇒ W or E = ½k x²It’ll show up in problems. I guarantee.

 

 

 

Stress, Strain, and Young’s Modulus

 

The stress on an object is the force applied over cross-sectional area (you can think of it as pressure).

P.S. The value of stress at which a material breaks is called U.T.S. – Ultimate Tensile Strength

The strain on an object is the fractional increase in the original length of the wire (Equals to extension [ by extension it is not meant the new length of the wire, but only the amount it extended.])

Young’s modulus is the ration of stress to strain.

  

How different materials behave when we 'extend them'
How different materials behave when we ‘extend them’

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