Understanding the Relationship Between Elasticity and Young's Modulus

[carnot cycle]

Homework Statement

This is a rather conceptual question, but is there a difference between elasticity and young's modulus? I know that the young's modulus can also be stated as the modulus of elasticity, but is it incorrect to say that a substance with a higher young's modulus has a low elasticity? Or should it be that a substance with a very high young's modulus has high elasticity? Are they merely synonyms?

Homework Equations

Young's modulus = stress/strain

The Attempt at a Solution

I am assuming that a high young's modulus equates to lower elasticity.

 

[Chestermiller]

Welcome to Physics Forums!

Elasticity refers to the ability of a material to fully recover its undeformed geometry when the stress is removed. For an elastic material, the stress can be a linear function of the strain, or it can be a non-linear function of the strain. Hooke's law, involving Young's modulus, describes the behavior of any material exhibiting a linear stress-strain relationship in the limit of small strains.

 

[carnot cycle]

Hi, thanks for the response and warm welcome!

Is this ability to recover to its undeformed geometry hindered by an increase in Young's modulus?

 

[Chestermiller]

Hi, thanks for the response and warm welcome!

Is this ability to recover to its undeformed geometry hindered by an increase in Young's modulus?

If you are referring to the Young's modulus increasing as a function of strain, then this question makes no sense since, by definition, Young's modulus applies only to materials exhibiting linear stress-strain behavior. If you are asking whether, if you have two linear elastic materials featuring different Young's moduli, will the magnitude of the Young's modulus influence their ability to recover elastically, the answer is no.

 

[Nickie]

This is because young's modulus is a measure of how much a material can resist deformation under stress, meaning a higher value indicates a stiffer material that is less easily deformed. However, it is important to note that elasticity and young's modulus are not exactly the same concept. Elasticity refers to a material's ability to return to its original shape after being deformed, while young's modulus specifically measures the amount of stress required to cause a certain amount of strain. So while a high young's modulus may indicate a lower elasticity, it is not necessarily incorrect to say that a substance with a high young's modulus also has high elasticity. It is also worth mentioning that young's modulus is just one measure of a material's elasticity, and there are other factors that can affect a material's overall elasticity. Overall, it is important to consider the specific context and definitions being used when discussing elasticity and young's modulus.