Question about elastic deformation.

[da_coolest]

Hi.. I need a good explanation for the following question. an explanation with a small mathematical calculation to prove the answer would be highly helpful.

A copper rod of cross-section 10 mm  10 mm is stretched along its axis, changing length from 1.000 m to 1.001 m. The deformation is elastic, or fully recoverable. Given that the modulus of copper is 110 GPa, the stress on the rod is approximately (choose the closest answer):

A 110 kPa
B 110 MPa
C 110 GPa
D 1/110 MPa
E 1/110 GPa



thanks in advance!

 

[Astronuc]

What is the relationship between stress and strain for elastic deformation?

What is the strain for a bar stretched 1.000 m to 1.001 m?

 

[da_coolest]

What is the relationship between stress and strain for elastic deformation?

What is the strain for a bar stretched 1.000 m to 1.001 m?

young's modulus

thanks, now i got an idea about how to do the calculation. to which units i should convert these into when calculating?

 

[Astronuc]

young's modulus

thanks, now i got an idea about how to do the calculation. to which units i should convert these into when calculating?

Strain is a ratio, and is dimensionless, or written as m/m or cm/cm or in/in.

 

[DeeNos]

The correct answer is B) 110 MPa.

Elastic deformation refers to the temporary change in shape or size of a material when a force is applied, but the material is able to return to its original shape once the force is removed. This behavior is described by Hooke's Law, which states that the stress (force per unit area) applied to a material is directly proportional to the strain (change in length per unit length) it experiences. Mathematically, this is represented as σ = Eε, where σ is stress, E is the elastic modulus, and ε is strain.

In this scenario, the copper rod is experiencing a change in length of 0.001 m (1.001 m - 1.000 m) over an original length of 1.000 m, giving a strain of 0.001/1.000 = 0.001. Using the given elastic modulus of 110 GPa (or 110,000 MPa), we can calculate the stress as σ = (110,000 MPa)(0.001) = 110 MPa.

In summary, the answer is B) 110 MPa, as this is the closest approximation of the stress experienced by the copper rod during elastic deformation.