11. you have two specimens both of which are cylindrical with a diameter of 20 mm and a length of 200 mm. one is made of a titanium alloy (e = 100 gpa) and the other is made out of stainless steel (e = 200 gpa). both of them are subjected to a tensile force of 500 n. which of them will have higher stress? which will develop higher strain? if possible, can you determine which of the specimens will be stronger?

Stress will be same for both specimen.

Titanium alloy have more strain as compare to stainless steel.

Stainless steel is more stronger as compare to titanium alloy.

Explanation:

Given that

d = 20 mm

L= 200 mm

P= 500 N

Specimen 1(titanium alloy):

E = 100 GPa

Specimen 2(Stainless steel):

E = 200 GPa

Stress given as

P=Load

A= Cross sectional area

σ = 1.59 MPa

Both the specimen have same force and same dimensions so the stress will be same for both specimen.

We know that

σ =  ε .E

σ= stress

ε = strain

E= Modulus of elasticity

Specimen 1(titanium alloy):

E = 100 GPa

σ =  ε .E

1.59 = 100 x 1000 x ε                       ( 1 GPa = 1000 MPa)

 ------1

Specimen 2(Stainless steel):

E = 200 GPa

σ =  ε .E

1.59 = 200 x 1000 x ε                    

-----------2

From equation 1 and 2

So we can say that titanium alloy have more strain as compare to stainless steel.

E for  stainless steel= 200 GPa

E for   titanium alloy = 200 GPa

E stainless steel is more then titanium alloy that is why stainless steel is more stronger .