Two rods are identical in all respects except one: one rod is made from aluminum

Question

Two rods are identical in all respects except one: one rod is made from aluminum (Young's modulus 5.1 x 1010 N/m2), and the other from tungsten (Young's modulus 2.5 x 1011 N/m2). The rods are joined end to end, in order to make a single rod that is twice as long as either the aluminum or tungsten rod. What is the effective value of Young's modulus for this composite rod? That is, what value YComposite of Young's modulus should be used in Equation 10.17 when applied to the composite rod? Note that the change LComposite in the length of the composite rod is the sum of the changes in length of the aluminum and tungsten rods.

Explanation / Answer

Youngs modlulus Y of a material is given Y = FL/ADL

A = area

DL = change of length

L = original length

F = force

so here we apply

extension of A be   DL of A = FL/AY

i.e Ext A = 1/Ya

Ext B = 1/Yb

so

total Extensiton = 1/Ya + 1/Yb

and since stress = 1

Yc = 1/total strain

Y = 2 Ya Yb/(Ya+ Yb)

Y = 2*5.1 e 10 * 2.5 e11/(5.1 e10 + 2.5 e11)

Y = 8.47 *10^10 N/m^2 -------------<<<<<<<<<<<<Answer

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.