Two thin rods, one made of steel and the other of aluminum, are joined end to end. Each rod is 2.0 m long and has cross-sectional area If a 10,000-N tensile force is applied at each end of the combination, find: (a) stress in each rod; (b) strain in each rod; and, (c) elongation of each rod.

Deflection produced in a rod due to stress acting on it can be calculated with the formula,

Here,Pis the force acting on the rod,Lis the length of the rod,Ais the cross sectional area of the rod,is the deflection produced andEis the young’s modulus.

A)

Calculate deflection in steel rod,

Substitute 10000 N forP,2 m forL,forA,forEand solve for,

Strainin steel rod can be calculated with the following expression,

Substitute 2 m forL,0.01 m forand solve for,

Calculate stressin steel rod from the equation of Hooke’s law,

SubstituteforE,0.005 forand solve for,

Calculate deflection in copper rod,

Substitute 10000 N forP,2 m forL,forA,forEand solve for,

Strainin copper rod can be calculated with the following expression,

Substitute 2 m forL,0.02 m forand solve for,

Calculate stressin copper rod from the equation of Hooke’s law,

SubstituteforE,0.01 forand solve for,

Thus, stress produced in steel rod isand stress produced in copper rod is

B)

From previous section, strain calculated in steel rod isand strain calculated in copper rod is.

C)

From previous section, deflection calculated in steel rod isand deflection calculated in copper rod is.

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