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Problem 3: A cylindrical steel rod 0.50 m long and 1 cm radius is subjected to a tensile force of 1 × 104 N. (a) What is the tensile stress? (b) What is tensile strain? (c) By what amount does the rod stretch?

Solution

Given                   

Length of the rod, L = 0.50 m

Radius of the rod, r = 1 cm = 1×10-2 m

Tensile force, F = 1 × 104 N

Required             (a) Tensile stress              (b) Tensile strain              (c) Stretching, ΔL

Formulae            

(i) Tensile stress = F/A  

(ii) Tensile strain = stress/K         

(iii) K = stress/strain

(a) To find the tensile stress, we first find the cross-sectional area of the cylinder. We know,

A = πr2

Put values,

Now put the values in formula (i)

 

(b) Now, for steel, the constant K = 200 mega pascals. Put in formula (ii)

 

(c) Now consider formula (iii). We know that strain =ΔL/L. Put this in the formula

Now put the values of K, L (from given) and stress (from equation 1),

3 Comments

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