A 1.50 m long wire with Young\'s Modulus of 7.8 x 10^10 N/m^2 and a radius of 4.

Question

A 1.50 m long wire with Young's Modulus of 7.8 x 10^10 N/m^2 and a radius of 4.0 x 10^-4 m is connected to a 2.00 m wire with Young's Modulus of 35 x 10^10 N/m^2 and the same radius. How much does the wire stretch if a 2.00 kg mass is attached to the end of it? (Hint: wires in series stretch the same way as springs in series.) (**Note: I already was given an answer to this question, but what I really need is the solution explained in a little more detail along with the answer so that I may get the concept)

Explanation / Answer

Since , wire are in series therefore force applied on them will be same i.e. m*g for wire 1, F = m*g = 2*9.8 = 19.6 N , l =1.5 m , Y =7.8 x 10^10 N/m^2 , r = 4.0 x 10^-4 m F / A = Y*x1 / l on substituting x1 = 0.75 mm for wire 2, F = m*g = 2*9.8 = 19.6 N , l =2 m , Y =35 x 10^10 N/m^2 , r = 4.0 x 10^-4 m F / A = Y*x2 / l on substituting x2 = 0.22 mm total extensions of wire = x1 + x2 = 0.97 mm

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