10.2 A wire is made out of a steel alloy with Y = 2.00×1011Paand breaking stress

Question

10.2 A wire is made out of a steel alloy with Y = 2.00×1011Paand breaking stress
1.00×109 Pa . The wire is 5m long and is secured at one endto the ceiling and hangs
vertically.

(a) A 10kg point mass is attached to one end, the wire elongates by1cm. What is the
cross section area of the wire? What is the diameter of the wire(assuming the cross
section is circular)?

(b) What is the largest mass that can be supported on the end ofthe wire before it breaks?

Now, I did part a and got 33.333 m^2, but that doesn't seem rightto me..

Can anyone help me out with this?

Explanation / Answer

(a)   Force / area = Y *L / L .         10 * 9.80 / A= 2 x 1011 * 0.01 / 5 . A =    24.5 x10-8   m2    this is r2  so        r =   0.2793mm and .      diameter =   0.5585mm . (b)   force / area = breakingstress .       force / 24.5 x10-8 = 1.00 x 109 .        force = 245N             mass = force / g =    25 kg .        force = 245N             mass = force / g =    25 kg

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