What is the cross sectional area of the wire? What is the radius of the wire?

Question

A steel wire is used to hang a plant from a ceiling in a building’s atrium. The wire is 25 meters long and the hanging plant has a weight of 150N. When the plant is attached to the wire, the wire increases its length by 5 cm. What is the cross sectional area of the wire? What is the radius of the wire?

Answer 1

Youngs modulus for various steels is about 200 x 10^9 N/m2 so we will use that.
E = stress / strain = (F / A) / (dL / L)
http://www.engineeringtoolbox.com/young-modulus-d_417.html
200 x 10^9 N/m2 = (150 N/A) / (.05/25)
A = 150N x 0.002 / (200 x 10^9 N/m2)
A = 0.3 / (2 x 10^7) m2
A = 0.15 x 10^-7 m2
A = 0.000000015 m2 = 0.015 mm2
A = Pi r^2
r = (A/Pi)^.5 = (0.015 / 3.14159)^.5 = 0.0690988591 mm

Answer 2

seems to me that your missing one piece of vital info, the distance a steel wire is stretched per N of force applied.

You can figure that 150N of force caused an increase in length of .2% (5cm=.05m so .05/25). This would be the telling characteristic, but not all the info is given.

You also know that the area of the wire is directly proportional to its tensile strength. So, if you knew this proportion, you could use the change in length to determine the area of a 25m wire.

Once you have the area of a circle (cross-section of wire), you know that A=(pi)r^2, so

r=sqrt(A/pi).

thats all I can do without the ratio of area to tensile strength...

Answer 3

The cross sectional area quadruples and the resistance will be 1/4 of the original.