. In constructing a large mobile, an artist hangs an aluminum sphere of mass 6.0 kg
from a vertical steel wire 0.50 m long and 2.5x10-3cm2 in cross-sectional area. On the
bottom of the sphere he attaches a similar steel wire, from which he hangs a Brass
cube of mass 10.0 kg. For each wire, compute (a) the tensile Strain and (b) the
elongation.

Question

. In constructing a large mobile, an artist hangs an aluminum sphere of mass 6.0 kg 
from a vertical steel wire 0.50 m long and 2.5x10-3cm2 in cross-sectional area. On the 
bottom of the sphere he attaches a similar steel wire, from which he hangs a Brass 
cube of mass 10.0 kg. For each wire, compute (a) the tensile Strain and (b) the 
elongation.

anonymous · Answer

As usual it helps to draw a force diagram or maybe two: one showing the forces acting on the the top steel wire and one showing the forces acting on the bottom steel wire.  The strain in each wire can be found in the equation for Young's modulus:$$E=\frac{ \sigma  }{\epsilon }$$where E is Young's modulus for the wire material; σ is the stress in the wire; and ε is the strain in the wire.  It will be useful to remember that stress is also given by:$$\sigma =\frac{ F }{ A _{O} }$$where F is the force acting on the wire cross-section; and AO is the wire's original cross section.  Strain will be given by:$$\epsilon =\frac{ \Delta L }{ L _{O} }$$where ∆L is the amount the wire stretches; and LO is the original length of the wire.