REAL life example about meachanic of material

1. Real Life Example
in
Mechanics of Material's
By Sina Abedini n

2. ELEMENTARY STRESS SYSTEMS
1.Stress and strain in uni -axial solid hollow bars
Explain:
Work through the example below:
An iPod ; with a mass 30 grams in dangled its earplug cable.
a)Assuming that copper wire of diameter 0.40mm
inside the cable carries the entire load ; evaluate the
stress in the wire due to the weight of the iPod
b)If the wire in (a) is1.50m long ; by how much will it
stretch?
c)Assuming that the plastic insulation ; which fits snugly
over the wire and has an external diameter of 1mm ;
carries the entire load ; evaluate the stress in insulation
due to the weight of iPod
d)If the insulation is made from uPVC calculate the
extension of the insulation in circumstances described
in (c)

3. 𝑎)𝜎 =
𝐹
𝐴
=
𝑚𝑔
𝜋
4
𝑑2
=
30 × 10−3
× 9.81
𝜋
4
× (0.4 × 10−3)2
0.4mm
𝐹
=
𝑚𝑔
=
30
×
10
−3
×
9.81
2.3 × 106
𝑁
𝑚2
1.5m
𝑏)δ =
𝑃𝑙
𝐴𝐸
=
𝑚𝑔 × 𝑙
𝜋
4
𝑑2 × 𝐸
=
30 × 10−3
× 9.81 × 1.5
𝜋
4
× (0.4 × 10−3)2× 110 × 109
31.9 × 10−6
𝑚

4. 0.4mm
1mm
1.5m
𝐹
=
𝑚𝑔
=
30
×
10
−3
×
9.81
0.2mm
c)𝜎 =
𝐹
𝐴
=
𝑚𝑔
𝜋
4
𝑑0
2
−𝑑1
2
𝐸
=
30×10−3×9.81
𝜋
4
(0.0012−0.0042)
0.29
𝑁
𝑚2
𝑑)𝛿 =
𝑃𝑙
𝐴𝐸
=
𝑚𝑔𝑙
𝜋
4
𝑑0
2
− 𝑑1
2
𝐸
=
30 × 10−3 × 9.81 × 1.5
𝜋
4
(0.0012 − 0.0042) × (2 × 109)
3.35 × 10−4𝑚