ELASTICITY

Question:

A telephone wire 120m long and 2.2mm in diameter is stretched by a force of 380N. What is the longitudinal stress? If the length after stretching is 120.10m, what is the longitudinal strain? Determine Young’s modulus for the wire.

Solution:

The cross-sectional area of the wire is……

A = πD² / 4

= π (2.2 x 10^-3 m)² / 4

= 3.8 x 10^-6 m²

Stress = F/A

= 380 N / (3.8 x 10^-6 m²)

= 100 x 10^6 N/m²

= 100 MPa

Strain = ∆l / l

= 0.01 m / 120 m

= 8.3 x 10^-4

Y = stress / strain

= 100 MPa / (8.3 x 10^-4)

= 120,000 Mpa

Question

The density of aluminum is 2.70g/cm³. What volume does 2.0kg occupy?

Solution:

Ρ = m/V or V = m/ρ

= 2000g / 2.70g/cm³

= 741 cm³

Question

The platform is suspended by four wires at its corners. The wires are 3m long and have a diameter of 2.0mm. Young’s modulus for the material of the wires is 180000Mpa. How far will the platform drop (due to elongation of the wires) if a 50kg load is placed at the center of the platform?

Solution:

· ∆L = (3m)(123N) / (3.14x10^-6m²)

= 65x10^-5m

= 0.65mm

Question

Determine the fractional change in volume as the pressure of the pressure of the atmosphere (0.1Mpa) around a metal block is reduced to zero by placing the block in vacuum. The bulk modulus for the metal is 125000 Mpa.

Solution:

B = ∆V / V

= -∆p / B

= - (-0.1) / 125000

= 8x10^-7

Question

Compute the volume change of solid copper cube, 40mm on each edge, when subjected to a pressure of 20 Mpa. The bulk modulus for copper is 125000Mpa.

Solution:

∆V = -V∆p / B

= -(40mm)³(20Mpa) / 125000Mpa

= -10mm³