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



Question

To inspect a 14,500 Ncar,it is raised with a hydraulic lift.if the radiusof the small piston is 4.0cm,and the radius of the large piston is 17cm, find the force that must be exerted on the small piston to lift the car.


Solution


F₁ = F₂(A₁/A₂)
= (14,500 N)(π(0.040m)²/(π(0.17m)²)
= 800 N