***********PLEASE INDICATE FINAL ANSWERS CLEARLY************* tem 7 In construct

Question

***********PLEASE INDICATE FINAL ANSWERS CLEARLY*************

tem 7 In constructing a large mobile, an artist hangs an aluminum sphere of mass 5.2 kg from a vertical steel wire 0.56 m long and 2.3x10-3 cm2 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 14.0 kg Part A Compute the tensile strain for the top wire. Express your answer using two significant figures. Al Submit My Answers Give U Part B Compute the tensile strain for the bottom wire. Express your answer using two significant figures. Al Submit My Answers Give U Part C Compute the elongation strain for the top wire. Express your answer using two significant figures. Al

Explanation / Answer

Given:
Mass of aluminium sphere, mA = 5.2 kg
Mass of brass cube, mB = 14.0 kg
Area of cross section of wire, A = 2.0×10^3 cm^2
Length of steel wire, l = 0.56 m

Solution:
A) Tensile strain for the top wire:

Total tension on the top wire is determined by

T = mA*g + mB*g
T = (mA + mB)*g
T = (5.2 kg +14.0 kg)*9.8 m/s^2
T = 188.16 N

Young's modulus = tensile stress/ tensile strain
tensile strain = tensile stress/Young's modulus
tensile strain = (tension/Area)/Young's modulus

Young's modulus of steel wire, E = 20*10^10 Pa
Tensile strain = T/(A*E)
Tensile strain = 188.16 N/(2.0×10^3 cm^2 * 20 * 10^10 Pa)
Tensile strain = 188.16 N/(2.0×10^7 m^2 * 20 * 10^10 Pa)
Tensile strain = 4.70*10^-3

b) Tensile strain for the bottom wire:

Total tension on the bottom wire is determined by

T = mB*g
T = 14.0 kg*9.8 m/s^2
T = 137.2 N

Tensile strain = (tension/Area)/Young's modulus

Young's modulus of steel wire, E = 20*10^10 Pa
Tensile strain = T/(A*E)
Tensile strain = 137.2 N/(2.0×10^3 cm^2 * 20 * 10^10 Pa)
Tensile strain = 137.2 N/(2.0×10^7 m^2 * 20* 10^10 Pa)
Tensile strain = 3.43*10^-3

c) Elongation for the top wire:

Tensile strain = elongated length/original length

Therefore, the elongation for the top wire is

Elongation = Tensile strain*original length
Elongation = 4.70*10^-3*0.56 m
Elongation = 2.632*10^-3 m or = 2.632 mm

d) Elongation strain for the bottom wire:

Elongation = Tensile strain*original length
Elongation = 3.43*10^-3 *0.56 m
Elongation = 1.92*10^-3 m or = 1.92 mm

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.