Q1:n constructing a large mobile, an artist hangs an aluminum sphere of mass 5.5

Question

Q1:n constructing a large mobile, an artist hangs an aluminum sphere of mass 5.5 kg from a vertical steel wire 0.57 m long and 2.1×103 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 11.2 kg .

a.Compute the tensile strain for the top wire.

b.Compute the tensile strain for the bottom wire.

Q:2

A 60.0-cm, uniform, 49.0-N shelf is supported horizontally by two vertical wires attached to the sloping ceiling (the figure (Figure 1) ). A very small 19.0-N tool is placed on the shelf midway between the points where the wires are attached to it.

Part A

Find the tension in left wire.

Part B

Find the tension in right wire.

Figure 1 of 1

c.Compute the elongation strain for the top wire.

d.Compute the elongation strain for the bottom wire.

A 60.0-cm, uniform, 49.0-N shelf is supported horizontally by two vertical wires attached to the sloping ceiling (the figure (Figure 1) ). A very small 19.0-N tool is placed on the shelf midway between the points where the wires are attached to it.

Part A

Find the tension in left wire.

TL =   N  

Part B

Find the tension in right wire.

TR =   N  

Figure 1 of 1

Explanation / Answer

Given:
Mass of aluminium sphere, mA = 5.5 kg
Mass of brass cube, mB = 11.2 kg
Area of cross section of wire, A = 2.1×10^3 cm^2
Length of steel wire, l = 0.57 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 = (5.5 kg +11.2 kg)*9.8 m/s^2
T = 163.66 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 = 163.66 N/(2.1×10^3 cm^2 * 20 * 10^10 Pa)
Tensile strain = 163.66 N/(2.1×10^7 m^2 * 20 * 10^10 Pa)
Tensile strain = 3.89*10^-3

b) Tensile strain for the bottom wire:

Total tension on the bottom wire is determined by

T = mB*g
T = 11.2 kg*9.8 m/s^2
T = 109.76N

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 = 109.6 N/(2.1×10^3 cm^2 * 20 * 10^10 Pa)
Tensile strain = 109.6 N/(2.1×10^7 m^2 * 20* 10^10 Pa)
Tensile strain = 2.60*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 = 3.89*10^-3*0.57 m
Elongation = 2.21*10^-3 m or = 2.21mm

d) Elongation strain for the bottom wire:

Elongation = Tensile strain*original length
Elongation = 2.60*10^-3*0.57 m
Elongation = 1.48*10^-3 m or = 1.48mm

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