Answer:
a. stress in steel rod is -9.6 X 10⁷pa while stress in brass rod is -7.2 X 10⁷pa
b. new junction from steel rod is 40.0192cm while new junction from brass rod is 30.024cm
Explanation:
<u>Step 1:</u> <u>identify the given parameters and standard parameters</u>
⇒Steel rod: length of rod = 40.000 cm
Young modulus(Υ) = 20 X 10¹⁰ pa
coefficient of linear expansion(α) = 1.2 X 10⁻⁵ K⁻¹
stress in the rod =?
⇒Brass rod: length of rod = 30.000 cm
Young modulus(Υ) = 9 X 10¹⁰ pa
coefficient of linear expansion(α) = 2.0 X 10⁻⁵ K⁻¹
stress in the rod =?
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<u>Step 2:</u> <u>calculate the stress in each rod</u>
⇒Steel rod: stress in the rod = -Y*α*ΔT
= (-20 X 10¹⁰ pa) (1.2 X 10⁻⁵ K⁻¹)(60-20)K
= (-20 X 10¹⁰ pa) (1.2 X 10⁻⁵ K⁻¹)(40)K
= -9.6 X 10⁷ pa
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⇒Brass rod: stress in the rod = -Y*α*ΔT
= (-9 X 10¹⁰ pa) (2.0 X 10⁻⁵ K⁻¹)(60-20)K
= (-9 X 10¹⁰ pa) (2.0 X 10⁻⁵ K⁻¹)(40)K
= -7.2 X 10⁷ pa
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∴ stress in steel rod is -9.6 X 10⁷pa while stress in brass rod is -7.2 X 10⁷pa
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<u>Step 3:</u> <u>calculate the new length of each rod</u>
⇒Steel rod: New length = ΔL + L₀
ΔL = α*L₀*ΔT
ΔL = (1.2 X 10⁻⁵ K⁻¹)(40cm)(40)K
ΔL = 1920 X 10⁻⁵ cm = 0.0192cm
New length = ΔL + L₀ = 0.0192cm + 40cm
New length = 40.0192cm
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⇒Brass rod: New length = ΔL + L₀
ΔL = α*L₀*ΔT
ΔL = (2.0 X 10⁻⁵ K⁻¹)(30cm)(40)K
ΔL = 2400 X 10⁻⁵ cm = 0.024cm
New length = ΔL + L₀ = 0.024cm + 30cm
New length = 30.024cm
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Therefore, new junction from steel rod is 40.0192cm while new junction from brass rod is 30.024cm
