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3 years ago

At 20 C, a steel rod of length 40.000 cm and a brass rod

Physics

1 answer:

balandron [24]3 years ago

8 0

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:

Step 1: identify the given parameters and standard parameters

⇒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 =?

--------------------------------------------------------------------------------------------

Step 2: calculate the stress in each rod

⇒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

--------------------------------------------------------------------------------------------

⇒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

--------------------------------------------------------------------------------------------

∴ stress in steel rod is -9.6 X 10⁷pa while stress in brass rod is -7.2 X 10⁷pa

--------------------------------------------------------------------------------------------

Step 3: calculate the new length of each rod

⇒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

--------------------------------------------------------------------------------------------

⇒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

--------------------------------------------------------------------------------------------

Therefore, new junction from steel rod is 40.0192cm while new junction from brass rod is 30.024cm

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