Respuesta :
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
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
