Question

An uniform steel rod of 5 sq. mm cross section is heated from 0° C to 25° C. Find the force which must be exerted to prevent it from expanding. Also find energy stored per unit volume. ( $\alpha_{steel}$ = 12 x 10⁻⁶/C, $Y_{steel}$ = 20 x 10¹⁰ N / m² )

Answer 1

Given :

A = 5 mm² = 5 × 10⁻⁶ m² ,

∆θ = (25 – 0) ⁰C = 25⁰C,  

αsteel = 12 × 10⁻⁶/ ⁰C  

Ysteel = 20 × 10¹⁰ N/m2  

F = Y α ∆θA  

= 20 × 10¹⁰ × 12 × 10⁻⁶ × 25 × 5 × 10⁻⁶

∴ F = 300 N

U =( ½) ( stress) ² /Y

U=1/2Y [F/A]²

U =( 1/2)x[20x10¹⁰]x (300/5x10⁻⁶)²

∴U=9000J/m3³

Answer 2

Answer:

Given :

A = 5 mm² = 5 × 10⁻⁶ m² ,

∆θ = (25 – 0) ⁰C = 25⁰C,  

αsteel = 12 × 10⁻⁶/ ⁰C  

Ysteel = 20 × 10¹⁰ N/m2  

F = Y α ∆θA  

= 20 × 10¹⁰ × 12 × 10⁻⁶ × 25 × 5 × 10⁻⁶

∴ F = 300 N

U =( ½) ( stress) ² /Y

U=1/2Y [F/A]²

U =( 1/2)x[20x10¹⁰]x (300/5x10⁻⁶)²

∴U=9000J/m3³