A 10mm diameter annealed steel wire is drawn through a die at a speed of 0-5 m-s to reduce the diameter by 20Neglecting friction and strain hardening- the stress required for drawing in MPa is

Diameter of steel wire d_i= 10 mm v = 0.5 m/s Final diameter of wire d_f= 0.8 × d_i=8 mm Drawing stress under ideal condition is given as, σ _d=σ _yt× ln ...

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Standard XII

Physics

Moment of Inertia of a Rod

A 10mm diamet...

Question

A 10mm diameter annealed steel wire is drawn through a die at a speed of 0.5 m/s to reduce the diameter by 20%. The yield stress of the material is 800 MPa

Neglecting friction and strain hardening, the stress required for drawing (in MPa) is

178.6

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357.0

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1287.5

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2575.0

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Solution

The correct option is B 357.0
Diameter of steel wire

$d_{i} = 10 m m$

$v = 0.5$ m/s

Final diameter of wire

$d_{f} = 0.8 \times d_{i} = 8 m m$

Drawing stress under ideal condition is given as,

$σ_{d} = σ_{y t} \times l n {(\frac{d_{i}}{d_{f}})}^{2}$

$= 800 \times 2 l n (\frac{10}{8})$

$= 357$ MPa

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A 10mm diameter annealed steel wire is drawn through a die at a speed of 0.5 m/s to reduce the diameter by 20%. The yield stress of the material is 800 MPa Neglecting friction and strain hardening, the stress required for drawing (in MPa) is

The correct option is B 357.0Diameter of steel wire di=10mm v=0.5 m/s Final diameter of wire df=0.8×di=8mm Drawing stress under ideal condition is given as, σd=σyt×ln(didf)2 =800×2ln(108) =357 MPa

A 10mm diameter annealed steel wire is drawn through a die at a speed of 0.5 m/s to reduce the diameter by 20%. The yield stress of the material is 800 MPa

Neglecting friction and strain hardening, the stress required for drawing (in MPa) is