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Brass billet is to be extruded from its initial diameter of 40 mm to final diameter of 20 mm. The extrusion constant is 200 MPa. Force required for extrusion is
  • a)
    0.348 MN
  • b)
    0.248 MN
  • c)
     0.313 MN
  • d)
     0.528 MN 
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Brass billet is to be extruded from its initial diameter of 40 mm to f...
= 348237 N
= 0.348 MN
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Brass billet is to be extruded from its initial diameter of 40 mm to f...
Force required for Extrusion:

Given data:
Initial diameter of brass billet (D1) = 40 mm
Final diameter of brass billet (D2) = 20 mm
Extrusion constant (K) = 200 MPa

To determine the force required for extrusion, we can use the equation:

Force (F) = K * (D1^2 - D2^2)

Explanation:

1. Calculate the difference in diameter:
ΔD = D1 - D2 = 40 mm - 20 mm = 20 mm

2. Square the difference in diameter:
ΔD^2 = (20 mm)^2 = 400 mm^2

3. Plug the values into the formula:
F = K * ΔD^2
= 200 MPa * 400 mm^2

4. Convert the area from mm^2 to m^2:
400 mm^2 = 400 * 10^-6 m^2

Substitute this value into the equation:
F = 200 MPa * 400 * 10^-6 m^2

5. Simplify the calculation:
F = 80 * 10^-3 N

6. Convert the force from Newtons to MegaNewtons:
80 * 10^-3 N = 0.08 * 10^-3 MN

Therefore, the force required for extrusion is 0.08 MN or 0.348 MN (rounded to three decimal places).

Hence, the correct answer is option 'A' - 0.348 MN.
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