Question

An arc welding process is being carried out with a power source of 6 kW to weld two similar metals. The total energy loss is 50%, the area of cross-section of the weld is \( 10 \ mm^2 \), and the specific energy needed to melt the metal is \( 15 \ J/mm^3 \).
The speed of welding is ______ mm/s.

• A. 10
• B. 20
• C. 30
• D. 40

Hint:

Net power = input power x efficiency. Melt rate = net power / specific energy. Speed = melt rate / weld area.

Answer 1

The Correct Option is B

Step 1: Understand the Question:
We get the input power, the loss in the process, the weld area and the energy needed per unit volume, and we need to find the welding speed.
Only half of the input power actually goes into melting metal, so we adjust for that loss first.

Step 2: Find the useful (net) power:
Input power is 6 kW, which equals 6000 W or 6000 J/s.
Since 50% of this power is lost, only 50% is left to melt the metal.
\[ P_{net} = 6000 \times 0.5 = 3000 \ J/s \]

Step 3: Find the volume melted per second:
Each mm^3 of metal needs 15 J of energy to melt, so we divide the net power by this value to get the melt rate.
\[ V_R = \frac{P_{net}}{U} = \frac{3000}{15} = 200 \ mm^3/s \]

Step 4: Convert melt rate into welding speed:
As the weld moves forward, it melts a strip of metal with cross-section 10 mm^2.
So the volume melted per second equals the weld area times the welding speed.
\[ v = \frac{V_R}{A} = \frac{200}{10} = 20 \ mm/s \]

Step 5: Check option (A) 10 mm/s.
This value only shows up if we wrongly split the energy loss or divide by the wrong specific energy, so it does not match our correct working.

Step 6: Check option (B) 20 mm/s.
This matches our calculated value exactly, so this is the correct speed.

Step 7: Check option (C) 30 mm/s.
This would only appear if we skipped the energy loss entirely and used the full 6000 J/s in the calculation, which is not correct here.

Step 8: Check option (D) 40 mm/s.
This value is too high for the given inputs and does not come from any correct combination of the numbers given, so we rule it out.

Final Answer:
The welding speed works out to 20 mm/s. \[ \boxed{v = 20 \ mm/s} \]