The ratio of press force required to punch a square hole of 30 mm side in a 1 mm thickaluminium sheet to that needed to punch a square hole of 60 mm side in a 2 mm thick aluminiumsheet is________(Important - Enter only the numerical value in the answer)Correct answer is '0.25'. Can you explain this answer?

Question

Answer

The ratio of press force required to punch a square hole in different aluminum sheets can be determined by considering the area of the hole and the thickness of the sheet. Let's calculate the press force required for each case and then find the ratio between them.

First Case: Square hole of 30 mm side in a 1 mm thick aluminum sheet

- Area of the hole = (Side length)^2 = (30 mm)^2 = 900 mm^2
- Thickness of the sheet = 1 mm

Second Case: Square hole of 60 mm side in a 2 mm thick aluminum sheet

- Area of the hole = (Side length)^2 = (60 mm)^2 = 3600 mm^2
- Thickness of the sheet = 2 mm

Now, let's calculate the press force required for each case using the formula:

Press Force = Area of the hole × Shear strength of the material × Thickness of the sheet

Assuming the shear strength of the aluminum material is the same in both cases, we can ignore it in the calculations. Thus, the press force required for each case can be simplified as follows:

First Case: Press Force 1 = Area of the hole × Thickness of the sheet 1 = 900 mm^2 × 1 mm = 900 mm^3

Second Case: Press Force 2 = Area of the hole × Thickness of the sheet 2 = 3600 mm^2 × 2 mm = 7200 mm^3

Now, let's find the ratio between Press Force 1 and Press Force 2:

Ratio = Press Force 1 / Press Force 2 = (900 mm^3) / (7200 mm^3) = 0.125

However, since we were asked to provide the numerical value only, we can round the ratio to two decimal places:

Ratio ≈ 0.13

Therefore, the correct answer is 0.13.

Note: The provided answer of 0.25 seems to be incorrect, as the calculated ratio is 0.13.

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