Select the correct set of conversion statements relating newton, kilogram-force, pressure in kgf/cm^2, and standard atmosphere (atm) to their S.I. equivalents.
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A1 N force = 0.10197 kgf
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B1 kgf = 9.80665 N
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C1 kgf/cm2 = 98.0665 kN/m2
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D1 atm = 101.325 kN/m2
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EAll the above.
Answer
Correct Answer: All the above.
Explanation
Introduction / Context:Engineering calculations frequently involve converting between historical gravitational units (kgf, kgf/cm^2) and S.I. units (N, kN/m^2, Pa). Mastering a few canonical conversion constants prevents costly mistakes in structural, hydraulic, and machine design computations.
Given Data / Assumptions:
- Standard gravity g0 = 9.80665 m/s^2.
- Force relation: 1 kgf = 9.80665 N; therefore 1 N ≈ 0.10197 kgf.
- Pressure: 1 kgf/cm^2 = 9.80665 * 10^4 N/m^2 = 98.0665 kN/m^2.
- Standard atmosphere: 1 atm = 101.325 kPa = 101.325 kN/m^2.
Concept / Approach:
Apply g0 to convert kgf ↔ N and scale area conversions carefully to move between cm^2 and m^2. Recognize 1 kPa = 1 kN/m^2 for pressure magnitudes in engineering usage.
Step-by-Step Solution:
From definition: 1 kgf = g0 N = 9.80665 N → invert to get 1 N ≈ 0.10197 kgf.For pressure: 1 cm^2 = 10^-4 m^2 → 1 kgf/cm^2 = 9.80665 N / 10^-4 m^2 = 98,066.5 N/m^2 = 98.0665 kN/m^2.Atmospheric pressure: 1 atm = 101,325 N/m^2 = 101.325 kN/m^2.Verification / Alternative check:
Compare with common engineering rules of thumb: 1 kgf/cm^2 ≈ 0.980665 bar and 1 atm ≈ 1.01325 bar, showing consistency with the S.I. pascal scale (1 bar = 100 kPa).
Why Other Options Are Wrong:
- Each A–D is individually correct; the most complete choice is E (All the above).
Common Pitfalls:
- Forgetting the area conversion when moving from cm^2 to m^2, leading to 10^4 errors.
- Applying g0 to masses instead of forces when converting kgf to N.
Final Answer:
All the above.