Gravitational unit check: select the S.I. force equivalent of one kilogram-weight (1 kgf).
Civil Engineering
SI Units
Difficulty: Easy
Choose an option
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A8.9 N in S.I. system
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B9.8 N in S.I. system
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C4.5 N in S.I. system
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D5.4 N in S.I. system
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E10.0 N in S.I. system
Answer
Correct Answer: 9.8 N in S.I. system
Explanation
Introduction / Context:Kilogram-weight (kgf) is a gravitational (non-S.I.) unit of force historically used in engineering. Converting kgf to newtons is essential when reconciling legacy specifications with modern S.I. calculations in design and testing.
Given Data / Assumptions:
- Standard gravity g0 ≈ 9.80665 m/s^2.
- 1 kgf is defined as the weight of 1 kg under g0, so 1 kgf = 9.80665 N.
- Rounded engineering value often used is 9.8 N.
Concept / Approach:Apply the definition of weight: W = m * g. For m = 1 kg at standard gravity, W = 9.80665 N. In many problems, 9.8 N is accepted given typical significant-figure constraints.
Step-by-Step Solution:
Define: 1 kgf = weight of 1 kg under g0.Compute: W = 1 * 9.80665 ≈ 9.80665 N.Round appropriately → 9.8 N.Verification / Alternative check:
Cross-check reciprocal: 1 N ≈ 0.10197 kgf; multiply 9.80665 N by 0.10197 kgf/N ≈ 1 kgf.Why Other Options Are Wrong:
8.9, 4.5, 5.4 N: numerically inconsistent with g0; too small.10.0 N: a rough round-up beyond standard 9.81; not the accepted value for 1 kgf.Common Pitfalls:
Confusing kilogram (mass) with kilogram-force (force).Using g = 10 m/s^2 for convenience without noting the approximation error.Final Answer:
9.8 N in S.I. system