Unit conversion — how many newtons are in one kilogram-force (kgf)?

Introduction / Context:
Engineering problems often require converting between kilogram-force (kgf) and newtons (N). The kilogram-force is a gravitational unit of force, while the newton is the SI unit. Knowing the approximate conversion is essential for quick calculations.

Given Data / Assumptions:

• Standard gravitational acceleration g ≈ 9.8 m/s^2 (more precisely 9.80665 m/s^2).
• 1 kilogram-force is defined as the weight of a 1 kg mass under standard gravity.

Concept / Approach:
Weight W equals mass m times gravitational acceleration g. Thus, the force corresponding to 1 kgf is W = 1 kg * g newtons. Using the standard value of g, this gives approximately 9.8 newtons.

Step-by-Step Solution:

Verification / Alternative check:
Compare with everyday approximations: many handbooks use 10 N as a quick mental estimate for 1 kgf; the more precise rounded value for exams is 9.8 N.

Why Other Options Are Wrong:

• 7.8 N and 8.9 N: Underestimate the gravitational force for 1 kg.
• 12 N: Overestimates standard gravity.
• 10.8 N: Not a standard approximation; too large.

Common Pitfalls:
Confusing mass (kg) and force (N). Mass is an intrinsic property; force depends on g. Always multiply mass by g to obtain weight in newtons.

Final Answer:
9.8 N