Unit equivalence: One Joule (J) is exactly equal to which of the following mechanical work units?

Introduction / Context:
Thermodynamics and mechanics share common energy units. The Joule is the SI unit of energy and work; establishing its equivalence with force–displacement units helps in converting between caloric, electrical, and mechanical quantities in problems and data sheets.

Given Data / Assumptions:

• SI base units: newton (N) for force, meter (m) for length, second (s) for time.
• Work defined as force times displacement along the direction of force.
• Power defined as work per unit time (watt = J/s).

Concept / Approach:
By definition, performing 1 newton of force through 1 meter of displacement does 1 joule of work. Therefore, 1 J = 1 N·m. Units involving per-second (N·m/s) are units of power (watts), not energy. kN·m is 1000 J, not 1 J.

Step-by-Step Solution:

Verification / Alternative check:
1 watt = 1 J/s confirms that adding “/s” converts energy units into power units; hence options with “/s” are not equal to a Joule.

Why Other Options Are Wrong:

• 1 kN-m: Equals 1000 J.
• 10 N-m/s and 10 kN-m/s: Units of power, not energy; and the magnitudes do not match 1 J.

Common Pitfalls:
Confusing energy with power; overlooking the factor of 1000 between N and kN.

Final Answer:
1 N-m