Suppose a man exerts $10~N$ as he lifts a $1~kg$ box a distance of $2~m$ against Earth's gravity.
To determine work we can use the following equation:
$$ W = F \cdot d \\ W = (10~N) \cdot (2~m) = 20~J $$
The work in this case is $20~J$.
Would work be the same if the man performed this task on the moon rather than the Earth?
Mathematically, the equation shows that if the man exerts the same force ($10~N$) over the same distance ($2~m$), then the work will remain the same ($20~J$) -- but I'm having trouble conceptualizing this.
$$ MoonGravity < EarthGravity $$
The force opposing our movement when lifting the box on the moon would be less than that on Earth since the gravity on the moon is far smaller. Conceptually, it seems that it'll be "easier" to lift the box on the moon, and thus should take less work.
Where is the fault in my logic?