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First let me say that Physics is not my area of expertise and my knowledge from school is pretty rusty, so I apologize in advance if I am asking a totally stupid thing or I have a mismatched understanding of basic concepts. Please treat this question in terms of Newtonian physics, not looking for any relativistic answers etc. because it's totally above my pay grade.

I had a shower thought about how gravity would possibly affect the industrial/work efficiency of a city on Mars based on lower gravity (38% that of Earth if I am not mistaken). Among other things the energy required to transport merchandise or passengers across a certain distance and what possibilities that might open up.

Found this formula about Work = Force x Distance and I know that Force = Mass x Acceleration, but I can't figure out how gravity and friction affect it. To transport an object (say it's placed on a platform with wheels i.e. vehicle, completely ignoring any internal mechanical inefficiencies) of mass M over a distance D on a flat plane (no height differences) I suppose there is some initial work done to accelerate it up to a certain speed, then work to move it keeping the speed constant and compensating for friction between wheels and ground, then some final work to stop the object.

My question is, does this kind of work scale linearly with gravity (say 38% energy required to move stuff on Mars compared to Earth i.e. less fuel consumption) and how do I go about calculating it if it's not? Intuitively I think that it's not because, unless I am mistaken, in 0 gravity you still need to do work to accelerate and stop and object, so that doesn't seem linear to me.

At least is it linear the amount of work required if we don't take into account the initial acceleration and final slowing down when they are negligible, for instance when the distance is very long and we only start/stop once? Does this relationship change if we start taking into account height differences along the route (hills etc.)?

Ideally, for negligible acceleration work there is a linear relationship with gravity so I can easily say we need 38% less fuel compared to Earth all other things being equal.

[I edited the text to add a few more clarifying points]

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The friction for rolling is not very dependent of the gravity, but you have almost no air on Mars, so this friction is mach smaller, but it matters only, if you move quiet fast, more than 5 miles/h But to transport something uphill you need only 38% of the energy, that why you can jump higher on mars or moon.

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  • $\begingroup$ I see. I am imagining conditions on Mars in a big metropolis (maybe under a sealed dome or something) in such a way that air pressure inside it is similar and we maintain vehicle travel speed also similar which certainly implies more than 5 miles/h - think highway speeds. Would friction still be negligible then or does it become a pretty dominant factor which makes lower gravity not that helpful? $\endgroup$ – Glugstar Sep 4 '20 at 21:17
  • $\begingroup$ at highway speeds, the air friction is the one big energy eating. the gravity then does not matter. $\endgroup$ – trula Sep 5 '20 at 14:02

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