Most treadmills have motors, but there are also unpowered treadmills in which the belt moves just from action of the user running on the treadmill. These manual treadmills are typically on an incline. The incline helps get things moving. If you just stand on it, you’ll roll backwards. Your running motion offsets the force pulling you backwards on the incline. The treadmill has some internal friction such that eventually your running force equals the internal friction and you basically stay running in the same place. But what would happen if there was no internal friction in the manual treadmill? The belt has friction so you can run on it, but there is no friction of the rollers and internal mechanisms. That is, once the belt started rolling, it would roll forever. If you were running on this kind of inclined treadmill, would you have to keep running faster and faster forever? Would you have to eventually run infinitely fast to keep yourself from going off the end of the treadmill?
All other considerations not-withstanding you’ll never exceed c.
It’s going to need some friction or you won’t be able to keep yourself on it. If the belt can move backwards too quickly, you won’t be able to push off on it and stay in place. It would be like trying to run up a hill covered in ice.
No.
There are treadmills like that a the gym - they are for sprinting.
You can’t run any faster on them then you can on flat ground.
Muscles don’t return energy to your body when something is making them move while they try to resist. They don’t reversibly convert between mechanical and chemical energy. In a purely mechanical sense, moving your leg back and forth against zero resistance doesn’t do any work, but in a physiological sense it does. For example, if you run on flat ground and a tailwind is matching your speed, you still expend a lot of effort.
There would be no friction but the belt would have momentum. I think that makes it very difficult to keep your feet moving at the same speed as the belt with a running gait resulting in a painful stumble. Maybe if you used a walk racing heel and toe gait you could maintain a steady speed but you wouldn’t accelerate past the speed of your feet anyway.
I guess I’m wondering about this more from the hypothetical physics aspect rather than the real person aspect. So imagine that a cyborg that can run unbelievably fast is put on an inclined treadmill that has no internal friction. When the cyborg is initially placed on the treadmill, the belt would start to roll backwards. The cyborg has been programmed to stay in the middle of the treadmill, so it starts moving its legs in a running motion to counter act the belt moving backwards. In this experiment, how fast would the cyborg need to run to stay in the middle of the treadmill?
Perhaps another way to think of this is to put a cyborg on a regular manual treadmill with normal internal friction. At some running speed, the cyborg can stay in the middle of the treadmill. But then if you improve the treadmill so the internal friction is reduced by half, how much faster would the cyborg run? If you again halved the friction, how much faster would the cyborg have to run? If you kept halving the friction over and over so that the internal friction approached zero, what running speed would the cyborg approach?
Actually human feet and legs do re-absorb a significant amount of energy; they are built to be springy. It’s one reason why humans have high endurance, and why a prosthetic like an old-fashioned rigid peg-leg works much worse than a natural foot. It doesn’t get transformed back to chemical energy but energy does get re-absorbed and re-used.
That said, entropy applies and the human foot is no more a perpetual motion engine than any other spring. It just works more efficiently than it would if it didn’t re-absorb energy.
You could stay on the treadmill for as long as you were able to maintain a steady acceleration, but that needed acceleration would be extremely high. First, take the acceleration that you’d have if you just stood “still” on the treadmill: That’s g times the sine of the angle that the treadmill is tilted at, which, for most reasonable treadmill inclinations, would be manageably small… but then, to stay on the treadmill and not just slide off, you’d need to multiply that by the ratio of your mass to the belt’s mass, and that ratio is going to be huge, somewhere in the triple-digit range.
In any event, there’s a limit to how long any physical system can maintain any steady acceleration, and it wouldn’t be very long.
Well, if you can imagine no internal friction, why not just imagine a human that can run unbelievably fast? Regardless, what ever it is that “can run unbelievably fast”, it will reach that unbelievable limit very quickly indeed.
There will be a limit - there won’t be an " infinitely fast".
Yeah, continuous acceleration adds up surprisingly quickly, so whatever limits exist will be reached relatively quickly. In this case, how fast a human can make their legs move, so the limit will be reached quickly indeed.
It would take about a year for a spacecraft to reach the edge of light speed with a continuous 1g acceleration in space, which is a close to zero friction environment. Which is nowhere near “infinite” of course. And assumes you somehow had unlimited fuel.
Point is that yes, eventually you’ll reach a limit, even with something a lot better at accelerating than a human.
One could also argue that the treadmill would accelerate faster than the equivalent of 1g.
Would it make a difference if you put the treadmill on a plane?
Yeah, but “a year to lightspeed at 1g” was the example I knew off the top of my head.
I guessed it would take 15 posts. Not bad.
It’s FQ. Couldn’t do it much earlier.
Do you want the treadmill on the plane, or under it?
In the aisle, blocking access to the bathrooms.
With zero internal friction you may as well make a comparison of a Bugatti on an inclined sheet of ice. No matter how fast the Bugatti can accelerate the speed of its tires, it’s just going to slide off the sheet of ice just as fast as a Model-T sitting idle.