[QUOTE=Hypno-Toad]
I think I should clarify an assumption of the OP. In my scenario, the treadmill is of the motorized type. Not one the user has to keep moving with his own effort. This is why I supposed that it is easier on the treadmill than the road. The legs aren’t really propelling the upper body. They’re simply counteracting the movement of the treadmill. And that movement is being powered by a motor.
To me, that’s a big difference. On the street, ALL of the energy involved is being supplied by my muscles. The motor is providing much of the energy for the treadmill.
[/QUOTE]
Put a dot on the treadmill. Regardless of whether it is moving on it’s own or you are propelling it, that dot will always move away from you (well, it will loop around and pass under you again, but that’s only because the treadmill is small - every time you pass it, you are a treadmill-circumference further away). Put a dot on the road, and you’ll get further away from it as you run, too.
If you apply no force on a self-propelled treadmill, then nothing happens. You stand still, and the dot stays beneath you. If you apply no force on an automatic treadmill, you move back with the treadmill but the dot stays beneath you. You essentially are not moving, and you expend the same amount of energy either way.
Now assume that you are running at a steady 5 mph, on a self-propelled treadmill. Your dot moves away from you at 5 mph. The force you are applying is enough to keep you going at 5 mph. You had to apply increasing force to get to that speed, and then a constant amount of force to maintain it.
The automatic treadmill is similar. You start it up, and it accelerates. Either you apply no force, and you get shot off the back of it like a bad cartoon, or you apply force to accelerate relative to the track of the treadmill, you reach a steady 5mph, and then apply a constant force to maintain that speed. Your dot moves away from you at 5mph, exactly as before.
I think, though, that you would actually exert less force on the automatic treadmill because you don’t have to overcome the friction of the track on the rollers; the motor would be taking care of that. It probably applies a little more than 5mph worth of force, the roller friction is applied, and the resultant is a 5mph track. But on a self-propelled treadmill, you’d have to add a little more force to deal with that opposing friction to maintain 5mph. I have no idea what the coefficient of friction is for a treadmill relative to its rollers. I don’t know how significant it is (presumably, the friction has been reduced as much as possible).