Regretfully from
the point of view of your room mate I have to agree with you. No matter what it may feel like
(I have run on both treadmills and the road) they are both exactly equivalent.
Think of it
like this.
First of all ignore the effects of air resistance (see later).
The two states are
basically two inertial frames – whether the road is moving under you (treadmill) or you are
moving over the road (normal case) the output of energy forma given speed is identical.
Remember that on the road you have to apply a force in the forward direction to get you
moving forwards while on the treadmill you have to apply a force ion the forward direction to
stop yourself being moved back and falling off the back of the treadmill.
If you simply
bounced up on the road you would land where you took off. Also if you bounced up on the
treadmill you would land on the same spot on the moving belt from which you took off
although this would be further "back" compared with the ground. This is because at the
moment of take off you had a velocity towards the back of the treadmill.
Now to
other effects.
The way in which you run on a treadmill might be different.
On the
treadmill there is no air moving past you so you get hot and also the air around you might
become "stale".
The only way in which the treadmill might be easier is that you do not
have to run through the air as you do on a road run. I have done a few half marathons and
the air resistance certainly makes a difference over those sorts of distances.