Treadmill Physics Questions (Similar to Airplane Question)

My body weight is *not* behind me. Nothing rolling me along.

Inertia is a measure of how resistant an object is to a change in velocity. The value of the initial velocity does not matter. You have the same inertia whether you are stationary or moving in a particular reference frame. Inertia is essentially the same as mass.

Momentum is mass x velocity. In an earth fixed reference frame you have no momentum when running on the treadmill. However in a reference frame fixed to the top surface of the treadmill belt, you have non-zero momentum. Running along the earth surface into a brick wall would hurt exactly the same as having the same brick wall fixed to the treadmill belt run into you.

Citizen Runner wrote:

Running along the earth surface into a brick wall would hurt exactly the same as having the same brick wall fixed to the treadmill belt run into you.

This sounds like a "Jackass" episode in the making.

you have momentum on a treadmill, just the same as outside. the only thing different is the lack of wind resistance (which you could recreate with a fan). Everything else is the same.

The airplane problem has nothing to do with inertia or momentum!! It is all fluid dynamics. If you were to place an airplane in a large wind tunnel, and the wind in the tunnel were to flow at the critical velocity where lift equals weight, the plane would rise off the ground.

Just like this problem, running on a treadmill is easier because of a lack of wind resistance. On a treadmill, only non-conservative forces are attributed to energy expenditure, namely friction in the body and the energy to pump your blood at an elevated rate.

The reason treadmill running may seem hard is because of the psychological aspect. Boredom makes you think more about pain than running on a trail with constant distractions.

When you pushoff the ground it is solid.

When you pushoff the treadmill it is moving away from you.

When you are running on the treadmill, whenever you have both feet off the belt it is still moving in the opposite direction.

If you bounce on the spot with the belt running it will still record that you are moving forward.

Fairly basic really. wrote:

When you pushoff the ground it is solid.

When you pushoff the treadmill it is moving away from you.

When you are running on the treadmill, whenever you have both feet off the belt it is still moving in the opposite direction.

If you bounce on the spot with the belt running it will still record that you are moving forward.

I'm not quite sure what you are getting at, but if your feet are off the treadmill then it doesn't matter what the treadmill belt is doing. You say the ground is "solid" but the belt is moving away from you, yet in reality the ground is moving at around 1000mph (Earth's rotation). Since we aren't accelerating we don't feel it.

Think of it as if you were standing on a train and you run from the front of the train to the back of the train (or back to front). It doesn't matter how fast the train is going, it could be 10mph or 100mph as long as it is a constant speed, the physics between you and the train floor will be the same. The floor of the train is no different from a treadmill belt.

No momentum since your body is not moving foward. You could have minimum and momentary momentum in your foot and lower leg during the short time it moves forward.

Relative to each running surface (ground or belt), your inertia is the same in both places. The belt moving backwards, it takes work to maintain your inertia of staying put.

Conundrum wrote:

No momentum since your body is not moving foward. You could have minimum and momentary momentum in your foot and lower leg during the short time it moves forward.

wrong, your body is moving relative to the belt and that is all that matters

The belt has inertia not you. If you are sliding a blocon the tread mill right behind you and the belt suddenly stops, the block has no inertia and will not move forward. It stops.

Uncle Rico wrote:

Conundrum wrote:

No momentum since your body is not moving foward. You could have minimum and momentary momentum in your foot and lower leg during the short time it moves forward.

wrong, your body is moving relative to the belt and that is all that matters

This just proves that people weren't meant to run on a treadmill, since it's contrary to the laws of physics.

Conundrum wrote:

If you are sliding a block on the tread mill right behind you and the belt suddenly stops, the block has no inertia and will not move forward. It stops.

The block stops (in an earth-fixed reference frame) because it was never moving (in an earth-fixed reference frame) and there is no longer any force being applied to it when the belt stops (assuming you stop pulling at the same instant the belt stops). That's what inertia does for you.

Everything is relative. Relative to the belt, you have "forward" momentum. The ONLY difference at a constant speed is there is no wind resistance on the treadmill. But this is a pretty big difference.

Consider this: I have a hard time breaking 20 minutes for a 5k on a treadmill (I am a 5'10" 182-lb sprinter). When I found out on letsrun that people consider 20 minutes a mere jog, I felt like an idiot, even though I don't train for the 5k distance. So I tried a 5k outdoors, on a track, wearing flats.

I finished relatively easily in 18 minutes! I could have gone substantially faster.

So I returned to the treadmill and found that I got fatigued running at 10 mph! Thinking that there was something wrong with the treadmill, I tried 2 others, different brands entirely, and got the same result.

Anybody else experience something similar?

Everything is relative to your frame of reference. You have inertia relative to the belt. Case in point: if the belt were to suddenly stop (not gradually slow), you would fall forward.

http://en.wikipedia.org/wiki/Inertia#Inertial_frames

"In a location such as a steadily moving railway carriage, a dropped ball (as seen by an observer in the carriage) would behave as it would if it were dropped in a stationary carriage. The ball would simply descend vertically. It is possible to ignore the motion of the carriage by defining it as an inertial frame. In a moving but non-accelerating frame, the ball behaves normally because the train and its contents continue to move at a constant velocity. Before being dropped, the ball was traveling with the train at the same speed, and the ball's inertia ensured that it continued to move in the same speed and direction as the train, even while dropping. Note that, here, it is inertia which ensured that, not its mass.

In an inertial frame all the observers in uniform (non-accelerating) motion will observe the same laws of physics. However observers in another inertial frame can make a simple, and intuitively obvious, transformation (the Galilean transformation), to convert their observations. Thus, an observer from outside the moving train could deduce that the dropped ball within the carriage fell vertically downwards.

However, in frames which are experiencing acceleration (non-inertial frames), objects appear to be affected by fictitious forces. For example, if the railway carriage were accelerating, the ball would not fall vertically within the carriage but would appear to an observer to be deflected because the carriage and the ball would not be traveling at the same speed while the ball was falling. Other examples of fictitious forces occur in rotating frames such as the earth. For example, a missile at the North Pole could be aimed directly at a location and fired southwards. An observer would see it apparently deflected away from its target by a force (the Coriolis force) but in reality the southerly target has moved because earth has rotated while the missile is in flight. Because the earth is rotating, a useful inertial frame of reference is defined by the stars, which only move imperceptibly during most observations.The law of inertia is also known as Isaac Newton's first law of motion.

In summary, the principle of inertia is intimately linked with the principles of conservation of energy and conservation of momentum."

Of course everything on Earth in absolute terms has momentum whether moving relative to the earth's frame of reference or not.The OP is refering to momentum in terms of the Earth's frame of reference. He wasn't looking for anamswer that everything has momentum.

Citizen Runner wrote:

Conundrum wrote:

If you are sliding a block on the tread mill right behind you and the belt suddenly stops, the block has no inertia and will not move forward. It stops.

The block stops (in an earth-fixed reference frame) because it was never moving (in an earth-fixed reference frame) and there is no longer any force being applied to it when the belt stops (assuming you stop pulling at the same instant the belt stops). That's what inertia does for you.

Of course everything on Earth in absolute terms has momentum whether moving relative to the earth's frame of reference or not.The OP is refering to momentum in terms of the Earth's frame of reference. He wasn't looking for anamswer that everything has momentum.

Citizen Runner wrote:

Conundrum wrote:

If you are sliding a block on the tread mill right behind you and the belt suddenly stops, the block has no inertia and will not move forward. It stops.

The block stops (in an earth-fixed reference frame) because it was never moving (in an earth-fixed reference frame) and there is no longer any force being applied to it when the belt stops (assuming you stop pulling at the same instant the belt stops). That's what inertia does for you.

The OP was trying to explain a difference in feel between running on the treadmill and running on the road in terms of momentum. This is incorrect because the only relevant measure of momentum is due to the relative velocity between the runner and the running surface.

There are typically differences between treadmill running and road running including still air on the treadmill, perhaps a less stable running surface, the psychological effect of running in close proximity to the treadmill console etc, poorly calibrated treadmill speed, and such and these can affect running form, but he's got the physics wrong.