Something amazing to tell you concerning physics and motion

[Jenson71]

This blows my mind.

Okay, say you have two ball bearings. You hold one in your hand and drop it. The other you put in a gun, point it straight forward, as level as the one in your hand, and pull the trigger, sending it hundreds of yards.

Which one lands first?

The one dropped in your hand right? RIGHT!?!?

No, actually they both hit the ground at the same time.

This is because the vertical component of motion is the same for both objects. They both fall vertically the same distance at about 10 meters per second squared (gravity, actually more like 9.8).

But Jenson, Jenson! What about the horizontal component of the gun-fired ball bearing? Actually, when air resistance is small enough to ignore as it is in this case (being that the bearings are exactly alike), the horizontal and vertical components of a projectile's velocity are completely independent of one another.

And, in this experiment, the gun-fired bearing is constantly falling from the moment it is fired. Yes, it looks like it is holding up in a straight line, but, it's actually falling and it's just hard to see with our eyes. And again, it is falling at exactly the same speed as the ball bearing you released in your hand -- the speed of gravity.

Post more cool science things in this thread.

I think I will later post Aristotle vs. Galileo and gravity, for a little history spin on science.

[MagicHef]

Originally Posted by cdcox

Force of jets - rolling resistance = large positive number

(large positive number) / (mass of jet) = acceleration

Lets say after 1 second, the jet is moving at 1 mph.

Jet speed 1 mph and gaining. Wheel speed 1 mph. Treadmill speed = 0.

Now start your treadmill. Run it at 100 mph.

Jet speed 1 mph and gaining. Wheel speed 101 mph. Treadmill speed = 100 mph.

Double the speed of the tread mill, same thing. Meanwhile, the jet just keeps on picking up speed relative to the ground.

The tread mill is just making the jet wheel free spin. The force of the engines cannot practically be overcome by spinning the wheels faster. Just like you can't break the rope by spinning the treadmill faster under the shopping cart. You just can't generate the force.

Thank you for including that. I agree completely. The problem is that the scenario is in no way practical.

[cdcox]

Originally Posted by orange

Let's not. The jet NEVER MOVES.

Where is the force coming from that keeps it from accelerating?

[MagicHef]

Originally Posted by Baby Lee

I think we figured that out long ago, when cdcox pointed out the ambiguity I applauded.

You view the hypothetical as inviolable, the way you read the wording the airplane CANNOT be allowed to move forward or the conveyor is failing in it's [ambiguously] stated mission. If a plane can't move forward it can't take off. And if it takes wheels with Herculean rolling resistance sufficient to counteract the thrust of 4 jumbo jet engines so be it.

However, hypotheticals generally assume [unless stated otherwise] negligable or no friction [rolling resistance]. And in that case the interactions of the wheels and the conveyor are akin to those of molecules flowing under a flying craft or in the water or ice under skids or pontoons on a thusly equipped craft, and they are irrelevant in the dominant force of forward thrust by the engines.

For an assumption to be valid, it should in no way change the outcome.

[cdcox]

Originally Posted by MagicHef

Thank you for including that. I agree completely. The problem is that the scenario is in no way practical.

By practical, I mean redesigning the wheel bearings to have extra friction or running the wheels so fast the materials fail, the wheel seizes, etc. I don't think any of that was intended in the original puzzler.

[MagicHef]

Originally Posted by cdcox

By practical, I mean redesigning the wheel bearings to have extra friction or running the wheels so fast the materials fail, the wheel seizes, etc. I don't think any of that was intended in the original puzzler.

I think the problem is that the conditions laid out in the original situation are contradictory and inherently impossible. Discussing the implications and practical outcomes of an impossible situation leads to discussions such as this one (Don't get me wrong, I've enjoyed every minute of it). Your points essentially prove that the situation is not possible, not that a situation like this would result in the plane taking off. For now, I have to go to a meeting, so I'll be gone for a little bit. Do not mistake my silence for agreement. I will show everyone the errors of their ways when I return.

[Baby Lee]

Originally Posted by MagicHef

For an assumption to be valid, it should in no way change the outcome.

Actually for an assumption to be valid it should correlate to empirical fact. And empirical fact weighs heavily to rolling resistance being non-existent wrt jet thrust. But this hypothetical ambiguously suggests an arrangement that demands factors counter to empirical fact [ie, the plane must not move forward so rolling resistance must be equal and opposite jet force].

[orange]

Originally Posted by cdcox

Where is the force coming from that keeps it from accelerating?

Not a perfect illustration but something to work with.


Let's say there is a point n where the vector N meets the circle. Let's add that this is the only point where the wheel meets the treadmill.

When the engines exert thrust (in direction -F) the plane tries to move forward F. Friction resists wheel point n moving. We are assuming this friction is high enough to stop n's motion, causing rolling and preventing sliding.

This happens because wheel point n pushes (i.e. exerts force) against treadmill point n. The resistance pushes back with an equal and opposite force, stopping the wheel from sliding. The energy from this causes the wheel to rotate forward (i.e. roll).

The force from the wheel against the treadmill also pushes the treadmill, causing it to rotate backward relative to the wheel.

These forces act equally and simultaneously. All the energy involved is from the engine, transmitted through the suspension and wheels.

[Hydrae]

Originally Posted by cdcox

Where is the force coming from that keeps it from accelerating?

Can the plane move forward, on the ground, without the wheels spinning at an equivalent speed? If so, then we can take off and I assume we are leaving long black marks behind us. If not then we do not move forward.

[orange]

Originally Posted by MagicHef

I think the problem is that the conditions laid out in the original situation are contradictory and inherently impossible.

I disagree. These aren't arbitrary wheels stuck on random planes. The wheels and transmissions are designed to carry their plane at full thrust. Spinning the ground under the plane isn't going to make the engines any more powerful.

And again, the treadmill doesn't have to be perfect. It only has to (1) have enough friction to require the wheels to roll; and (2) have equal or less resistance to spinning than the resistance to the plane moving forward (from air etc.).

Even in your motorized treadmill scenario, if the treadmill can spin as fast or faster than the plane's wheels spin at full thrust along the ground, the plane is going nowhere.

Now that I think of it, in the Mythbusters experiment, their problem was a fixed treadmill moving at a fixed rate. The treadmill wasn't allowed to slip forward, forcing all the slipping due to imperfect friction to be by the plane.

[Jenson71]

Originally Posted by Kyle DeLexus

Congrats on your middle school graduation! Be sure to get a Transam and have The Stroke playing when you pull into the parking lot on your first day of high school. It would also help your popularity if you wear a denim jacket and REO Speedwagon shirt to match.

Baaack to skuuuwel, baaaack to skuuuwel, to prove to daddy I'm not a foooool.

[MagicHef]

Originally Posted by orange

I disagree. These aren't arbitrary wheels stuck on random planes. The wheels and transmissions are designed to carry their plane at full thrust. Spinning the ground under the plane isn't going to make the engines any more powerful.

And again, the treadmill doesn't have to be perfect. It only has to (1) have enough friction to require the wheels to roll; and (2) have equal or less resistance to spinning than the resistance to the plane moving forward (from air etc.).

Even in your motorized treadmill scenario, if the treadmill can spin as fast or faster than the plane's wheels spin at full thrust along the ground, the plane is going nowhere.

Now that I think of it, in the Mythbusters experiment, their problem was a fixed treadmill moving at a fixed rate. The treadmill wasn't allowed to slip forward, forcing all the slipping due to imperfect friction to be by the plane.

Even if it has less resistance than the plane moving forward through the air, the plane will still move forward. If you have two resistors in parallel, current will still go through whichever has the higher resistance, just not as much as will go through the resistor with less resistance. The only way for the treadmill to exactly match the wheelspeed is for it to be controlled to do such. However, the wheel is not able to move. The only way for the wheel to start moving is if the plane starts moving, which is impossible. As I stated before, both the wheel and the treadmill would need to instantaneously and simultaneously go from zero velocity to infinite velocity (Actually, now that I think about it, maybe it isn't infinite velocity, but some specific and very high velocity).

[Simply Red]

[MagicHef]

Awesome movie.

[Frosty]

Originally Posted by Baby Lee

You view the hypothetical as inviolable, the way you read the wording the airplane CANNOT be allowed to move forward or the conveyor is failing in it's [ambiguously] stated mission. If a plane can't move forward it can't take off. And if it takes wheels with Herculean rolling resistance sufficient to counteract the thrust of 4 jumbo jet engines so be it.

However, hypotheticals generally assume [unless stated otherwise] negligible or no friction [rolling resistance]. And in that case the interactions of the wheels and the conveyor are akin to those of molecules flowing under a flying craft or in the water or ice under skids or pontoons on a thusly equipped craft, and they are irrelevant in the dominant force of forward thrust by the engines.

Exactly. The way the question was worded originally would result in a take-off. Then, during the thread, all these conditions kept getting added in that made it ridiculous (magic tires and bearings, materials that can somehow add incredible horizontal forces through friction, etc).

[MagicHef]

Originally Posted by Baby Lee

Actually for an assumption to be valid it should correlate to empirical fact. And empirical fact weighs heavily to rolling resistance being non-existent wrt jet thrust. But this hypothetical ambiguously suggests an arrangement that demands factors counter to empirical fact [ie, the plane must not move forward so rolling resistance must be equal and opposite jet force].

Okay, maybe that's not the definition of a valid assumption, but it certainly is a sign of a good assumption. Perhaps the fact that an assumption that correlates to empirical fact changes the outcome of the situation so drastically should be a sign that this situation can't exist in reality.