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.

[orange]

Nope. The force exerted by the jet on the treadmill and the force exerted by the treadmill on the jet are going to be exactly the same length - EQUAL AND OPPOSITE. You've just tossed out an example that assumes your final answer is right.

Once you make that adjustment, you then have to translate those forces into actual rotational velocity for the wheels and the treadmill. Since we are allowing for no sliding (as our starting point), you can set those velocities so that the "teeth per second" of both are equal and work backward to see the net forces.

[orange]

Originally Posted by prhom

Wow, I'm amazed that you guys are still arguing the plane on the treadmill. This is a classic physics test question that takes something that seems to complicate the problem (the treadmill) but is really just a distraction. Planes only fly based on AIRSPEED. Anything related to the groundspeed is irrelevant as to whether the plane will fly or not!! Besides, there would only be an extremely neglible force imparted to the treadmill by the plane's wheels. This would be from friction generated in the wheel bearings and rolling resistance in the tires. Bottom line the plane is going to fly no matter how fast or slow the treadmill is going.

It will never fly, it will never move forward, there will never be any air over the wings. Its airspeed starts and remains 0. That's why planes take off from a runway. They have to build up to a high groundspeed before they can ever dream about airspeed.

[prhom]

Originally Posted by orange

Nope. The force exerted by the jet on the treadmill and the force exerted by the treadmill on the jet are going to be exactly the same length - EQUAL AND OPPOSITE.

So you are arguing that the plane will not fly?

[prhom]

Originally Posted by orange

It will never fly, it will never move forward, there will never be any air over the wings. Its airspeed starts and remains 0. That's why planes take off from a runway. They have to build up to a high groundspeed before they can ever dream about airspeed.

Wait just a minute orange, pilots NEVER care about groundspeed! If you were to tie a model plane to a string in a very high wind it could fly even though it's not moving relative to the ground. You can't deny that would be true.

[headsnap]

Originally Posted by prhom

Wow, I'm amazed that you guys are still arguing the plane on the treadmill. This is a classic physics test question that takes something that seems to complicate the problem (the treadmill) but is really just a distraction. Planes only fly based on AIRSPEED. Anything related to the groundspeed is irrelevant as to whether the plane will fly or not!! Besides, there would only be an extremely neglible force imparted to the treadmill by the plane's wheels. This would be from friction generated in the wheel bearings and rolling resistance in the tires. Bottom line the plane is going to fly no matter how fast or slow the treadmill is going.

no, no, no, orange thinks the wheels are what makes a jet fly...


why else would it take bicycle makers to make the first airplane...

[orange]

Originally Posted by prhom

So you are arguing that the plane will not fly?

Originally Posted by prhom

Wait just a minute orange, pilots NEVER care about groundspeed! If you were to tie a model plane to a string in a very high wind it could fly even though it's not moving relative to the ground. You can't deny that would be true.

Yes.

When you're on the ground, yes. In this problem, the plane never acquires any airspeed - because it never moves from it's starting point. It actually never acquires any groundspeed either - but its wheels are spinning. All of the energy from that spinning is being transferred to the treadmill which is spinning under the plane.

Suppose we had an airplane that could take off on a windless day at 100 mph (liftoff airspeed is 100 mph). We are at an airport with an east-west runway that is 1 mile long. The wind is blowing 20 mph towards the west and the airplane takes off going east. The wind is blowing towards the aircraft which we call a headwind. Since we have defined a positive velocity to be in the direction of the aircraft's motion, a headwind is a negative velocity. While the plane is sitting still on the runway, it has a ground speed of 0 and an airspeed of 20 mph:

Airspeed = Ground Speed (0) - Wind Speed (-20) = 20 mph

The airplane starts its take off roll and has a constant acceleration a. From Newton's second law of motion, the ground speed V at any time t is:

V = a * t

and the distance d down the runway at any time is:

d = 1/2 * a * t^2

For a fixed length runway, this specifies the time to be used in the velocity equation. Let's assume that at 5000 feet down the runway, the velocity is 80 mph. Then the airspeed is given by

Airspeed = Ground Speed (80) - Wind Speed (-20) = 100 mph

and the airplane begins to fly. Now another pilot, with exactly the same airplane decides to take off to the west. The wind is now in the same direction as the motion and this is called a tailwind. The sign on the wind speed is now positive, not negative as with the headwind. The acceleration along the ground is the same, so at 5000 feet down the runway, the ground speed is again 80 mph. The airspeed is then given by:

Airspeed = Ground Speed (80) - Wind Speed (20) = 60 mph

This airplane doesn't have enough airspeed to fly. It runs off the end of the runway!

http://www.grc.nasa.gov/WWW/K-12/airplane/move.html

[headsnap]

Originally Posted by cdcox

Okay.

a new question:

Q: Orange's Smart Car is traveling 60mph southbound, my Nissan Aramada is traveling 60 mph northbound and we hit head on.

A: I am traveling 30mph northbound and orange is traveling to the morgue.

[headsnap]

Originally Posted by orange

Yes.

When you're on the ground, yes. In this problem, the plane never acquires any airspeed - because it never moves from it's starting point. It actually never acquires any groundspeed either - but its wheels are spinning. All of the energy from that spinning is being transferred to the treadmill which is spinning under the plane.

HOW????

[cdcox]

Originally Posted by orange

Nope. The force exerted by the jet on the treadmill and the force exerted by the treadmill on the jet are going to be exactly the same length - EQUAL AND OPPOSITE. You've just tossed out an example that assumes your final answer is right.

Once you make that adjustment, you then have to translate those forces into actual rotational velocity for the wheels and the treadmill. Since we are allowing for no sliding (as our starting point), you can set those velocities so that the "teeth per second" of both are equal and work backward to see the net forces.

Your equal and opposite forces between the gear and the bar are true, consider it another set of equal sized arrows between the two diagrams. I tossed out an example that showed that your statement of less resistance in the treadmill doesn't preclude my argument.

Say the teeth per second relative to each other is 10. You could get that by having the jet moving forward at 9 teeth per second relative to the ground and the bar moving backward at 1 tooth per second relative to the ground.

[Pitt Gorilla]

Physics 101. Good stuff.

[headsnap]

Originally Posted by Pitt Gorilla

Physics 101. Good stuff.

it's almost as bad as Econ 101 over in DC...

[prhom]

Originally Posted by orange

Yes.

When you're on the ground, yes. In this problem, the plane never acquires any airspeed - because it never moves from it's starting point. It actually never acquires any groundspeed either - but its wheels are spinning.

I don't think there's anyway I convince you otherwise unless I draw a force diagram for the landing gear. You're equal and opposite force comment tells me you are thinking of the the wheels as a fixed entity. In reality the equal and opposite forces acting on the wheel are a force couple. One force being the axle pushing forward from the center of the wheel. The other force is the friction force between the wheel and treadmill. All this is going to do is make the wheel spin. The only forces that can affect the plane are friction forces in the wheel bearings and rolling resistance. These would be too complicated to draw up and I just don't have the motivation to do it...yet.

[orange]

Originally Posted by cdcox

Your equal and opposite forces between the gear and the bar are true, consider it another set of equal sized arrows between the two diagrams. I tossed out an example that showed that your statement of less resistance in the treadmill doesn't preclude my argument.

Say the teeth per second relative to each other is 10. You could get that by having the jet moving forward at 9 teeth per second relative to the ground and the bar moving backward at 1 tooth per second relative to the ground.

That would require some resistance to cause the bar to move less rapidly than the jet. My free-spinning treadmill (bar) has no such resistance. It will move at 5 tps to match the jet's 5 tps.

[headsnap]

Originally Posted by orange

That would require some resistance to cause the bar to move less rapidly than the jet. My free-spinning treadmill (bar) has no such resistance. It will move at 5 tps to match the jet's 5 tps.

HOW IS THE JET PUSHING THE TREADMILL?

[orange]

Originally Posted by prhom

I don't think there's anyway I convince you otherwise unless I draw a force diagram for the landing gear. You're equal and opposite force comment tells me you are thinking of the the wheels as a fixed entity. In reality the equal and opposite forces acting on the wheel are a force couple. One force being the axle pushing forward from the center of the wheel. The other force is the friction force between the wheel and treadmill. All this is going to do is make the wheel spin. The only forces that can affect the plane are friction forces in the wheel bearings and rolling resistance. These would be too complicated to draw up and I just don't have the motivation to do it...yet.

The bolded statement is incorrect. The force at that friction point is going to make the treadmill spin equally and opposite.

I put up an illustration of this earlier:

Originally Posted by orange

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.

p.s. Did you catch my groundspeed during takeoff example above? It took a few minutes to find a good, simple one, but I don't want you to miss it. You'll continue to think that pilots never are concerned with groundspeed.