Long rod question

mangobreeder said:
V = s0 / at

S = s0 + 1/2 (v0 + v)t

S = s0 + v0t + 1/2 at^2

V^2 = V0 ^2 + 2aD2

S = S0 + VT - 1/2at^"

where...

v is the body's initial velocity
s is the body's initial position

and its current state is described by:

v the velocity at the end of the interval
s the position at the end of the interval (displacement)
D the time interval between the initial and current states
a the constant acceleration, or in the case of bodies moving under the influence of gravity, g.
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You can't use simple A-level physics to answer this. The rod would compress as it moves.
 
right for the rod:

assuming the rod is made out of a normal material that conforms to all usual physical laws

as you pull the rod the force you apply creates tension in the rod as you are accelerating the end the bit next to the end also needs to be accelerated for the rod to stay in one piece. this tension is eefectively the force you put on the end of the rod divided by the cross sectional area to give a tensile stress. the tensile stress will propogate down the rod. the speed of the wave will depend on the material but since it is a longitudinal pressure wave it will be the same as the speed of sound for that material.

so for a steel rod the wave speed would be ~4500m/s so for a 10 mile long rod it would take ~3.5s.

however this means that the rod is stretching.

to answer the OPs question if the rod was infinately stiff so couldn't stretch (ie infinite bulk modulus) then the speed of sound for that material would be infinite (the speed of sound being the square root of the bulk modulus over the density) so the whole thing would move at once with no delay.

for the plane:

the plane requires air speed over its wings to create lift. no air speed, no lift, no take off. however the air just above the moving belt would be dragged along with the belt as part of the fluid boundary layer so it may be possible to create enough air speed using just the belt with the plane not moving relative the the rest of the world to create enough lift to take off but ass soon as it moved out of the boundary layer it would lose lift and drop.

for the plane to properly take off it would need to be moving fast enough relative to the aire away from the belt (and hence the ground assuming there is no freak hurricane or the like) it could probably still do this as mentioned above the jet engines drive the plane forward through thrust not powering the wheels, hence the wheel speed is not relevent to flight.
 
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atpbx said:
The problem with the aeroplane question is that in most cases it is badly or incorrectly worded, therefore allowing people to come to seemingly correct answers.

A plane cannot fly without airspeed, it doesnt matter where the airspeed comes from, whether its a high wind or the plane being pushed or pulled through the air (Propeller powered planes dont fly because the prop pushes air over the wings which ever loon said that in this thread).
Thats all that matters in the question, not friction, not wheel bearings, air MUST travel over the wings to generate lift, thats all people need to worry about.

(N.B we are not talking about rockets either, with no wings, that isnt the question)
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oh god, i hope your just confirming something and we dont have to spend ages converting you like the others ?

air does travel over the wings in the treadmill situation.
 
arknor said:
what if the plane had ski's instead of wheels :D
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it'd depend how big the skis were and what the friction between the skis and the treadmill was like, but I imagine the plane would still take off...

Just as I imagine I could ski uphill on tarmac if I had a jet engine strapped to my back!
 
this is really silly now. people who think the plane wont take off please read the thread

theres idiots like this on my engineering course and it really peeves me off that they do better than me in maths exams and stuff when they cant understand basic things like this :p
 
atleast people sort of understood that. theres a total failure of basic physics for the rest of the thread

i still dont know how on earth people think a treadmill magically stops the plane moving forwards
 
If they have no understanding of how a plane actually works? maybe they think the massive jet engines somehow power the wheels and it magically just keeps going once it's in the air or something?

I don't understand it either?

usually it's just a case of people misunderstanding the question and thinking that the treadmill somehow makes a plane stand still relative to an object that isn't on the treadmill.
 
How this thread hasn't been locked I don't know.

But seeing as we have two topics going on in this thread, how about I throw a spanner in the works by asking this question.

If you take a sandwich and cut it in half do you end up with two sandwiches? :confused:






Taxi :D
 
Rebelius said:
usually it's just a case of people misunderstanding the question and thinking that the treadmill somehow makes a plane stand still relative to an object that isn't on the treadmill.
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how many times have we explained this though :p

i must have mentioned it about 10 times myself using rollerblades


then they ignore it completly and come back saying but it needs air. it needs aiiiir !! arghh it neeeds air !!



atleast the sandwhich thing doesnt really have a proper answer:p
 
if it started with 2 pieces of bread, it will always be one sandwich in my eyes. If I ever get those double packs from the shop which are 4 triangular sandwiches, people always call me greedy, it's still only 2 sandwiches!
 
Well I'll define a sandwich as "two (or more) slices of bread with a filling between them." By that definition, half a sandwich is also a sandwich.

So both answers are correct ;)
 
Rebelius said:
it'd depend how big the skis were and what the friction between the skis and the treadmill was like, but I imagine the plane would still take off...

Just as I imagine I could ski uphill on tarmac if I had a jet engine strapped to my back!
Click to expand...

10ft x 2ft ski's with a 5inch thick rubber coating
 
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