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Help with maths (maybe physics)

sprouts-car - 9/1/10 at 12:04 AM

maths problem

Hope this challenges someone!

austin man - 9/1/10 at 12:12 AM

depends whether he was running backwards or forwards ? and which end he was holding at the time

liam.mccaffrey - 9/1/10 at 12:36 AM

is it a relativity question

if c is speed of light then he is traveling at 1.83 the speed of light

MikeR - 9/1/10 at 12:39 AM

the room is 5 feet deep, 10 feet tall ....... how wide is it? Who says he's holding the pole end on? couldn't he hold the middle and have it going from his left to his right?

(thinking laterally after a bit of cider)

jimgiblett - 9/1/10 at 12:50 AM

Insufficient information.

He could be carrying the pole vertically in which case all three are possibilities.

The man closing the door could be inside or outside the room.

Confused but excited. - 9/1/10 at 12:54 AM

The room is a Tardis.
They are both Time Lords.
Sorted.

craig1410 - 9/1/10 at 01:23 AM

This sounds like a relativity question. Not my area of expertise but I'll have a go...

It says he is running in direction PQ at sqrt(3)/2 times c (assuming c is speed of light). Which is approximately 1.732/2 * c or 0.866 c. (Not 1.83 as stated by Liam)

It says the room is 10 ft long and the Q end of the pole is hitting the wall as the door is closed and the athlete is holding end P.

Using the Lorentz transformation (http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/tdil.html) The length would contract to 0.5 of the original length at Sqrt(3)/2 * c so the pole would be 10 ft long and would appear to fit in the room.

However, from the athlete's frame of reference the room is moving towards him at the above speed and thus it will experience length contraction and will appear to be only 5ft long.

So, the athlete will be outside the room when the pole hits the wall.

HOWEVER, the shock of the impact cannot travel faster than light down the pole so it may be possible that the shock won't arrive at P until some time later by which time the athlete may actually be inside the room.

Okay my head just exploded, I need to go clean up the mess...

Anywhere close???

Craig.

liam.mccaffrey - 9/1/10 at 01:39 AM

quote:
Originally posted by craig1410
It says he is running in direction PQ at sqrt(3)/2 times c (assuming c is speed of light). Which is approximately 1.732/2 * c or 0.866 c. (Not 1.83 as stated by Liam)

Quite right my bad, I use sqrt(3)/2 every day. Schoolboy error by me.

This has to be a relativity question though with the speeds quoted

[Edited on 9/1/10 by liam.mccaffrey]

ReMan - 9/1/10 at 02:04 AM

Speed bit is irrelevant?
And the 10ft room could be the height so allso irrelevant if its 50ft wide?
Too many variables I say (tired)

RK - 9/1/10 at 03:05 AM

Anybody holding the end of his P will look silly if seen by anybody. He will be more likely to be seen outside the room, I would think.

Richard Quinn - 9/1/10 at 08:23 AM

Athletes... speed of light... Time for some performance enhancing drug testing!

matt_gsxr - 9/1/10 at 10:04 AM

You need to draw the space-time diagram (as they say). Try this for help
caltech_link

The "barn-ladder" paradox is very similar to your problem and you can search on that.

Isn't it interesting about the fact that this is one of the more difficult past exam questions and it is in imperial units. And they say exams are not getting easier.

Matt

02GF74 - 9/1/10 at 12:41 PM

this is what I think, given that I've not thunk too much about it.

he is outside the room holding pole at one end and pole is upright.

he allows the far end to fall daon under gravity until it fits under the door and starts running.

the lower end now is moving faster than the far end and this causes the pole to be raised so he ends up insdie the room with the pole almost vertical, and he fits insdie.the room. the room can be lessthan 20 ft high.

if you have ever try to balance a broom on its end, you'll know what I mean.

ReMan - 9/1/10 at 01:40 PM

quote:
Originally posted by 02GF74
this is what I think, given that I've not thunk too much about it.

he is outside the room holding pole at one end and pole is upright.

he allows the far end to fall daon under gravity until it fits under the door and starts running.

the lower end now is moving faster than the far end and this causes the pole to be raised so he ends up insdie the room with the pole almost vertical, and he fits insdie.the room. the room can be lessthan 20 ft high.

if you have ever try to balance a broom on its end, you'll know what I mean.

Thats my sort of thinking , too many complications/ red herrings, wtf has closing the door got to do with it

bigpig - 9/1/10 at 02:33 PM

There is an industrial wood chipper in the middle of the room

Bluemoon - 9/1/10 at 02:36 PM

It's a classic physics degree level question, not worked it out but you probably can get the 20ft pole into a 5ft space and close the door if you do it fast enough.. If you don't get why it's because we are thinking in terms of classical physics and you probably don't need to worry about it..

Dan

quote:
Originally posted by ReMan

quote:
Originally posted by 02GF74
this is what I think, given that I've not thunk too much about it.

he is outside the room holding pole at one end and pole is upright.

he allows the far end to fall daon under gravity until it fits under the door and starts running.

the lower end now is moving faster than the far end and this causes the pole to be raised so he ends up insdie the room with the pole almost vertical, and he fits insdie.the room. the room can be lessthan 20 ft high.

if you have ever try to balance a broom on its end, you'll know what I mean.

Thats my sort of thinking , too many complications/ red herrings, wtf has closing the door got to do with it

davidwag - 9/1/10 at 04:30 PM

What if the window was open?

David

craig1410 - 9/1/10 at 05:35 PM

quote:
Originally posted by ReMan

quote:
Originally posted by 02GF74
this is what I think, given that I've not thunk too much about it.

he is outside the room holding pole at one end and pole is upright.

he allows the far end to fall daon under gravity until it fits under the door and starts running.

the lower end now is moving faster than the far end and this causes the pole to be raised so he ends up insdie the room with the pole almost vertical, and he fits insdie.the room. the room can be lessthan 20 ft high.

if you have ever try to balance a broom on its end, you'll know what I mean.

Thats my sort of thinking , too many complications/ red herrings, wtf has closing the door got to do with it

You are trying to think of this in terms of a "trick question" but it is more likely that this is from an actual physics past paper or something and is a serious question. As I mentioned earlier, it defines the direction of the pole as PQ which is the same direction as the direction of travel so you can forget about balancing the pole like a broom shaft etc as has been suggested above. This is a relativistic physics question not a newtonian physics question.

I'll see if I can remember how to do space-time diagrams after dinner if nobody beats me to it. As I recall, space is usually represented in one dimension only (usually the x direction which is the same as PQ in the question) and time is represented in the y direction.

Standing still is represented as a vertical line (ie. time advances but space is static) and infinite velocity is represented by a horizontal line (space advances but time stands still). I think the speed of light is represented by a 45 degree line to show that space and time are advancing together and lesser speeds are represented by angles between 45 degrees and vertical.

I'll see if I can sketch this after dinner.
Craig.

[Edited on 9/1/2010 by craig1410]

craig1410 - 9/1/10 at 08:03 PM

Okay, here's what I've come up with. Sorry it's a bit rough but this is my first time using my little Wacom Bamboo graphics tablet for sketches. Takes a bit of getting used to and it's not really designed for this sort of thing...

Space Time Diagram

Anyway, some explanation of the diagram:

P and Q are the ends of the pole
W is the event where the Q end of the pole hits the wall. The door and wall are stationary hence they are vertical lines 10 ft apart.

Firstly this diagram is drawn in the frame of reference of the guy who closes the door of the room. Due to length contraction he will see the pole as being only half its length as described in my other post. This is why he can close the door when it enters the room.

However, in the athlete's frame of reference the pole is actually 20 ft long so point L indicates the position of the P end of the pole when the Q end strikes the wall in the frame of reference of the athlete. Hence he thinks that P is outside the room at impact. By the way, the room appears to the athlete to be only 5ft long due to the same length contraction effect but from his frame of reference this time.

But, the shock of the impact cannot travel down the pole any faster than the speed of light. Line WS shows the 45 degree line which represents the movement of the shock of impact IF it could travel at light speed. As you can see it does not reach the P end of the pole until it is well inside the room. In reality the shock would travel much slower by which time P would be almost at the wall.

If this turns out to be a trick question then I won't be happy...

[Edited on 9/1/2010 by craig1410]

Ninehigh - 9/1/10 at 09:28 PM

He won't be seen, he's in the room alone with the door closed.

Toltec - 9/1/10 at 10:26 PM

quote:
Originally posted by craig1410In reality the shock would travel much slower by which time P would be almost at the wall.

He may just notice the gamma radiation a little earlier though.

craig1410 - 10/1/10 at 01:50 PM

quote:
Originally posted by Toltec

quote:
Originally posted by craig1410In reality the shock would travel much slower by which time P would be almost at the wall.

He may just notice the gamma radiation a little earlier though.

Perhaps but even gamma can't travel faster than light.