Relitivistic length contraction,solve a puzzle?

Question

suppose a very strong house measures 20m in length and a rod measures 25m.when rod moves at 70% the speed of light(.7c) so that its length shrinks to 18m and it would fit the in house and we could slam the door shut.but if we were on the rod and moving with it,the house would appear to move at .7c so that its length would shrink to 14m and rod wont fit in the house.
so will the rod fit in the house or not???

to answerer2,
assume that we will close the door (v.quickly)before the rod comes to rest while it is in the house so that when it comes to rest,the door is already closed.the house is strong enough so that it doesnt break with the subsequent collision and expansion of rod.

Answer 1

At that point they would be in the same frame of reference as their relative velocities would be zero, so the rod would not fit.

Nice try, though. :-)

Answer 2

Hmm... this sounds like one of Einstein's "thought experiments."

I suppose whether or not the rod fits in the house – while it's moving – depends on your frame of reference. If you're in the house, you'll see the entire rod inside before the leading end exits the other side. If you're on the rod, you'll see the lading end exit the house before the trailing end enters.

Of course, if the rod stops moving when it enters the house, then the conditions are no longer relativistic, and the answer is no.

Answer 3

This is the "Pole In Barn" paradox.

If you are in the frame of the barn, the guy in charge of slamming the door closed when the pole is inside, the order of events goes like this.

1. Front of pole enters barn.
2. Back of pole enters barn.
3. You slam the door closed.
4. Front of pole hits the back wall of the barn.
5. Shock wave travelling at speed of light reaches the end of the pole. Pole resumes original length with respect to the barn and bows upward or breaks.

If you are in the frame of the pole, the guy running it into the barn, then the order of events is like this:

1. Front of pole enters barn.
2. Front of pole hits back of barn.
3. Back of pole enters barn.
4. Door slams shut.
5. Shockwave reaches back of pole, pole resumes rest length with respect to the barn and bows upward or breaks.

The race in the latter frame occurs between the shockwave moving at c from the front of the pole (at the back of the barn) toward the back of the pole, and the passage of the back of the pole, still moving in at 0.7 c, through the barn door.

It works out. I did this one as one of my undergraduate seminars.