00:01
Okay, we have a brass rod with a diameter of 2 .002 centimeters, and we have a steel ring with an inside diameter of 2 .000 centimeters.
00:17
We're also given the outside diameter of the steel, but that does not matter.
00:23
We're told our initial temperature is 20 degrees, and what we want to do is we want to change the temperature of both objects.
00:30
We're going to keep them at the same temperature all the time until the brass rod will fit through the steel ring.
00:40
Okay, so what's going to happen is as they are cooled, they are both going to contract.
00:48
And the brass is going to contract slightly more than the steel does because its coefficient of linear expansion is small, is larger than that.
01:01
For the steel.
01:03
So the brass will contract more than the steel does.
01:07
And so there will be a temperature where the inside diameter of the steel ring and the outside diameter of the brass rod will be the same.
01:24
So our formula for the final diameter after we do that contraction is the initial diameter plus the alpha d0 times delta t and we want the two like i said the two final diameters to be the same and this is just our standard handy -dandy formula for um what happens with length contraction just because we're talking about diameter doesn't mean anything it's still a length as far as what we're trying to do so we want the final diameter of the iron to equal the final diameter of the iron to equal the final diameter of the brass.
02:19
So there's the final diameter of the brass, and there's the final diameter of the steel, and that's equal to our final diameter, which has to be, like i said, the same for both of them.
02:39
Okay, so we know everything in this equation except for delta t.
02:45
So let's do some algebra and rearrange it.
03:01
So i'm going to bring the terms that don't involve the temperature over to one side of the equation and put the terms that do involve the temperature on the other side.
03:28
Okay, so there's an equation...