Size of cavity on expansion

1. Dec 7, 2011

sodaboy7

There's a metal plate with a circular hole/cavity in it. Consider its width negligible. Now the plate is uniformly heated. Textbook says that size of hole/cavity increases along with the dimensions of the plate. But my intuition says dimensions of cavity should increase and size of hole/cavity should decrease. Its just like the "expanding" metal plate is "pushing" the metal inwards the cavity/hole making it smaller. Need Explanation to this.

2. Dec 7, 2011

technician

I think you have to say the hole gets bigger. There is a standard school demonstration of expansion called a 'ball and ring'. You heat up the ball and, not surprisingly, it does not fit through the ring.
Now you heat up the ring and the ball goes through.
Metal tyres for cartwheels and metal rims for railway wheels are heated to make them expand to fit over the wheel. When they are cooled they tighten onto the wheel.

3. Dec 7, 2011

Stonebridge

Imagine a circular metal plate on which you have drawn a chalk circle about half way between the centre and the rim.
Heat the plate. Does the chalk circle expand or contract?
Now cut out a hole in the plate marked out by the chalk but with the chalk line just visible.
Heat the plate. Does the chalk circle expand? Does the hole?

4. Dec 7, 2011

rplatter

The metal on the edge of the hole expands. This causes the ring to expand.
Think of it like this. You have a bunch of metal molecules. Think of them like balls. These balls are placed in a ring and then super glued together. As the balls expand they have to move outwards. Away from the center because it's the only way they can expand and stay connected. Now on a disk with a hole in the center. If the Disk is large enough the circumferal expansion will be greater than the radial expansion. This can lead to the warping of the disk introducing a wave pattern into the plane of the disk. This is what happens in brake rotors when they get warped.

5. Dec 7, 2011

sodaboy7

Thank you, thats the explaination I needed.