Thermal Expansion of copper sphere Problem

[acgold]

This one is giving me trouble because I don't know the final radius and I don't know how to find it.

1. A copper sphere of radius 2.000 cm is placed over a hole of radius 1.990 cm in an aluminum plate at 20 deg. C. At what common temperature will the sphere pass through the hole?
Ans. 747 degrees C

I'm assuming that finding the final radius is the whole point of this problem since once you know the radius the temperature is easy to calculate. Unfortunately I don't know how to find it

 

[AKG]

This one is giving me trouble because I don't know the final radius and I don't know how to find it.

1. A copper sphere of radius 2.000 cm is placed over a hole of radius 1.990 cm in an aluminum plate at 20 deg. C. At what common temperature will the sphere pass through the hole?
Ans. 747 degrees C

I'm assuming that finding the final radius is the whole point of this problem since once you know the radius the temperature is easy to calculate. Unfortunately I don't know how to find it

It falls through when the radii (of the hole and sphere) are equal. I'm guessing there's some formula like \Delta r = k_{copper}\Delta T. Well, it obviously can't be that simple. But you know the initial temperatures and sizes, some sort of constants or material properties for copper and aluminum, and you should be able to express the final size of the copper in terms of the aluminum, or vice versa. That gives you two unknowns (final size and final temperature), and two equations (one for copper one for aluminum), then solve.

 

[acgold]

Man I need to get some sleep or something. The answer was sitting right in front of me. I already had both equations all setup...all I need to do was solve for r and substitute it into the other equation.

Thanks