Someone recently gave me the following simple physics problem: an ice cube is floating in a glass of water. The ice cube then melts. Does the water level in the glass go up, go down, or stay the same?
My intuitive guess would be that since the ice and the water in the glass have the same density, the water level stays the same. I’m sort of confused now, however. Is this problem about weight or density? I’m trying to connect this problem to Archimedes and his bathtub test to determine the composition of a crown, but I’m not seeing it. Is my guess correct? How would the problem work if, instead of water, the ice cube was floating on top of some other liquid, or if the cube itself was not composed of water?
The water level stays the same. The floating ice cube displaces it’s weight in water. So if it weighs X grams it displaces the volume that X grams of water would displace. When it melts it becomes X grams of water and displaces it’s volume which is equal to X grams of water.
Does that make sense? Is it correct? I’ve succeeded only in confusing myself, but I’m sticking woth this answer until someone else comes up with a better one.
Actually, ice is less dense; that’s why it floats.
But yes, the water level will stay the same.
E.g., You have 10 cc (cubic centimeters) of water, which has a mass (“weighs”) of 10 grams. You also have a 1 gram ice cube. It will have a volume of about 1.1 cc.
Placing the ice cube in the water, it will displace 1 gram of water to keep it buoyed. 1 gram of water = 1 cc, so the water level will go up to where 11 cc of water would’ve gone. Additionally, 0.1 cc of the ice cube will be above the water’s surface.
When the ice melts, you now simply have 11 grams of water with a volume of 11 cc.