Understanding Ice Melting and Water Level

Let's analyze what happens to the water level when a piece of ice floating in a glass of water melts completely.

When an object floats in a fluid, it displaces a volume of fluid that has a weight equal to the weight of the floating object. This is based on Archimedes' Principle.

Why Ice Floats in Water

• Ice is less dense than liquid water. This is why it floats.
• When ice floats, a portion of the ice is submerged in the water, and a portion is above the water surface.
• The weight of the ice block is supported by the buoyant force from the displaced water. According to Archimedes' principle, the buoyant force is equal to the weight of the fluid displaced. Therefore, the weight of the ice is equal to the weight of the water it displaces.

What Happens When Ice Melts?

• When the ice melts, it turns into liquid water.
• The mass of the ice remains the same as the mass of the water it becomes. Mass is conserved during melting.
• Since mass is conserved, the weight of the melted ice (now water) is exactly the same as the original weight of the ice.

Connecting Displacement and Melted Volume

• We know that the weight of the ice floating is equal to the weight of the water it displaces.
• Let \(W_{ice}\) be the weight of the ice.
• Let \(W_{displaced\_water}\) be the weight of the water displaced by the floating ice.
• According to Archimedes' Principle, \(W_{ice} = W_{displaced\_water}\).
• When the ice melts, it forms water with weight \(W_{melted\_water}\). Since mass is conserved, \(W_{melted\_water} = W_{ice}\).
• Therefore, \(W_{melted\_water} = W_{displaced\_water}\).
• Since the density of liquid water is constant (at a given temperature), equal weights of water occupy equal volumes.
• So, the volume occupied by the melted ice (as water) is equal to the volume of water that the ice displaced while it was floating.

Conclusion

The water from the melted ice fills exactly the space that was previously occupied by the submerged part of the ice (the displaced volume). The volume of the melted ice is equal to the volume of water that was displaced by the floating ice.

Therefore, when the ice melts completely, the level of water in the glass will remain the same.

This is a classic physics problem demonstrating the application of Archimedes' principle and the concept of conservation of mass.