Does Melting Ice Change the Water Level in a Glass?

[ussrasu]

Some help with this question please?

a) An ice cube floats in a glass of water. When the ice melts, will the water level in the glass rise, fall, or remain unchanged? Justify your answer.

b) If the ice had been made from pure water, and the water in the glass was salt water (denser than pure water) how would this change your answer, if at all? Justify your answer.

for a) I am assuming the water level will not change, as the ice cube will have already increased the water level when it was placed in the glass, and when it melts it will remain at this level as it is simply just turning to liquid. Any better way of explaining that?

for b) - would the ice float higer on the surface as it is less dense than the water in the glass - and therefore displace less water as an ice cube, but when it melts the water level will rise - as it is still the same mass of ice as before? Not sure?

Thanks in advance!

 

[Andrew Mason]

Some help with this question please?

a) An ice cube floats in a glass of water. When the ice melts, will the water level in the glass rise, fall, or remain unchanged? Justify your answer.

b) If the ice had been made from pure water, and the water in the glass was salt water (denser than pure water) how would this change your answer, if at all? Justify your answer.

for a) I am assuming the water level will not change, as the ice cube will have already increased the water level when it was placed in the glass, and when it melts it will remain at this level as it is simply just turning to liquid. Any better way of explaining that?

for b) - would the ice float higer on the surface as it is less dense than the water in the glass - and therefore displace less water as an ice cube, but when it melts the water level will rise - as it is still the same mass of ice as before? Not sure?

These questions are a good way of understanding Archimedes' principle.

The principle is: the volume of water displaced by the floating ice has a mass equal to the mass of the ice. Since salt water is more dense than pure water, the floating ice cube displaces a smaller volume in salt water than it does in pure water.

Just apply that princple and you will have the answers.

AM

 

[ussrasu]

So what i have sounds right?

 

[Andrew Mason]

So what i have sounds right?

You could guess the answer and have a 50-50 chance of being right. It is the reasoning that counts. Your reasons have to be given in terms of Archimedes' principle.

The level in the glass depends on the amount of water displaced by the ice cube. This depends only on the mass of the ice cube. Imagine the ice cube wrapped in a massless waterproof membrane while it melted. Does the mass change when it melts? (you can ignore the m=E/c^2 part of the mass).

AM