GS-2 Physical Sciences Question 35

[admin]

It is very important to read and understand Archimedes Principle (PHY 6.1.2 in the Gold Standard book).

Nonetheless, in response to your questions:

"How does the fact that the density of ice is less than the density of water come into play here?"

When you have ice in the liquid water, a small amount of the ice is above the surface of the water. When the ice melts, it becomes more dense and thus shrinks to fit the exact volume that the solid form used to have below the surface of the water: thus the water level is unchanged.

"As a portion of the volume of ice melts it will become water of the same volume but of a greater mass wouldn't this mean the water level would have to change in some way?"

There is incorrect information in your question. When the ice melts, its density increases (D = m/V), NOT because of an increase in mass (after all, where would the extra molecules come from??) but rather the increase is due to a DECREASE in volume as alluded to in response to your first question.

Here is another illustration of Archimedes Principle (as discussed in the Archimedes Principle Video, $3, in the Physics section: http://www.mcat-prep.com/publicvideos/physics.php): imagine that you have a bucket of water. Take a styrofoam block and put it in the bucket. Of course, as soon as you put the styrofoam in the bucket, the level of the water will go up commensurate with the weight in volume of water displaced by the styrofoam.

Now take the styrofoam and crush it into a smaller volume and put it back in the bucket. Will the styrofoam push aside any more or less water than before? Of course, because the weight has not changed, the styrofoam has no more force to push aside more or less water. Thus the level of the water does not change.

NB: for the superkeeners: of course if the styrofoam is crushed into a super dense ball that cannot even float but rather, it's sooooo dense that it sinks to the bottom (!!!), then of course the level of the water would decrease.

[mcat_premed3832]

You did not take into account that part of the volume of the less dense (greater volume) ice occupies a little space ABOVE the surface of the liquid water. Upon melting, that extra space is now empty (ie just air).

[johnjsun2264]

So the deciding factor is that there is a part of the ice cube above the surface of the water. If there weren't, then would the water level go down?

[mcat_premed3832]