Answer:
of that piece of ice would be above the freshwater. Assumptions:
- the density of the ice is
, and - the density of freshwater is
.
Explanation:
The volume of that chunk of ice can be split into two halves: volume above water
, and volume under water
. The mass of the whole chunk of ice would be:
.
Let
be the acceleration due to gravity. The gravity on the entire chunk of ice would be
.
On the other hand, the size of buoyant force on an object is equal to the weight of the liquid that it displaces. That is:
.
Recall that
is the volume of the ice above the water, and
is the volume of the ice under the water.
The mass of water displaced would be equal to:
.
The weight of that much water would be
.
Apply the equation
. The bouyant force on this chunk of ice would be equal to
.
Since the ice is floating, the forces on it need to be balanced. In other words,
.
On the other hand, recall that
.
Combine the two halves to obtain:
.
.
Divide both sides by
(assume that
) to obtain:
.
Rearrange to obtain:
.
However, the question is asking for
, the fraction of the volume above water. Note that
.
Therefore,
.
That's equivalent to
.