關於阿基米德原理

Why not do a mathematical calculation to find out the answer?
Let the volume of the ice cube = V(ice)
volume of stone = V(stone)
Given the density of stone = 1.6 g/cm3, density of ice = 0.9 g/cm3, and density of water = 1 g/cm3
When the ice cube (with stone inside) floats on water, the volume of water displaced = f.V(ice), where f is the fraction of ice volume submerged in water.
hence, by the Principle of Floatation,
upthrust = weight of water displaced = f.V(ice).g
where g is the acceleration due to gravity
But weight of ice and stone = 0.9V(ice).g + 1.6V(stone).g
Therefore, f.V(ice).g = 0.9V(ice).g + 1.6V(stone).g
i.e. V(stone) = (f - 0.9)V(ice)/1.6
Apparently, the value of f must be greater than 0.9 and smaller or equal to one.
[Note: f= 0.9 means there is no stone inside the ice cube, f=1 means the ice cube, with stone inside, is just able to float.]
Now, after the ice cube has melted and the stone dropped into the water, the total volume V(total) of water (from the melted ice) and stone
= 0.9V(ice) + V(stone)
= 0.9V(ice) + (f - 0.9)V(ice)/1.6
= [0.9 - 0.9/1.6 + f/1.6].V(ice)
= [0.3375 +f/1.6].V(ice)
Assume, for example, a situation that the ice cube with stone just float on water, i.e. f = 1,
V(total) = 0.9625V(ice)
That is to say, there is a reduction in volume
= V(ice) - 0.9625V(ice) = 0.0375V(ice)
Hence, the water level will drop.
The physical reason behind is obvious. Since water has a density lower than stone ( 1 g/cm3 against 1.6 g/cm3), the volume of water displaced by the floating ice in order to support the weight of the stone must be larger than the volume of the stone itself. This will gives a decrease in total water volume when the stone drops into the water.

推理一,
水凝固為冰後會膨脹，所以冰密度比水低，因此浮於水面。
但當冰溶化后,石頭就會下沉增加了水的密度,就好似波波池
中有人沉下去波波上升的原理一樣,so水位上升(但這個問顯表面簡單,其實很困難,如冰本身會膨脹很易理解,但.冰里含有石頭時
會否改變其內部分子結構從而影響其膨脹的特性呢?我相信很難
解釋!而且石頭的位置都有所影響

2009-08-04 11:30:40 補充：
石頭的位置是指在冰內,如在冰的下方時會否一開始就下沉呢?所以難以看到變化!水的密度呢?當水愈多密度愈少所以引到水位甚至沒有上升!
水溫呢?是否一百度?會否走了的水等於上升的水位使得沒有變化!

水位都應該係上升
因為你到最後均是增加了水/放了沉的物體進去
所以最後都是上升