密度:冰(10分)急

這個現象常常見,但竟然被一問下不知道答案....

2010-11-21 00:28:55 補充：
答案我不是100%肯定的。

冰為什麼會有一半浮,一半沉呢?
這個問題其實應該是部分正確。密度=質量/體積。
因為我們知道浮力與密度(density)是有極大關係的, 密度愈少, 浮力愈大(因為未學過有關的題材, 所以我不肯定密度與浮力是否反正比), 在一粒浮冰上的力只有浮力與重力, 這兩個力是相反方向而且量值是相同的, 否則冰會自動加速, 同時, 浮力的大小取決於冰在水褢的體積(也可以說成質量,因為密度是常數), 當浸在水褢的體積愈大, 浮力就愈大, 所以冰是有部分浮在水上, 有部分沉在水下。

你可以想想, 如果你把冰用力推入水底, 它會自己升上原本的高度, 因為當你把冰推入水底時, 冰的體積完全在水褢, 浮力最大,當你放手時, 只餘下重力和浮力面個力, 浮力大過重力, 所以冰會自己升上來。

所以我推斷冰是部分梁,部分沉。只有在特別的條例下(例如冰的形狀), 冰是一半浮, 一半沉。

2010-11-24 18:56:19 補充：
To 天同:
雖然我未學過浮力的公式, 但跟據你的回答, 浮力 = 密度 x 體積 x g?
你的公式可以簡化做浮力 = 質量 x g, 我有2個疑點。

1. 浮力與地心吸力的公式一樣?
2. 質量與浮力成正比?愈重的東西浮力愈大?

No, you are wrong. It is NOT half of the ice submerged under water and half above water.

In fact, it is around 90% of the volume of the ice submerges under water and the remaining 10% is above water. The reason is apparent, it is because the density of ice is about 0.9 g/cm^3, or 90% of that of water (which is 1 g/cm^3)

The upthrust on the ice, if there is 90% of the ice volume V submerged under water, is equal to the weight of water displaced, i.e.
upthrust = (0.9V) x 1g N , where g is the acceleration due to gravity.
thus, upthrust = 0.9Vg N

But (0.9V) is just the mass of ice because ice density is 0.9 g/cm^2.
Hence, upthrust = (ice mass)g = weight of ice
The ice thus floats with only 10% of its volume above water.