在高處磅重,同在低處磅重會5會有偏差???

2007-06-20 11:42 pm
在高處磅重(例如在80層),同在低處(例如在地下)磅重會5會有偏差???

因為在高處墮物,由於地心吸力,物件墮落ge速度會快d ba~~

回答 (7)

2007-06-21 12:10 am
✔ 最佳答案
根據 Newton's second law of motion, F=ma, 即係... 推動物件移動ge力同物件移動ge加速率係成正比的.
磅重其實係磅人踏落個磅到ge力, F, 因為F=ma, m係人ge mass(質量), 即係唔會變ga la, 而a, acceleration加速率, 就即係地心吸力gravity (o係地球每一個位置都係常數, 大約=9.8ms^-2),
因為兩個數字都不變, 所以你o係地球每個地方磅重得出黎ge數字都會一樣
除非你o係一個acceleration會改變ge空間入面磅, 例如升降機
如果架lift係向上行緊, 磅出黎ge數字應該會大左
相反就會細左

至於由高處墮物, 會將物件ge potential energy (PE) 全部轉化做kinetic energy (KE), idealy, 因為實際上有部分gePE係會用左黎overcome空氣阻力
PE = mgh, m=mass, g=gravity , h=height
KE = 1/2 mv^2
所以idealy, 當物件去到地面ge時候, 最初gePE=最終geKE, mgh = 1/2 mv^2,
由於.. m, g 都係常數,
所以我地得出.... 放物件ge高度同物件墮落ge速度ge**二次方係成正比的 ( h directly proportional to v^2)

但注意... 以上兩個case完全無關, 不能混為一談
第一個case講ge係加速率而第二個case講ge係速率
2007-06-22 3:22 am
讓我回答你的這一條的問題吧!
在不同的高度,地心加速度會有不同.離地心越遠,地心加速度越小.
然而,物體的重量=地心加速度x物體的質量.
因為物體的質量不變,而高度不同,所以地心加速度會有不同,因此物體的重量會不同的.
不過,地心加速度隨高度的變化極小,因此物體的重量變化不大(近乎0),所以不用太在意.

另外,在高處墮物和在低處墮物,它們的初速是一樣的,但末速不一樣(高處的較大).這是因為在高處墮落有較多的距離加速,和問題無關.
2007-06-22 2:34 am
磅重時, 你是在靜止狀態. 應用的理論應該是牛頓的萬有引力定律, 即在宇宙里兩個物體之間的引力與兩者的質量和距離有關. (F= K m1 m2 / d^2).

所以磅重時, "稱"所反影的是地球對你身體質量的引力的表示. 如前所述, 由於引力與兩個物質的質量和距離有關, 所以你站在高地與站在低處(即d出現了變化), "稱"重的表示是有差異的, 只是市場賣的"稱"的精度無法顯示那微少的差異而已.
2007-06-21 1:39 am
理論上有, 因為在愈高的地方, 物件距離地心愈遠, 即是說地心吸力會少d, 所以磅重會有偏差,但事實上你不會察覺到.
2007-06-21 12:45 am
重力的大小以mg表示,即W=mg。
這裡,m表示物體的質量,g表示物體所在點的重力加速度,一般計算採用標準重力加速度,即g=gn=9.80665ms-2。

重力加速度的數值受高度、緯度及地球自轉的影響。一般計算中g可近似的取作標準重力加速度,即g=gn=9.80665ms-2。

But g=Gm/r^2
r 是物件與地球中心距離,所以當足夠高 g 是不同的(細少少 如在高地)


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2007-06-21 12:42 am
There are two question in your statement,
1) Your weight are different at a higher place.
2) Oject will fall faster at higher place.


Answer to your question
1) Do you know what is the different between mass (質量) and weight (重量)?
Mass is define by the change of momentum. Mass will not change.
Weight is the value of mass under the gravitational pull, if you in space without gravitation, you still have mass but no weight.

In very high place, the gravitational force is weaker, for example it is almost 9.8m/s at ground while if you are in a place is 1km high, you will feel a ~0.03% lost in your weight.
The different is very small in our daily life. (Earth's radius ~6400km).

2) The gravitation force at different height is different, but even you fall from 100km above the ground, the different is 3.2% (100km high is almost the boundary of space). We can take g, the gravitataion acceleration is constant at oyr daily life.

Two objects located at 10m and 100m higher repectively, the times for them to fall to the ground are s=0.5gt^2, we take g=10m/s for simple case.
a) s=10m , t=1.414s, final speed v=gt=14.142m/s
b) s=100m, t=4.472s, v=gt=44.721m/s

In your question, if you mean the final speed, an ojbect drop from high place will have a higher final speed, if you mean the time needed to reach the ground, the high the oject is, the more time it need to reach the ground.

There is a another way to think, even the oject is located at 100m, the time for it to travel at the first 10m is the same as the time need of object located at 10m high to fall to the ground. So the object at 100m will never able to reach the ground early then any one lower than it.
2007-06-20 11:47 pm
'由於地心吸力,物件墮落ge速度會快d'呢個講法是錯的


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