Two balls of same sizes...how their acceleration different?

👨🏻‍🏫 學術台其他 - 科學

jason

2007-02-02 3:48 am

If there are two falling ball of the SAME SIZE but different masses,
how their acceleration different?

1) Is it correct?
- I suppose that same size have SAME FRICTION(air resistance) due to same surface area. Differnt masses shouldn't affect the accleration and speed if f is equal.

2) f is friction, m1>m2
F1 = m1a1 = W1-f (m1g-f)
F2 = m2a2 = W2-f (m2g-f)
then F1>F2 and W1>W2
Can sb prove that a1>a2 or sth...?

更新1:

sorry...I'll further explain my question first, m1 is larger than m2

更新2:

If air resistance is negigible, F=W F1=m1a1 W1=m1a1 m1g=m1a1 a1=g F2=m2a2 W2=m2a2 m2g=m2a2 a2=g Therefore, a1=a2 Ojects with DIFFERENT MASSES will fall with the SAME ACCELERATION which is uniform.

更新3:

However when there is air resistanve, F=W-f F1=m1a1 W1-f=m1a1 m1g-f=m1a1 F2=m2a2 W2-f=m2a2 m2g-f=m2a2 m1 LARGER THAN m2 therefore, m1g-f LARGER THAN m2g-f thus F1 LARGER THAN F2, m1a1 LARGER THAN m2a2

更新4:

this is my second question, I still cant't prove that a1 is LARGER THAN / EQUAL TO / SMALLER THAN a2....

更新5:

yeah..that's exactly my question: 兩個膠波，一個塞滿羽毛 , 另一個塞滿鐵釘一齊放手 , 邊個到地先呢? I cannot compare their acceleration, so i dont know thier speed....

回答 (2)

Rinka

2007-02-02 6:18 am

✔ 最佳答案

HMM.....詳細的Proof唔識寫
不過你可考慮兩個膠波 (抽扭蛋果d)
一個塞滿羽毛 , 另一個塞滿鐵釘
一齊放手 , 邊個到地先呢?

2007-02-09 01:01:47 補充：
I catch your point now~1 , absolutely correct about "air resistance negliable" conditionall object (neglect of their mass) fall in same accelerationthere is a experiment about a feather and a coin which place in vaccum , you can see they fall in same high speed (also accelration)

2007-02-09 01:05:20 補充：
2 , if air resistance is taken into accountmg - f = maa = g - (f / m)for larger m , the minus factor is smallerhigher mass 's acceleration is larger than smaller mass's accelerationthis become our daily situation , a steel feather fall faster than a real feather

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Jess Kwok

2007-02-03 1:55 pm

1) acceleration will change when the masses of the object is different. because of the equation F=ma. (F=Force, M = mass & a = acceleration)
eg. 100N = 10 x a
a = 10m/s/s
100N = 20 x a
a = 5 m/s/s
Therefore, when the masses of an object is bigger, the object will accelerate slower. DIfferent masses will affect the acceleration and speed.

2) sorry, dun get your second question.

hope i can help you on the first question. =]

參考: myself

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