驗證牛噸第二定律的三條問題?

Question

a:小車受到的拉力是否就等於砝碼所受的重力呢?如果不是的話,在什麼情況下才可將小車受到的拉力認為就等於可砝碼所受的重力呢?
b:若不采用數據采集器,可用什麼方法測出物體的加速度?
c:實驗數據的圖象中的數據點可吾直接連起來呢?為什麼?

※:唔該可唔可以幫我呀~每一條多于50個字呀~唔該灑呀>.

Answer 1

(a) Let m be the mass of the weight-pieces
M be the mass of the trolley
T be the tension on the string
a be the acceleration of the trolley (and weights)

hence, mg-T = ma
and T = Ma
adding, mg = (M+m)a, this gives a = mg/(M+m)
thus T = Ma = mg[M/(M+m)]

since the factor M/(M+m) is smaller than unity, as M must be smaller than (M+m), the tension pulling the trolley T is smaller than the weight mg of the weight-pieces.

When the mass of the trollet M is much greater than the mass m of the weight-pieces used in the experiment, the factor M/(M+m) is close to unity. Under such situation, the tension T pulling the trolley can be treated as more or less equal to the weight mg of the weight-pieces.

(b) By measuring the distance travelled by the trolley s within a time period t,
then applying the equation of motion: s=ut+(1/2)at^2
assume the trolley starts from rest, u=0 m/s
thus a = 2s/t^2

(c) It is usually not advisable to do so, as there are bound to be experimental uncertainities in each data point.