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2014-06-05 9:49 pm
一輛玩具車的車頂放了1塊100g重的鐡塊,
另一輛玩具車的車頂沒有放任何東西,
如果2架車同時放在同一塊斜了的木板上,
那一輛玩具車的滑下速度較快?爲甚麼?

回答 (2)

2014-06-05 11:25 pm
✔ 最佳答案
兩車的速度相等。

中二的解釋:
車頂放置一塊 100 g 鐵塊的玩具車
1. 受較大的地心吸力。若其他條件不變,玩具車的推動力較大,速度較快。
2. 玩具車的質量較大。若其他條件不變,質量較大的玩具車,速度較慢。
以上兩個因素互相抵消,故兩車速度相等。


較高級別的物理科解釋:
設兩車質量均為 m kg,斜板與水平成的角度為 θ。根據公式 F = ma
無負重的車: m g cosθ = m a
有負重的車: (m + 0.1) g cosθ = (m + 0.1) a
故兩車的加速度 a 相等。
根據動力學公式 v² = u² +2as
兩車的初速度(u = 0)、加速度(a)和位移(s)均相等,故此兩車速度(v)相等。
參考: 土扁
2014-06-05 11:30 pm
Assume the wooden plank is smooth, i.e. frictional force is negligible. The two toy cars would have the same acceleration down the plank, and hence possess the same speed.

The gravitational force F pulling the toy car down the plank is given by,
F = mg.sin(b)
where m is the mass of the toy car, g is the acceleration due to gravity, b is the angle of the sloping plank.

By Newton's Second Law, the acceleration a of the toy-car is,
a = force/mass = mg.sin(b)/m = g.sin(b)

That is, the acceleration is independent of the mass of the toy car. In other words, the one that carries a 100 g load has the same speed and acceleration as the other unloaded toy car does.



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