圓周運動:以下哪個關係式正確?

Resolve the normal reaction N vertically and horizontally.
Vertically: N.cos(θ) = mg (for equilibrium in the vertical direction)
Horizontally: N.sin(θ) = mv^2/r

Dividing: N.sin(θ)/N.cos(θ) = v^2/rg
i.e. tan(θ) = v^2/rg
v^2 = rg.tan(θ)

From above, you could see that option A is right. Options B, C, D and E are wrong.


2014-09-21 00:32:06 補充：
Your suppl question:
As you can see from my answer, N.cos(θ) = mg, i.e. N = mg/cos(θ)
The normal reaction N is greater than mg.....

2014-09-21 00:32:29 補充：
(cont'd)...This is a typical situation in circelar motion. The reason is because the centrifugal force (i.e. inertia force) presses the vehicle against the circular track, hence increasing the normal reaction

2014-09-21 00:36:19 補充：
(cont'd)...Should N.cos(θ) = mg is right, there would be an unbalance force mg.sin(θ) acting downward along slant surface of the circular track. This would make the vehicle to move inward. But this did not happen in practice.

Correction:

suppl = supplement

Sorry! = ="

圖:photo.pchome.com.tw/forever2015/141094562013