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circular2.gif (523 bytes)




Legend

ac

= centripetal acceleration

v

= velocity

r

= radius
Fc = centripetal force

m

= mass
FN = normal force
Ff = force of friction
Ff = force of gravity
banked.jpg (16097 bytes)
跑道轉彎時是傾斜的,如此便不需要完全靠靜摩擦來當向心力•子可以越快而不打滑•

傾斜圓周運動

建築師可以將道路傾斜使得法向反作用力 (normal force FN) 成為向心力的一部份•如此便不需要完全靠靜摩擦來當向心力•現在法向反作用力 (normal force FN) 便有了水平和垂直的分量•

Image of a car on a banked curved surface, like a racing track often is

因為沒有垂直作用力:

Fy = FNcos - Fg = 0

但是有水平作用力所以:

Fx = max

aH = ac:

FNsin = Fc = mv2/r

要解便將以上兩個有的公式合起來相除:

(FNsin) / (FNcos) = (mv/r) / mg

結果:

tan = v2/gr

這是沒有打滑的條件•如果知道傾斜角度,便得知物體可以開多快,不管此物體多重•這便是賽車跑道轉彎時是傾斜的原因tan 越大,物體可以越快而不打滑•

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