以36km/hr的速度在半徑200m的彎路上行駛之火車

2013-01-25 2:35 am
以36km/hr的速度在半徑200m的彎路上行駛之火車 欲使鐵軌不受側壓 則外側鐵軌應較內側鐵軌高出若干 (但兩軌之間距離為120m 而g=10m/s平方)
更新1:

36 km/h = 10 m/s mgtan西搭= m*v平方/R tan西搭=v平方/gR h/120 =10平方/10*200 h=6cm

回答 (1)

2013-01-25 7:56 am
✔ 最佳答案
36 km/h = 10 m/s

Let d be the difference in height between the inner and outer rails.
Hence, tan(a) = d/1.2
where angle a is the angle subtended by the outer rail at the inner rail
[please check the given firgure for the separation between the rails, 120 m is unrealistic, I presume that it is 120 cm, or 1.2 m]

Let R1 and R2 be the normal reaction on the inner wheels and outer wheels of a train car.
Hence, (R1+R2).sin(a) = m(10^2)/200
and (R1+R2).cos(a) = mg
where m is the mass of a train car

Dividing, tan(a) = 10^2/200g = 0.05
thus, d/1.2 = 0.05
d = 1.2 x 0.05 m = 0.06 m = 6 cm


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