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The fast train known as the TGV (Train à Grande Vitesse) that runs south from Paris, France, has a scheduled average speed of 216 km/h. (a) If the train goes around a curve at that speed and the acceleration experienced by the passengers is to be limited to 0.050g, what is the smallest radius of curvature for the track that can be tolerated? 7347 m (b) If there is a curve with a 0.90 km radius, to what speed must the train be slowed to keep the acceleration below the limit?

Respuesta :

Answer:

Explanation:

Given

average speed of train[tex](v_{avg})=216 kmph\approx 60 m/s[/tex]

Maximum acceleration=0.05g

Now centripetal acceleration is

[tex]a_c=\frac{v^2}{r}[/tex]

[tex]0.05\times 9.8=\frac{60^2}{r}[/tex]

r=7346.93 m

(b)Radius of curvature=900 m

therefore [tex]a_c=\frac{v^2}{r}[/tex]

[tex]v=\sqrt{a_cr}[/tex]

[tex]v=\sqrt{0.05\times 9.8\times 900}[/tex]

[tex]v=\sqrt{441}=21 m/s[/tex]

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