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Schienenversatz in Eisenbahnkurve

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Exercise

https://texercises.com/exercise/schienenversatz-in-eisenbahnkurve/

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The following quantities appear in the problem: Masse \(m\) / Kraft \(F\) / Geschwindigkeit \(v\) / Ortsfaktor \(g\) / Radius \(r\) / Winkel \(\theta\) /

The following formulas must be used to solve the exercise: \(\cos\alpha = \dfrac{b}{c} \quad \) \(F = mg \quad \) \(\sin\alpha = \dfrac{a}{c} \quad \) \(F = m\dfrac{v^2}{r} \quad \)

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Exercise:
In einer Eisenbahnkurve mit m Radius sind die Schienen so nach innen geneigt dass bei einer Gschwin-dig-keit von keine Querkräfte auftreten. Um wie viele Zentimeter ist folglich die äussere Schiene gegenüber der inneren bei einer Spurweite von mm überhöht?

Solution:
Skz center tikzpicturescale defang defs. % Spurweite defb. % Breite Zug defh. % Höhe Zug deft. % Schienenhöhe filldrawcolorgreen!!black fillgreen!!white -- arc :ang:--cycle; nodecolorgreen!!black at ang/:. alpha; draw--; scoperotateang coordinate A at ; coordinate B at +*s; drawvery thick--; filldrawcolorblack . rectangle .t; filldrawcolorblack .+*s rectangle .+*st; drawcolorred -latex t/--+*st/ nodemidway above rotateang dmm; filldrawcolorblack fillblack!!white +s-b+..+*h+--+s-b+.+*h+.--+s-b.+*h --+s-bt+.*--+s-*b/t+.--+s+*b/t+.--+s+bt+.*--+s+b.+*h--+s+b-.+*h+.--+s+b-..+*h+--cycle; %arc::*.--cycle; coordinate SP at +s h+; filldraw SP circle .cm; scope filldrawcolorgreen!!black fillgreen!!white SP--+:. arc :+ang:.--cycle; filldrawcolorgreen!!black fillgreen!!white SP+-:.cm--SP+-:cm arc :+ang:.--cycle; drawcolorblue- latex B--B|-A nodemidway right h?; drawcolorbluedotted A--A-|B; drawcolorred-latex SP--+-:.cm nodebelow sscFG; drawcolorredthick -latex SP--++ang:.*sinang nodeleft F_parallel; drawcolorbluethick-latex SP--+:.*sinang/cosang nodeabove sscFZ; tikzpicture center Für den Neigungswinkel der Schienen gilt: FZ cos alpha FG sin alpha tan alpha fracv^rg alpha arctanfracv^rg arctanfrac.^m .q ang. .rad Die Schiene muss demnach um h d sinalpha d sinarctanfracv^rg d fracfracv^rgsqrtleftfracv^rgright^+ d fracv^sqrtv^^+rg^ .m sinang. .mmm erhöht werden.

Meta Information

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Contained in these collections:

Eisenbahnkurve by TeXercises

1 | 6
Eisenbahnkurve by TeXercises

2 | 3
Dynamik der Kreisbewegung 1 by uz

7 | 10

Asked Quantity: Höhe \(h\) in Meter \(\rm m\)

Attributes & Decorations

Branches	Circular Motion, Dynamics
Tags	dynamik, eisenbahn, eisenbahnkurve, kreis, kreisbewegung, mechanik, physik, trigonometrie, zentripetalkraft
Content image
Difficulty	(3, default)
Points	3 (default)
Language	(Deutsch)
Type	Calculative / Quantity
Creator	uz
Decoration
File
Link

Physical Quantity

Höhe \(h\)

lotrechter Abstand von Referenzfläche

Meter (\(\rm m\))

Seemeile (\(\rm NM\))

Unit

Meter (\(\rm m\))

Der Meter ist dadurch definiert, dass der Lichtgeschwindigkeit im Vakuum \(c\) ein fester Wert zugewiesen wurde und die Sekunde (\(\rm s\)) ebenfalls über eine Naturkonstante, die Schwingungsfrequenz definiert ist.

Radius (\(r\))

Umfang (\(u\))

Länge (\(\ell\))

Strecke (\(s\))

Durchmesser (\(d\))

Höhe (\(h\))

Amplitude (\(\hat y\))

Elongation (\(y_t\))

Dicke (\(d\))

Breite (\(b\))

Wellenlänge (\(\lambda\))

Impuls (\(p\))

Gitterkonstante (\(d\))

Brennweite (\(f\))

Bildweite (\(b\))

Gegenstandsweite (\(g\))

\(\rm 1\,Å=1\cdot 10^{-10}\,m\)

\(\rm 1\,in=2.54\cdot 10^{-2}\,m\)

\(\rm 1\,ft=0.3048\,m\)

\(\rm 1\,yd=0.9144\,m\)

\(\rm 1\,mi=1.609344\cdot 10^{3}\,m\)

\(\rm 1\,NM=1.852\cdot 10^{3}\,m\)

Base? SI? Metric? Coherent? Imperial?