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Radius eines Loopings

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Level 5 -
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Exercise

https://texercises.com/exercise/radius-eines-loopings/

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Solution

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The following quantities appear in the problem: Masse \(m\) / Kraft \(F\) / Energie \(E\) / Geschwindigkeit \(v\) / Ortsfaktor \(g\) / Höhe \(h\) / Radius \(r\) /

The following formulas must be used to solve the exercise: \(F = mg \quad \) \(E_{\rm \scriptscriptstyle kin} = \dfrac12 mv^2 \quad \) \(E_{\rm \scriptscriptstyle pot} = mgh \quad \) \(F = m\dfrac{v^2}{r} \quad \)

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Exercise:
Der Wagen einer Freizeitbahn habe im tiefsten Punkt eines Loopings eine Geschwindigkeit von . Welchen Radius darf der Looping maximal haben damit der Wagen oben gerade noch auf der Bahn bleibt? Alle Reibungseffekte etc. sind zu vernachlässigen.

Solution:
Am obersten Punkt muss gelten: FG FZ mg mfracv_uparrow^r gr v_uparrow^ Ausserdem gilt der Energieerhaltungssatz: E_uparrow E_downarrow mg r + frac mv_uparrow^ frac mv_downarrow^ rg + v_uparrow^ v_downarrow^ Setzt man die obere Gleichung für v_uparrow^ ein so erhält man: rg + rg v_downarrow^ r fracv_downarrow^g fracmeterpersecond^ .meterpersecondsquared .m r fracv_downarrow^g .m

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Attributes & Decorations

Branches	Dynamics
Tags	dynamik, gleichungen, kreis, kreisbahn, looping, mechanik, physik, todesspirale
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Difficulty	(4, default)
Points	3 (default)
Language	(Deutsch)
Type	Calculative / Quantity
Creator	uz
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