Exercise
https://texercises.com/exercise/radius-einer-halbkreisformigen-glasrinne/
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The following quantities appear in the problem: Masse \(m\) / Kraft \(F\) / Ortsfaktor \(g\) / Radius \(r\) / Winkelgeschwindigkeit / Kreisfrequenz \(\omega\) / Winkel \(\theta\) /
The following formulas must be used to solve the exercise: \(\cos\alpha = \dfrac{b}{c} \quad \) \(F = mg \quad \) \(\sin\alpha = \dfrac{a}{c} \quad \) \(F = mr\omega^2 \quad \)
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Exercise:
Welchen Radius müsste eine halbkreisförmige Rinne haben damit eine Kugel in ihr sofern die Rinne sich mit wO um ihre vertikale Achse dreht hO über dem tiefsten Punkt horizontal kreist? center tikzpicture drawdashed ---; node at tikz x.cmy.cmline width.ex-stealthrotate colorgreen!!black solid draw arc -:: and ;; drawultra thick black arc :-:; filldrawcolorblack fillred -.-. circle .cm; tikzpicture center

Solution:
Es gilt dass: FZ costheta FG sheta mtilde romega^ costheta mg sheta mrshetaomega^ costheta mg sheta romega^ costheta g costheta fracgromega^ fracr-hr fracgromega^ r-h fracgomega^ r fracgomega^ + h fracncgqtyw^ + h r
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Exercise:
Welchen Radius müsste eine halbkreisförmige Rinne haben damit eine Kugel in ihr sofern die Rinne sich mit wO um ihre vertikale Achse dreht hO über dem tiefsten Punkt horizontal kreist? center tikzpicture drawdashed ---; node at tikz x.cmy.cmline width.ex-stealthrotate colorgreen!!black solid draw arc -:: and ;; drawultra thick black arc :-:; filldrawcolorblack fillred -.-. circle .cm; tikzpicture center

Solution:
Es gilt dass: FZ costheta FG sheta mtilde romega^ costheta mg sheta mrshetaomega^ costheta mg sheta romega^ costheta g costheta fracgromega^ fracr-hr fracgromega^ r-h fracgomega^ r fracgomega^ + h fracncgqtyw^ + h r
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Attributes & Decorations
Branches
Circular Motion, Dynamics
Tags
dynamik, kreis, kreisbewegung, mechanik, physik, zentrifugalkraft, zentripetalkraft
Content image
Difficulty
(3, default)
Points
5 (default)
Language
GER (Deutsch)
Type
Calculative / Quantity
Creator uz
Decoration
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Link