Flaschenzug II
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Exercise:
Für den Flaschenzug in der Abbildung soll center tikzpicturescale. % Decke draw fillgraydrawnone - rectangle .; draw thick - -- ; % Flaschenzug draw drawblackfillgraythick circle .cm; draw drawblackfillblack circle .cm; draw very thick -- ++ -; draw drawblackfillgraythick circle .cm; draw drawblackfillblack circle .cm; draw very thick -- ++ -; % Untere Rolle Links draw drawblackfillgraythick circle .cm; draw very thick -- ++ ; draw drawblackfillblack circle .cm; % Untere Rolle Rechts draw drawblackfillgraythick circle .cm; draw very thick -- ++ ; draw drawblackfillblack circle .cm; % Seil draw -. -- ++ -; draw . -- ++ -; draw . -- ++ -; draw . -- ++ -; draw -- ; draw -- ; draw . -- ++ -.; draw -- ++ -.; % Kraft draw Dandelion-thick .. -- node right fns vec F ++ -; % Masse draw drawbrown fillbrown! .. rectangle node brown fns m ++ -.; tikzpicture center enumerate item die Kraft F für eine Masse von m t berechnet werden. item Welche Strecke verrichten Sie falls die Masse um h meter angehoben werden soll? enumerate
Solution:
Für den Flaschenzug in der Abbildung soll center tikzpicturescale. % Decke draw fillgraydrawnone - rectangle .; draw thick - -- ; % Flaschenzug draw drawblackfillgraythick circle .cm; draw drawblackfillblack circle .cm; draw very thick -- ++ -; draw drawblackfillgraythick circle .cm; draw drawblackfillblack circle .cm; draw very thick -- ++ -; % Untere Rolle Links draw drawblackfillgraythick circle .cm; draw very thick -- ++ ; draw drawblackfillblack circle .cm; % Untere Rolle Rechts draw drawblackfillgraythick circle .cm; draw very thick -- ++ ; draw drawblackfillblack circle .cm; % Seil draw -. -- ++ -; draw . -- ++ -; draw . -- ++ -; draw . -- ++ -; draw -- ; draw -- ; draw . -- ++ -.; draw -- ++ -.; % Kräfte draw redthick- . -- node right tiny vec F ++ .; draw redthick- . -- node left tiny vec F ++ .; draw redthick- . -- node right tiny vec F ++ .; draw redthick- -. -- node left tiny vec F ++ .; draw redthick- -- node left tiny vec F ++ -; draw redthick- -- node left tiny vec F ++ -; % Kraft draw Dandelion-thick .. -- node right fns vec F ++ -.; % Masse draw drawbrown fillbrown! .. rectangle node brown fns m ++ -.; tikzpicture center enumerate item Nach dem man alle Kräfte eingezeichnet hat sieht man vgl. Abb. d.h. F fracF_g approx .kilonewton. item Die Arbeit muss für beide gleich sein d.h. W_ F_g h F y W_ Rightarrow y fracF_gF h meter. enumerate
Für den Flaschenzug in der Abbildung soll center tikzpicturescale. % Decke draw fillgraydrawnone - rectangle .; draw thick - -- ; % Flaschenzug draw drawblackfillgraythick circle .cm; draw drawblackfillblack circle .cm; draw very thick -- ++ -; draw drawblackfillgraythick circle .cm; draw drawblackfillblack circle .cm; draw very thick -- ++ -; % Untere Rolle Links draw drawblackfillgraythick circle .cm; draw very thick -- ++ ; draw drawblackfillblack circle .cm; % Untere Rolle Rechts draw drawblackfillgraythick circle .cm; draw very thick -- ++ ; draw drawblackfillblack circle .cm; % Seil draw -. -- ++ -; draw . -- ++ -; draw . -- ++ -; draw . -- ++ -; draw -- ; draw -- ; draw . -- ++ -.; draw -- ++ -.; % Kraft draw Dandelion-thick .. -- node right fns vec F ++ -; % Masse draw drawbrown fillbrown! .. rectangle node brown fns m ++ -.; tikzpicture center enumerate item die Kraft F für eine Masse von m t berechnet werden. item Welche Strecke verrichten Sie falls die Masse um h meter angehoben werden soll? enumerate
Solution:
Für den Flaschenzug in der Abbildung soll center tikzpicturescale. % Decke draw fillgraydrawnone - rectangle .; draw thick - -- ; % Flaschenzug draw drawblackfillgraythick circle .cm; draw drawblackfillblack circle .cm; draw very thick -- ++ -; draw drawblackfillgraythick circle .cm; draw drawblackfillblack circle .cm; draw very thick -- ++ -; % Untere Rolle Links draw drawblackfillgraythick circle .cm; draw very thick -- ++ ; draw drawblackfillblack circle .cm; % Untere Rolle Rechts draw drawblackfillgraythick circle .cm; draw very thick -- ++ ; draw drawblackfillblack circle .cm; % Seil draw -. -- ++ -; draw . -- ++ -; draw . -- ++ -; draw . -- ++ -; draw -- ; draw -- ; draw . -- ++ -.; draw -- ++ -.; % Kräfte draw redthick- . -- node right tiny vec F ++ .; draw redthick- . -- node left tiny vec F ++ .; draw redthick- . -- node right tiny vec F ++ .; draw redthick- -. -- node left tiny vec F ++ .; draw redthick- -- node left tiny vec F ++ -; draw redthick- -- node left tiny vec F ++ -; % Kraft draw Dandelion-thick .. -- node right fns vec F ++ -.; % Masse draw drawbrown fillbrown! .. rectangle node brown fns m ++ -.; tikzpicture center enumerate item Nach dem man alle Kräfte eingezeichnet hat sieht man vgl. Abb. d.h. F fracF_g approx .kilonewton. item Die Arbeit muss für beide gleich sein d.h. W_ F_g h F y W_ Rightarrow y fracF_gF h meter. enumerate