Exercise

Berechne den Schwerpunkt sscxs, sscys des folg abgebildeten Kreisabschnittes in Abhängigkeit von delta. center tikzpicture[scale.] draw[colorgreen!!black, ->,>latex] -.,--., node[right] x; draw[colorgreen!!black, ->,>latex] ,-.--,. node[above] y; draw[colorblue] -, arc::; draw[colorgreen!!black, dashed] -.,.---.,-. node[below] -delta; draw[colorgreen!!black, dashed] .,.--.,-. node[below] delta; filldraw[fillred!!white, opacity.] -.,. arc:: -- cycle; tikzpicture center
M rho _V ddV rho _x _y _z ddxddyddz rho _-delta^delta ddx _-sqrt-x^^sqrt-x^ ddy _^d ddz rho cdot d cdot _-delta^delta ddx _sqrt-delta^^sqrt-x^ ddy rho cdot d cdot _-delta^delta ddx [y]_sqrt-delta^^sqrt-x^ rho cdot d cdot _-delta^delta leftsqrt-x^ - sqrt-delta^ rightddx rho cdot d cdot _-delta^delta leftsqrt-x^ - sqrt-delta^ rightddx rho cdot d cdot _-delta^delta sqrt-x^ddx - rho cdot d cdot _-delta^deltasqrt-delta^ ddx rho cdot d cdot _-delta^delta sqrt-x^ddx - rho cdot d cdot sqrt-delta^ cdot [x]_-delta^delta rho cdot d cdot _-delta^delta sqrt-x^ddx - delta rho d sqrt-delta^ rho cdot d cdot left[fracleftxsqrt-x^+arcsin xrightright]_-delta^delta - delta rho d sqrt-delta^ rho cdot d cdot deltasqrt-delta^+arcsindelta - delta rho d sqrt-delta^ rho cdot d arcsindelta - rho d delta sqrt-delta^ rho d leftarcsindelta - delta sqrt-delta^right Die Schwerpunktskoordinate ist somit: sscys fracM _M y ddm fracM _V y rho ddV fracrhoM _x _y _z y ddxddyddz fracrhoM _-delta^delta _sqrt-delta^^sqrt-x^ _^d y ddxddyddz fracrhoM _-delta^delta ddx _sqrt-delta^^sqrt-x^ y ddy _^d ddz fracrho dM _-delta^delta ddx _sqrt-delta^^sqrt-x^ y ddy fracrho dM _-delta^delta ddx left[frac y^right]_sqrt-delta^^sqrt-x^ fracrho dM _-delta^delta ddx leftfrac -x^-frac-delta^right fracrho dM _-delta^delta fracleftdelta^-x^right ddx fracrho dM frac left[delta^x-fracx^right]_-delta^delta fracrho dM frac delta^ fracrho drho d leftarcsindelta - delta sqrt-delta^right frac delta^ frac fracdelta^arcsindelta - delta sqrt-delta^right
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Berechne den Schwerpunkt sscxs, sscys des folg abgebildeten Kreisabschnittes in Abhängigkeit von delta. center tikzpicture[scale.] draw[colorgreen!!black, ->,>latex] -.,--., node[right] x; draw[colorgreen!!black, ->,>latex] ,-.--,. node[above] y; draw[colorblue] -, arc::; draw[colorgreen!!black, dashed] -.,.---.,-. node[below] -delta; draw[colorgreen!!black, dashed] .,.--.,-. node[below] delta; filldraw[fillred!!white, opacity.] -.,. arc:: -- cycle; tikzpicture center

Metadata

Contained in these collections:
  1. Schwerpunkt 3 (uz)
Tags integral, kreisabschnitt, massenmittelpunkt, mathematik, mechanik, physik, schwerpunkt, statik
Default Difficulty
Default points 6
Language GER
Type Calculative / Quantity