Rod as a one-sided lever
Question
Solution
Short
Video
\(\LaTeX\)
Need help? Yes, please!
The following quantities appear in the problem:
Drehmoment \(\vec M\) /
The following formulas must be used to solve the exercise:
\(\sum \stackrel{\curvearrowleft}{M} \stackrel{!}{=} \sum \stackrel{\curvearrowright}{M} \quad \)
Exercise:
A mass of mO is attached to one of a rotatably mounted rod mSO with lSO in length. lFO from this same FO are acting on the rod in upward direction holding the rod in equilibrium. How far from the other is the pivot po see sketch? center tikzpicture filldrawcolorblack fillblack!!white rectangle .; filldrawcolorblack .. circle .cm; drawsnakebrace .-.---.; node at .-. ?; draw ---.; drawthick colorblack fillorange .-. rectangle .-.; drawthick- latex colorblue --.; tikzpicture center
Solution:
newqtymskg newqtyl.m newqtymg.kg newqtylprm newqtyFoN % unknownx % DrehmomentSchritte % PGleichungM_uparrow sscMS + sscMG PGleichungF_uparrow ell_uparrow sscFS sscellS + sscFG sscellG PGleichungF_uparrow ell - ell'-uk sscmSg leftfracell-uk right + sscmGg ell-uk MGleichungF_uparrow ell - ell'-F_uparrow uk sscmSg ell -sscmSg uk + sscmGg ell-sscmGguk MGleichungsscmSg uk +sscmGg uk -F_uparrowuk sscmSg ell + sscmGg ell-F_uparrow ell-ell' MGleichungsscmS+sscmG-F_uparrow uk sscFS ell + sscFG ell-F_uparrow ell-ell' MGleichunguk fracsscmSgell + sscmGgell-F_uparrowell-ell'sscmSg+sscmGg-F_uparrow % PHYSMATH % Der Drehpunkt ist solqtyxfracsscmSgell + sscmGgell-F_uparrowell-ell'sscmSg+sscmGg-F_uparrowmsn*ncgn*ln+*mgn*ncgn*ln-*Fon*ln-lprn/*msn*ncgn+mgn*ncgn-Fonm al x xf nprv fracmsncgl+mgncgl-Fol-lprqtymsncg+mgncg-Fo prv fracmsncgl+mgncglqtymsncg+mgncg-Fo nonumber &qquad + frac-Fol-lprqtymsncg+mgncg-Fo x Tecx- vom anderen Ende entfernt. center tikzpicture filldrawcolorblack fillblack!!white rectangle .; filldrawcolorblack .. circle .cm; drawsnakebrace darkred .-.---.; drawsnakebrace darkgreen -. -- nodebelowell ++-; drawsnakebrace darkgreen . -- nodeaboveell' ++; drawsnakebrace orange .. -- nodeaboveell - ell' - x.; drawsnakebrace orange -. -- nodebelowfracell-x.-.; nodedarkred at .-. x; draw ---.; drawthick colorblack fillorange .-. rectangle .-.; drawthick- latex colorblue --. nodeabove darkgreenF_uparrow; drawthick- latex colordarkgreen ---. nodebelow darkgreensscFG; drawthick- latex colordarkgreen ---. nodebelow darkgreensscFS; tikzpicture center
A mass of mO is attached to one of a rotatably mounted rod mSO with lSO in length. lFO from this same FO are acting on the rod in upward direction holding the rod in equilibrium. How far from the other is the pivot po see sketch? center tikzpicture filldrawcolorblack fillblack!!white rectangle .; filldrawcolorblack .. circle .cm; drawsnakebrace .-.---.; node at .-. ?; draw ---.; drawthick colorblack fillorange .-. rectangle .-.; drawthick- latex colorblue --.; tikzpicture center
Solution:
newqtymskg newqtyl.m newqtymg.kg newqtylprm newqtyFoN % unknownx % DrehmomentSchritte % PGleichungM_uparrow sscMS + sscMG PGleichungF_uparrow ell_uparrow sscFS sscellS + sscFG sscellG PGleichungF_uparrow ell - ell'-uk sscmSg leftfracell-uk right + sscmGg ell-uk MGleichungF_uparrow ell - ell'-F_uparrow uk sscmSg ell -sscmSg uk + sscmGg ell-sscmGguk MGleichungsscmSg uk +sscmGg uk -F_uparrowuk sscmSg ell + sscmGg ell-F_uparrow ell-ell' MGleichungsscmS+sscmG-F_uparrow uk sscFS ell + sscFG ell-F_uparrow ell-ell' MGleichunguk fracsscmSgell + sscmGgell-F_uparrowell-ell'sscmSg+sscmGg-F_uparrow % PHYSMATH % Der Drehpunkt ist solqtyxfracsscmSgell + sscmGgell-F_uparrowell-ell'sscmSg+sscmGg-F_uparrowmsn*ncgn*ln+*mgn*ncgn*ln-*Fon*ln-lprn/*msn*ncgn+mgn*ncgn-Fonm al x xf nprv fracmsncgl+mgncgl-Fol-lprqtymsncg+mgncg-Fo prv fracmsncgl+mgncglqtymsncg+mgncg-Fo nonumber &qquad + frac-Fol-lprqtymsncg+mgncg-Fo x Tecx- vom anderen Ende entfernt. center tikzpicture filldrawcolorblack fillblack!!white rectangle .; filldrawcolorblack .. circle .cm; drawsnakebrace darkred .-.---.; drawsnakebrace darkgreen -. -- nodebelowell ++-; drawsnakebrace darkgreen . -- nodeaboveell' ++; drawsnakebrace orange .. -- nodeaboveell - ell' - x.; drawsnakebrace orange -. -- nodebelowfracell-x.-.; nodedarkred at .-. x; draw ---.; drawthick colorblack fillorange .-. rectangle .-.; drawthick- latex colorblue --. nodeabove darkgreenF_uparrow; drawthick- latex colordarkgreen ---. nodebelow darkgreensscFG; drawthick- latex colordarkgreen ---. nodebelow darkgreensscFS; tikzpicture center