Naloge iz energije

[Aniviller]

Iz prvih dveh izrazis koeficient. Potem lepo izracunas hitrost v tretjem primeru.

[Rokerda]

torej
\(k_t= \frac{F_1 - mg sin \alpha}{mg cos \alpha}\)
\(k_t= \frac{F_2 + mg sin \alpha}{mg cos \alpha}\)

to vnesem v \(F_3 = mgk_t\)?
ne pridem čisto do želenega razultata

[Rokerda]

mja....

\(k_t = k_t\)
\(\frac{F_1 - mg sin \alpha}{mg cos \alpha} = \frac{F_2 + mg sin \alpha}{mg cos \alpha}\)
\(F_1 - mgsin \alpha = F_2 + mg sin \alpha\)
\(F_1 = F_2 + 2mgsin \alpha\)

naj bi tole kaj pomagalo....

[Rokerda]

še neki sm ugotovu

\(F_1 = F_2 + 2mgsin \alpha\)
\(F_1 v_1 = F_2 v_2\)
\((F_2 + 2mgsin \alpha ) v_1 = F_2 v_2\)
\(F_2 v_1 + 2mgsin \alpha v_1 = F_2 v_2\)
\(2mgsin \alpha v_1 = F_2 v_2 - F_2 v_1\)
\(2mgsin \alpha v_1 = F_2 (v_2 - v_1)\)
\(F_2 = \frac{2mgsin \alpha v_1}{(v_2 - v_1)}\)

potem \(F_2 v_2 = F_3 v_3\)
\(\frac{2mgsin \alpha v_1}{(v_2 - v_1)} = mgk_t v_3\)
\(\frac{2sin \alpha v_1 v_2}{(v_2 - v_1)}= k_t v_3\)
\(k_t v_3= 11,57\)

sm že bližje
\(\frac{F_1 - mg sin \alpha}{mg cos \alpha} v_3 = 11,57\) namesto \(k_t\) vstavim \(k_t= \frac{F_1 - mg sin \alpha}{mg cos \alpha}\)
\(\frac{F_2 + 2mgsin \alpha - mg sin \alpha}{mg cos \alpha} v_3 = 11,57\) namest \(F_1\) vstavim \(F_1 = F_2 + 2mgsin \alpha\)
\(\frac{\frac{2mgsin \alpha v_1}{(v_2 - v_1)} + 2mgsin \alpha - mg sin \alpha}{mg cos \alpha} v_3 = 11,57\)

prava zmeda....sem vsaj na pravi poti?

[drevo]

\(P_1 = P_2\)
\(mg\left (sin\alpha + k_tcos\alpha\right ) v_1= mg\left (k_t cos\alpha - sin\alpha\right ) v_2\)
\(\left (sin\alpha + k_t cos\alpha\right ) v_1= \left (k_t cos\alpha - sin\alpha\right ) v_2\)
\(sin\alpha v_1 + k_t cos\alpha v_1 = k_tcos\alpha v_2 - sin\alpha v_2\)
\(k_t = \frac{-sin\alpha\left (v_2 + v_1\right )}{cos\alpha\left (v_1 - v_2\right)}\)

Pol daš pa ta \(k_t\) v enačbo \(P_2 = P_3\) iz katere \(v_3\) ven izračunaš. Upam, da se nism kje zmotu

[Rokerda]

najlepša hvala

[Rokerda]

neki mi ne pride prav....noro

\(P_2 = P_3\)
\(F_2 v_2 = F_3 v_3\)
\(mg(k_t cos \alpha - sin \alpha) v_2 = mgk_t v_3\)
\(( \frac{-sin\alpha\left (v_2 + v_1\right )}{cos\alpha\left (v_1 - v_2\right)} cos \alpha - sin \alpha) v_2 = \frac{-sin\alpha\left (v_2 + v_1\right )}{cos\alpha\left (v_1 - v_2\right)} v_3\)
\(( \frac{-sin \alpha (v_1 + v_2)}{v_1 - v_2} - sin\alpha) v_2 = -tg \frac{v_1 + v_2}{v_1-v_2} v_3\)
\(-sin\alpha \frac{v_1+v_2}{v_1-v_2}v_2 - sin\alpha v_2 = -tg \frac{v_1 + v_2}{v_1-v_2} v_3\)
\(-sin \alpha \left v_2 \left (\frac{v_1+v_2}{v_1-v_2} + 1) = -tg \frac{v_1 + v_2}{v_1-v_2} v_3\)
\(\frac{-sin \alpha \left v_2 \left (\frac{v_1+v_2}{v_1-v_2} + 1)}{-tg \frac{v_1 + v_2}{v_1-v_2}}=v_3\)
\(v_3=\frac{cos\alpha \left (\frac{v_1+v_2}{v_1-v_2} + 1)}{\frac{v_1 + v_2}{v_1-v_2}}\)
\(v_3=\frac{cos10° (\frac{20+50}{20-50} +1)}{\frac{20+50}{20-50}}\)
\(v_3=\frac{cos10° (-1,33)}{-2,33}\)
\(v_3=°\frac{1,33cos10}{2,33}=0,56 \frac{m}{s}\)

kaj je tuki narobe? moralo bi priti \(28,14 \frac{m}{s}\)

hvala

[Majstor]

neki mi ne pride prav....noro

\(P_2 = P_3\)
\(F_2 v_2 = F_3 v_3\)
\(mg(k_t cos \alpha - sin \alpha) v_2 = mgk_t v_3\)
\(( \frac{-sin\alpha\left (v_2 + v_1\right )}{cos\alpha\left (v_1 - v_2\right)} cos \alpha - sin \alpha) v_2 = \frac{-sin\alpha\left (v_2 + v_1\right )}{cos\alpha\left (v_1 - v_2\right)} v_3\)
\(( \frac{-sin \alpha (v_1 + v_2)}{v_1 - v_2} - sin\alpha) v_2 = -tg \frac{v_1 + v_2}{v_1-v_2} v_3\)
\(-sin\alpha \frac{v_1+v_2}{v_1-v_2}v_2 - sin\alpha v_2 = -tg \frac{v_1 + v_2}{v_1-v_2} v_3\)
\(-sin \alpha \left v_2 \left (\frac{v_1+v_2}{v_1-v_2} + 1) = -tg \frac{v_1 + v_2}{v_1-v_2} v_3\)
\(\frac{-sin \alpha \left v_2 \left (\frac{v_1+v_2}{v_1-v_2} + 1)}{-tg \frac{v_1 + v_2}{v_1-v_2}}=v_3\)
\(v_3=\frac{cos\alpha \left (\frac{v_1+v_2}{v_1-v_2} + 1)}{\frac{v_1 + v_2}{v_1-v_2}}\)
\(v_3=\frac{cos10° (\frac{20+50}{20-50} +1)}{\frac{20+50}{20-50}}\)
\(v_3=\frac{cos10° (-1,33)}{-2,33}\)
\(v_3=°\frac{1,33cos10}{2,33}=0,56 \frac{m}{s}\)

kaj je tuki narobe? moralo bi priti \(28,14 \frac{m}{s}\)

hvala

tanges v števcu je malo zašel ane

lp

[Rokerda]

ja moralo bi biti \(\frac{sin}{cos}\) kar pa je enako \(tg\)

a ne?

[drevo]

Iz osme v deveto vrstico si \(v_2\) izgubil. Mogoče je še kaj drugega.. Meni pride \(k_t\) približno \(0.4\) in potem hitrost približno \(28\frac{m}{s}\). V tem primeru je bolj praktično, če \(k_t\) kar izračunaš in vstaviš, namesto da vlečeš tisto kačo s seboj.

[Rokerda]

ja lol, to je to
\(v_2\) sem pozabil

najlepša hvala