Opgave 3.68, 3.70, 3.71


Opgave 3.68

A
LaTex: \begin{eqnarray} m &=& 5 kg\\ r &=& 0,8m\\ T &=& \frac{35s}{10} = 3,5 s\\ \omega &=& \frac{2\cdot\pi}{T} = 1,795 s^{-1} \end{eqnarray}
B
LaTex: \begin{eqnarray} v &=& \omega\cdot r = 1,44 \frac{m}{s}\\ \end{eqnarray}
C
LaTex: \begin{eqnarray} a &=& \omega\cdot v = 2,59 \frac{m}{s^2}\\ \end{eqnarray}
D
LaTex: \begin{eqnarray} F &=& a\cdot m = 12,89N\\ \end{eqnarray}

Opgave 3.70

Billede:Opg370A.png

LaTex: \begin{eqnarray} \mu &=& 0,8\\ T &=& 2,3s\\ \omega &=& \frac{2\cdot\pi}{T} = 2,73 s^{-1}\\ F_g &=& F_{cen}\\ m\cdot \omega^2\cdot r &=& m\cdot g\cdot \mu\\ \omega^2\cdot r &=& g\cdot \mu\\ r &=& \frac{g\cdot \mu}{\omega^2} = 1,05m\\ \end{eqnarray}

Opgave 3.71

LaTex: \begin{eqnarray} m &=& 2 kg\\ r &=& 50 cm\\ L_s &=& 1,5 m\\ \end{eqnarray}

Billede:Opg371A.png

B
LaTex: \begin{eqnarray} F_g &=& g\cdot m = 19,61 N\\ \alpha &=& sin^{-1}\left(\frac{r}{L_s}\right) = 19,47^\circ\\ F_{snor} &=& \frac{F_g}{cos(\alpha)} = 20,8 N\\ \end{eqnarray}


C
LaTex: \begin{eqnarray} F_{cen} &=& -F_{snor}\cdot sin(\alpha) = 6,93 N\\ F_{cen} &=& -m\cdot\omega^2\cdot r \\ \omega &=& \sqrt{\frac{F_{cen}}{-m\cdot r}} = 2,63 s^{-1}\\ T &=& \frac{2\cdot\pi}{\omega} = 2,38s\\ \end{eqnarray}
Hentet fra "http://jopsen.dk/wiki/Opgave_3.68%2C_3.70%2C_3.71/"