Fysik opgaver Galilei (Rep)


Indholdsfortegnelse

Opgave 1 - Galilei

A
LaTex: \begin{eqnarray} g &=& 9,81 \frac{m}{s^2}\\ t &=& 3,35 s\\ s &=& \frac{1}{2}\cdot g\cdot t^2 = 55,05 m\\ \end{eqnarray}
B
LaTex: \begin{eqnarray} m &=& 1,5 kg\\ E_{pot} &=& m\cdot g\cdot h = 810,01 J\\ \end{eqnarray}
C
LaTex: \begin{eqnarray} t &=& 2 s\\ v &=& g \cdot t\\ E_{kin} &=& \frac{1}{2}\cdot m\cdot v^2 = 288,71 J\\ \end{eqnarray}

Opgave 2 - Vandskiløberen

A
LaTex: \begin{eqnarray} m &=& 80 kg\\ v_0 &=& 60 \frac{km}{h} = 16,667 \frac{m}{s}\\ F_{modstand} &=& -110 N\\ a &=& \frac{F_{modstand}}{m} = -1,375\frac{m}{s^2}\\ \end{eqnarray}
B
LaTex: \begin{eqnarray} v &=& 6 \frac{km}{h} = 1,667 \frac{m}{s}\\ s &=& \frac{v^2-v_0^2}{2\cdot a} = 100 m\\ \end{eqnarray}

Opgave 3 - pumpen

A
LaTex: \begin{eqnarray} Pumpe &=& 2500 \frac{L}{min} = 41,667 \frac{L}{s}\\ \eta &=& 0,7\\ h &=& 9 m\\ \rho &=& 1 \frac{kg}{L}\\ P_{nytte} &=& \rho \cdot Pumpe \cdot h\cdot g\\ P_{effektiv} &=& \frac{P_{nytte}}{\eta} = 5,261 kW\\ \end{eqnarray}
B
LaTex: \begin{eqnarray} cos(\phi) &=& 0,82\\ \eta &=& 0,85\\ U &=& 400 V\\ P_{motor} &=& \frac{P_{effektiv}}{\eta}\\ I &=& \frac{P_{motor}}{\sqrt{3}\cdot U\cdot cos(\phi)} = 10,894 A\\ \end{eqnarray}

Opgave 4 - Klodsen

A
LaTex: \begin{eqnarray} m &=& 3 kg\\ v_0 &=& 2 \frac{m}{s}\\ F_{frem} &=& 37,5 N\\ t &=& 2,9 s\\ \mu &=& 0,47\\ F_g &=& m\cdot g\\ F_n &=& -F_g\\ F_{gnidning} &=& F_n\cdot \mu\\ F_{res} &=& F_{frem} + F_{gnidning}\\ a &=& \frac{F_{res}}{m} = 7,885 \frac{m}{s^2}\\ \end{eqnarray}
B
LaTex: \begin{eqnarray} v &=& a\cdot t + v_0 = 24,865 \frac{m}{s}\\ \end{eqnarray}
C
LaTex: \begin{eqnarray} a_{brems} &=& \frac{F_{gnidning}}{m}\\ s &=& \frac{-v^2}{2\cdot a_{brems}} = 66,979 m\\ \end{eqnarray}

Opgave 5 - brødristeren

A
LaTex: \begin{eqnarray} U_{samlet} &=& 230 v\\ R_{kedel} &=& 35 \Omega\\ R_{rister} &=& 75 \Omega\\ R_{samlet} &=& \frac{1}{\frac{1}{R_{rister}} + \frac{1}{R_{kedel}}} = 23,86\\ I_{samlet} &=& \frac{U}{R_{samlet}} = 9,638 A\\ \end{eqnarray}
B
LaTex: \begin{eqnarray} P_{samlet} &=& U_{samlet}\cdot I_{samlet} = 2,217 kW\\ \end{eqnarray}
C
LaTex: \begin{eqnarray} I_{samlet} =\frac{P_{samlet} + P_{kaffe}}{U} = 12,247 A\\ \end{eqnarray}
Sikringen vil brænde over da belastningen på den er større end 10 A.
Hentet fra "http://jopsen.dk/wiki/Fysik_opgaver_Galilei_%28Rep%29/"