Fysik opgaver tog (Rep)

Nogle repitations opgaver, ikke relateret til tog projektet.

Indholdsfortegnelse

Opgave 1

a
LaTex: \begin{eqnarray} v_1 &=& 108 \frac{km}{h} = 30 \frac{m}{s}\\ t &=& 30 s\\ a &=& \frac{v_1}{t} = 1 \frac{m}{s^2}\\ s_1 &=& \frac{1}{2}\cdot a\cdot t^2 = 450 m\\ \end{eqnarray}
b
LaTex: a = \frac{v_1}{t} = 1 \frac{m}{s^2}
c
LaTex: \begin{eqnarray} a &=& 0,6 \frac{m}{s^2}\\ t &=& 20 s\\ v &=& a\cdot t + v_1 = 42 \frac{m}{s} = 151,2 \frac{km}{h}\\ \end{eqnarray}
d
LaTex: \begin{eqnarray} s &=& \frac{1}{2} \cdot a\cdot t^2 +v_1\cdot t + s_1 = 1170 m\\ \end{eqnarray}

Opgave 2

a
LaTex: \begin{eqnarray} m &=& 36000 \cdot 6 = 216000 kg\\ E_{kin_0} &=& \frac{1}{2}\cdot m\cdot v_1^2 = 97,2 MJ\\ E_{kin_1} &=& \frac{1}{2}\cdot m\cdot v^2 = 190,512 MJ\\ \Delta E_{kin} &=& E_{kin_1} - E_{kin_0} = 93,312 MJ\\ \end{eqnarray}
b
LaTex: \begin{eqnarray} v_{tog} &=& 160\\ v_{bil} &=& 110\\ \Delta v &=& v_{tog}- v_{bil} = 50 \frac{km}{h} = 13,889 \frac{m}{s}\\ l_{tog} &=& 108 m\\ t &=& \frac{l_{tog}}{\Delta v} = 7,776 s\\ \end{eqnarray}
c
LaTex: \begin{eqnarray} \mu = 0,18\\ F_n &=& m\cdot -g\\ F_g &=& F_n \cdot \mu\\ a &=& \frac{F_g}{m} = -1,7676 \frac{m}{s^2}\\ \end{eqnarray}

Opgave 3

a
LaTex: \begin{eqnarray} m_{vogn} &=& 31 Mg\\ F_g &=& m_{vogn}\cdot g = 304,42 kN\\ \end{eqnarray}
b
LaTex: \begin{eqnarray} h &=& 0,75 m\\ A &=& h\cdot F_g &=& 228,315 kJ\\ \end{eqnarray}
c
LaTex: \begin{eqnarray} E_{pot} &=& m\cdot g\cdot h = 228,315 kJ\\ \end{eqnarray}
d
LaTex: \begin{eqnarray} t &=& 25 s\\ P &=& \frac{A}{t} = 9,133 kW\\ \end{eqnarray}
e
LaTex: \begin{eqnarray} P_{til} &=& 10,7 kW\\ \eta &=& \frac{P}{P_{til}} \cdot 100 = 85,35\percent\\ \end{eqnarray}

Opgave 4

a
LaTex: \begin{eqnarray} m &=& 200 kg\\ \mu &=& 0,5\\ F_g &=& m \cdot g\\ F_n &=& -F_g\\ F_{gniding} &=& \mu\cdot F_n\\ F_{start} &=& -F_{gniding} = 982 N\\ \end{eqnarray}
b
LaTex: \begin{eqnarray} a &=& 0,8 \frac{m}{s}\\ F_{res} &=& a\cdot m = 160 N\\ F_{til} &=& F_{start} + F_{res} = 1142 N\\ \end{eqnarray}
c
LaTex: \begin{eqnarray} F_{tot} &=& F_{res} = a\cdot m = F_{til} + F_{gnidning} = 160 N\\ \end{eqnarray}
d
LaTex: \begin{eqnarray} t &=& 10 s\\ v &=& a \cdot t = 8 \frac{m}{s}\\ \end{eqnarray}
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