Fysik Mekanik Opgaver


Indholdsfortegnelse

Opgave 1

LaTex: \begin{eqnarray} f_{frem} &=& 75 N\\ f_{x} &=& cos(40) \cdot f_{frem} = 57,45 N\\ S &=& 20 m\\ m &=& 51,5 kg\\ A &=& f_{x}\cdot S = 1149,07J\\ \Delta E_{kin} &=& \frac{1}{2}\cdot m\cdot v_{slut}^2 = A = 1149,07J\\ v_{slut} &=& \sqrt{\frac{\Delta E_{kin}}{\frac{1}{2}\cdot m}} = 6,68 \frac{m}{s} \end{eqnarray}

Opgave 2

LaTex: \begin{eqnarray} f_{frem} &=& 25,5 N\\ S &=& 8 m\\ A &=& f_{frem}\cdot S = 204J\\ v_1 &=& 12\frac{m}{s}\\ m &=& 6,2 kg\\ E_{kin_1} &=& \frac{1}{2}\cdot m\cdot v_1^2 = 446,4 J\\ E_{kin_0} &=& E_{kin_1} - A = 242,4J\\ v_0 &=& \sqrt{\frac{E_{kin_0}}{\frac{1}{2}\cdot m}} = 8,84 \frac{m}{s}\\ a &=& \frac{v_1^2-v_0^2}{2 \cdot S} = 4,12\frac{m}{s^2}\\ t &=& \frac{v_1-v_0}{a} = 0,77s \end{eqnarray}

Opgave 3

LaTex: \begin{eqnarray} h_0 &=& 8m\\ h_1 &=& h_0\cdot (1-\frac{15}{100}) = 6,8 m\\ h_n &=& 1,8m\\ n_{hop} &=& \frac{log(\frac{h_n}{h_0})}{log(1-\frac{15}{100})} = 9,17 \approx 10 \end{eqnarray}

Opgave 4

LaTex: \begin{eqnarray} h_0 &=& 10,5 + \frac{0,6}{2} - cos(65^{\circ}) \cdot (10,5 m +\frac{0,6}{2}) = 6,24 m\\ E_{mek_0} &=& E_{pot_0} = h_0\cdot g\cdot m\\ h_1 &=& 10,5 + \frac{0,6}{2} - cos(10^{\circ}) \cdot (10,5 m + \frac{0,6}{2}) = 0,16m\\ E_{pot_1} &=& h_1\cdot g\cdot m\\ \Delta E_{kin} &=& E_{mek_0} - h_1\cdot g\cdot m\\ v &=&\sqrt{\frac{\Delta E_{kin}}{\frac{1}{2}\cdot m}} = 10,93 \frac{m}{s} \end{eqnarray}

Opgave 5

LaTex: \begin{eqnarray} p &=& 20 kW\\ &=& 20000 W\\ v &=& 90 \frac{km}{h}\\ &=& \frac{90}{3,6} = 25 \frac{m}{s}\\ F_{frem} &=& \frac{p}{v}\\ F_{frem} &=& 800 N\\ F_{res} &=& F_{frem} - F_{gnidning}\\ &=& 0\\ F_{gnidning} &=& F_{frem}\\ &=& 800N\\ m &=& 800 kg\\ a &=& \frac{F_{gnidning}}{m}\\ &=& 1 \frac{m}{s^2}\\ v_1 &=& 60\frac{km}{t}\\ &=& \frac{60}{3,6} = 16,667 \frac{m}{s}\\ t &=& \frac{v_1-v}{a}\\ &=& 8,33s\\ \end{eqnarray}

Opgave 6

LaTex: \begin{eqnarray} h &=& 400m\\ \frac{E_{pot}}{s} &=& 50000000\cdot (1+1-0,85)\\ &=& 57500000\\ &=& h\cdot g\cdot m\\ m &=& \frac{E_{pot}}{g\cdot h}\\ &=& 14638,49 \frac{kg}{s} \end{eqnarray}

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