Fysik opgaver Impuls (Rep)

Indholdsfortegnelse

1 Opgave 8.1
2 Opgave 8.2
3 Opgave 8.3
4 Opgave 8.4
5 Opgave 8.5

Opgave 8.1

$LaTex: \begin{eqnarray} F &=& -50N\\ m &=& 20kg\\ t &=& 4 s\\ a &=& \frac{F}{m} = -2,5 \frac{m}{s^2}\\ v_0 &=& a \cdot t = 10 \frac{m}{s}\\ \Delta P &=& m\cdot v_0 = 200 Ns\\ \end{eqnarray}$

Opgave 8.2

A: $LaTex: \begin{eqnarray} m &=& 850 kg\\ v &=& 40 \frac{km}{h} = 11,11\frac{m}{s}\\ t &=& 0,15 s\\ a &=& \frac{v}{t} = 74,07 \frac{m}{s^2}\\ F &=& m\cdot a = 62,96 kN\\ \end{eqnarray}$

B: $LaTex: \begin{eqnarray} a &=& 74,07 \frac{m}{s^2}\\ \end{eqnarray}$

C: $LaTex: \begin{eqnarray} s &=& -\frac{1}{2}\cdot a \cdot t^2 + v_0\cdot t = 2,5 m\\ \end{eqnarray}$

Opgave 8.3

$LaTex: \begin{eqnarray} v &=& 100 \frac{km}{t} = 27,77 \frac{m}{s}\\ t &=& 0,02 s\\ m &=& 0,15 kg\\ a &=& \frac{v}{t}\\ F &=& m\cdot a = 208,33 N\\ \end{eqnarray}$

Opgave 8.4

A: $LaTex: \begin{eqnarray} m &=& 500g = 0,5kg\\ v &=& 3,8 \frac{m}{s}\\ t &=& 0,03 s\\ a &=& \frac{v}{t} = 126,67 \frac{m}{s^2}\\ \Delta P &=& m\cdot v = 1,9 Ns\\ \end{eqnarray}$

B: $LaTex: \begin{eqnarray} F &=& m\cdot a = 63,33N\\ \end{eqnarray}$

C: $LaTex: \begin{eqnarray} s &=& -\frac{1}{2}\cdot -a \cdot t^2 + v_0\cdot t = 0,171 m\\ \end{eqnarray}$

Opgave 8.5

A: $LaTex: \begin{eqnarray} m_{projektil} &=& 20g = 0,02 kg\\ m_{pistol} &=& 0,87 kg\\ s &=& 10 cm = 0,1 m\\ v_{projektil} &=& 600 \frac{m}{s}\\ P_{projektil} &=& m_{projektil}\cdot v_{projektil} = 12 Ns\\ P_{pistol} &=& P_{projektil} = m_{pistol} \cdot v_{pistol}\\ &\downarrow &\\ v_{pistol} &=& \frac{P_{projektil}}{m_{pistol}} = 13,79 \frac{m}{s}\\ \end{eqnarray}$

B: $LaTex: \begin{eqnarray} a_{projektil} &=& \frac{v_{projektil}^2}{s\cdot 2} = 1,8\cdot 10^6\frac{m}{s^2}\\ \end{eqnarray}$

C: $LaTex: \begin{eqnarray} t &=& \frac{v_{projektil}}{a_{projektil}} = 0,333 \cdot 10^{-3} s\\ F_{pistol} &=& \frac{P_{pistol}}{t} = 36 kN\\ \end{eqnarray}$