Impuls

Zentraler elastischer Stoβ

$$\sum^{2}_{n=1}p =p_{1}+p_{2}=m_{1}\cdot v_{1}+m_{2}\cdot v_{2}$$ $$\sum^{2}_{n=1}p^{\prime }=p^{\prime }_{1}+p^{\prime }_{2}=m_{1}\cdot v^{\prime }_{1}+m_{2}\cdot v^{\prime }_{2}$$ $$\sum^{2}_{n=1} E_{kin}=E_{kin_{1}}+E_{kin_{2}}=\frac{1}{2} \cdot m_{1}\cdot v^{2}_{1}+\frac{1}{2} \cdot m_{2}\cdot v^{2}_{2}$$ $$\sum^{2}_{n=1} E^{\prime }_{kin}=E^{\prime }_{kin_{1}}+E^{\prime }_{kin_{2}}=\frac{1}{2} \cdot m_{1}\cdot v^{2^{\prime }}_{1}+\frac{1}{2} \cdot m_{2}\cdot v^{2^{\prime }}_{2} $$ $$\sum \overrightarrow{p} =\sum \overrightarrow{p^{\prime }} $$ $$\sum E_{mech}=\sum E^{\prime }_{mech}$$

Zentraler unelastischer Stoβ

$$\sum^{2}_{n=1}p =p_{1}+p_{2}=m_{1}\cdot v_{1}+m_{2}\cdot v_{2}$$ $$\sum^{2}_{n=1} p^{\prime }=p^{\prime }_{1}+p^{\prime }_{2}=\left( m_{1}m_{2}\right) \cdot v^{\prime }$$ $$\sum^{2}_{n=1} E_{mech}=E_{kin_{1}}+E_{kin_{2}}=\frac{1}{2} m_{1}v^{2}_{1}+\frac{1}{2} m_{2}v^{2}_{2}$$ $$\sum^{2}_{n=1} E^{\prime }_{mech}=\frac{1}{2} \left( m_{1}m_{2}\right) \cdot v^{2^{\prime }}$$ $$\sum \overrightarrow{p} =\sum \overrightarrow{p^{\prime }} $$ $$\sum E_{mech}>\sum E^{\prime }_{mech}$$

Spezielle Formel

$$\overrightarrow{p} =\overrightarrow{p^{\prime }} $$ $$\Longleftrightarrow m_{1}\overrightarrow{v_{1}} +m_{2}\overrightarrow{v_{2}} = \left( m_{1}+m_{2}\right) \overrightarrow{v^{\prime }} $$ $$\overrightarrow{v^{\prime }} =\frac{m_{1}\overrightarrow{v_{1}} +m_{2}\overrightarrow{v_{2}} }{m_{1}+m_{2}} $$

Impulserhaltungssatz

Im abgeschlossenen System

$$\Sigma \overrightarrow{p} =\Sigma \overrightarrow{p^{\prime }} $$