Formeln auflösen
in Frage&Antwort
© bGeiring hGeiring v12 2013
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`v = s/t` `s = ?`
`v = s/t` |`*t`
`v*t = s`
`R = rho*s/A` `A = ?`
`rho`: lies rho
`R = rho*s/A` |`*A`
`R*A = rho*s` | : `R`
`A = rho*s/R`
`s = 1/2 a*t^2` `a = ?`
`s = 1/2 a*t^2` |`*2`
`2s = a*t^2` | : `t^2`
`(2s)/(t^2) = a`
`U = R*I` `R = ?`
`U = R*I` | : `I`
`U/I = R`
`W_"kin" = 1/2 m*v^2` `v = ?`
`W_"kin" = 1/2 m*v^2` |`*2`
`2 W_"kin" = m*v^2` | : `m`
`(2 W_"kin")/m = v^2` |`sqrt(\ )`
`sqrt((2 W_"kin")/m) = v`
Die zweite mathematische Lösung `-sqrt((2 W_"kin")/m) = v_2`
ist physikalisch meist sinnlos.
`U = W/Q` `W = ?`
`U = W/Q` `|*Q`
`U*Q = W`
`v = s/t` `t = ?`
`v = s/t` |`*t`
`v*t = s` | : `v`
`t = s/v`
`F = G*(m_1*m_2)/r^2` `m_1 = ?`
`F = G*(m_1*m_2)/r^2` | : G
`F/G = (m_1*m_2)/r^2` | : `m_2`
`F/(G*m_2) = m_1/r^2` `|*r^2`
`(F*r^2)/(G*m_2) = m_1`
`{:1/f:} = {:1/g:} + 1/b` `f = ?`
`{:1/f:} = {:1/g:} + 1/b` | auf einen Bruch bringen
`{:1/f:} = b/(bg) + g/(bg)`
`{:1/f:} = (b+g)/(bg)` | Kehrwert
`f = (bg) /(b+g)`
`m = m_0/sqrt(1-v^2 / c^2)` `v = ?`
`m = m_0/sqrt(1- v^2 / c^2)` `|*sqrt(\ )\ |` : m
`sqrt(1- v^2 / c^2) = m_0/m` `|()^2`
`1- v^2 / c^2 = m_0^2/m^2` `|+v^2/c^2-m_0^2/m^2`
`1- m_0^2/m^2 = v^2 / c^2` `|*c^2`
`(1- m_0^2/m^2)*c^2 = v^2` `|sqrt(\ )`
`sqrt(1- m_0^2/m^2)*c = v`
`{:1/f:} = {:1/g:} + 1/b`
also
`f = g + b`
Richtig?
Nein.
Man muss auf beiden Seiten den
Kehrwert nehmen, also
`f = 1 /({:1/g:} + 1/b)`
Weiterrechnen ergibt
`f = (bg) /(b+g)`