Physics

Velocity V of a streched string depends on tension T and mass per unit length M of the string. Create an equation for velocity V using dimensional analysis?

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  1. v = k T^a M^b

    m/s = (kg m/s^2)^a (kg/m)^b

    m^1/s^1 = kg^a kg^b * m^a /m^b * 1/s^2a

    looks like a = .5 for s^-1 = s^-2a

    b must be -a for kg^(a+b) =kg^0 = 1
    so b = -.5

    now m
    m^1 = ?? m^.5/m^-.5 = m^(.5+.5)= m^1 yes

    so
    v = k T^.5 M^-.5
    v = k sqrt (T/M)

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