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A 1.6 kg mass and a 6 kg mass are connected by a massless string over a pulley that is in the shape of a solid wheel having a radius 0.13 m and mass 5.5 kg. Determine the linear acceleration of the blocks.

  • Physics -

    m₁a=- m₁g+T₁ …….(1)
    - m₂a=T₂- m₂g ……(2)
    Iε=(T₂-T₁)R => T₂-T₁ = Iε/R=Ia/R²
    If the wheel is disc I=mR²/2 =>
    T₂-T₁= Iε/R= mR²a/2R²=ma/2
    subtract (2) from (1)
    m₁a+ m₂a= - m₁g +T₁- T₂+m₂g.
    a(m₁+ m₂) = g(m₂-m₁) - (T₂-T₁)=
    = g(m₂-m₁) - ma/2.
    a(m₁+ m₂+m/2)= g(m₂-m₁)
    a= g(m₂-m₁)/(m₁+ m₂+m/2)

    (If the wheel is the hoop I=mR² =>
    T₂-T₁= Iε/R= mR²a/R²=ma)

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