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Math Help - Hard A-Level Question

  1. #1
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    Exclamation Hard A-Level Question

    A particle of mass 4kg rest on a smoothplane inclined at 60(degrees) to the horizontal. The particle is attached to one end of a light inelastic string which passes over a fixed smooth pulley at the top of the plane and carried a particle of mass 2kg at the other end.
    Find
    a)the acceleration of the system
    b)the tension in the string

    Thanks
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  2. #2
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    Quote Originally Posted by helpishere View Post
    A particle of mass 4kg rest on a smoothplane inclined at 60(degrees) to the horizontal. The particle is attached to one end of a light inelastic string which passes over a fixed smooth pulley at the top of the plane and carried a particle of mass 2kg at the other end.
    Find
    a)the acceleration of the system
    b)the tension in the string

    Thanks
    Hard A-Level Question-phys001.jpg

    F_1=m_1g \sin(\theta)-T=m_1a

    F_2=T-m_2g=m_2a

    Since the acceleration of the system is constant we can solve the above equations for "a" and set them equal to each other.

    g\sin(\theta)-\frac{T}{m_1}=\frac{T}{m_2}-g

    We can clear the fractions by multiplying by m_1m_2

    m_1m_2g\sin(\theta)-m_2T=m_1T-m_1m_2g

    m_1m_2g(1+\sin(\theta))=(m_1+m_2)T

    T=\frac{m_1m_2(1+\sin(\theta))}{m_1+m_2}

    Just plug in and finish from here.

    I hope this helps and good luck.
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