Load B is moving down with velocity vb Determine the velocit

Load B is moving down with velocity vb. Determine the velocity and acceleration of crate A in terms of the motion of load B and the parameters shown.

P3.17-5) Load B is moving down with velocity VB crate A in terms of the motion of load B and the parameters shown. Il P3.17-5

Solution

The normal force on mass A is,

   N = Tsin@ - m_Ag

   N = T[h/S_A] - m_Ag

The horizontal force on the mass A is,

   Fx = T cos@

    m_A a = T [S_A/sqrt[S_A^2 + h^2]]

net force on the load B is,

    mBa = mBg - T

      T = mBg - mBa

Thus the acceleration:

       m_A a = T [S_A/sqrt[S_A^2 + h^2]]

       m_A a = [ mBg - mBa] [S_A/sqrt[S_A^2 + h^2]]

       m_A a = [S_A/sqrt[S_A^2 + h^2]] * mBg -[mBa] [S_A/sqrt[S_A^2 + h^2]]

then,

    a = { [S_A/sqrt[S_A^2 + h^2]] * mBg}/[ m_A +m_B [S_A/sqrt[S_A^2 + h^2]] ]

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velocity is,

    v = sqrt[2as] = sqrt[2s_A{{ [S_A/sqrt[S_A^2 + h^2]] * mBg}/[ m_A +m_B [S_A/sqrt[S_A^2 + h^2]] ]}]