Mechanics - 10

Find the sum of the magnitudes of the acceleration of the blocks \(a \text{ m/s}^2\) and tension in the string \(T \text{ N}\).

Assumptions and Details:

  • Mass of block \(A\), \(m_A = \text{ 3 kg}\)
  • Mass of block \(B\), \(m_B = \text{5 kg}\)
  • \(\theta_1 = \sin^{-1} \dfrac45, \theta_2 = \sin^{-1} \dfrac35\)
  • Acceleration due to gravity, \(g = \text{10 m/s}^2\)
  • The string is massless and inextensible.
  • The pulley is massless and there is no friction between the blocks and the incline plane, in the pulley and with the string.

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