Mechanics - 8

Find the sum of the magnitudes of the acceleration of the blocks \(a \text{ m/s}^2\), tension in the string \(T \text{ N}\), frictional force acting on \(A\) by the inclined surface \(f_A \text{ N}\) and frictional force acting on \(B\) by the inclined surface \(f_B \text{ N}\). Give your answer to one decimal.

Assumptions and Details:

  • The coefficient of friction between the inclined surface and block \(A\) is \(\mu_A = 0.2\) and that between the inclined surface and block \(B\) is \(\mu_B = 0.1\).
  • The string is massless and inextensible.
  • The pulley is massless and there is no friction in the pulley and with the string.
  • Mass of block \(A\), \(m_A = \text{3 kg}\)
  • Mass of block \(B\), \(m_B = \text{5 kg}\)
  • Angle of incline, \(\theta = \sin^{-1} \dfrac35\)
  • Acceleration due to gravity, \(g = \text{10 m/s}^2\)

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