Mechanics - 8

Find the sum of the magnitudes of the acceleration of the blocks a m/s2a \text{ m/s}^2, tension in the string T NT \text{ N}, frictional force acting on AA by the inclined surface fA Nf_A \text{ N} and frictional force acting on BB by the inclined surface fB Nf_B \text{ N}. Give your answer to one decimal.

Assumptions and Details:

  • The coefficient of friction between the inclined surface and block AA is μA=0.2\mu_A = 0.2 and that between the inclined surface and block BB is μB=0.1\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 AA, mA=3 kgm_A = \text{3 kg}
  • Mass of block BB, mB=5 kgm_B = \text{5 kg}
  • Angle of incline, θ=sin135\theta = \sin^{-1} \dfrac35
  • Acceleration due to gravity, g=10 m/s2g = \text{10 m/s}^2

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