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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