Two blocks are connected by a string over a pulley. The hanging block has a mass of 8-kg and the one on the plane has a mass of m2. If the coefficient of static friction is .8 what is the minimum mass that m2 must be in order for the objects to be in a state of static equilibrium.

Let f be force of friction on the blocks kept on inclined plane. T be tension in the string

For motion of block on the inclined plane in upward direction

T - m₁gsin40 - f = m₁a

f = μ m₁gcos40

For motion of hanging  block on  in downward direction

m₂g  - T = m₂ a

Adding to cancel T

m₂g - - m₁gsin40 -  μ m₁gcos40 = a ( m₁+m₂ )

a =   g (m₂ - - m₁sin40 -  μ m₁cos40) / ( m₁+m₂ )

Putting the values

a = 9.8 ( 4.75 - 2.12-1.045) / 7.6

2.04 m s⁻²

M₂ will go down and M₁ will go up with acceleration .

Explanation: