Ablock with mass m1 of 2.85 kg moves along an inclined plane that makes an angle of 40.0 degrees with the horizontal, and is connected by a string that passes over a pulley to a second block that has a mass m2 of 4.75 kg. both blocks are composed of the same material. the string and pulley have negligible mass and the pulley exerts no friction force on the string. the coefficient of kinetic friction between the plane and the block is 0.55. determine the magnitude and direction of the acceleration.

Explanation:

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 .

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