The acceleration of the 50-kg carriage A in its smooth vertical guides is controlled by...

The acceleration of the 50-kg carriage A in its smooth vertical guides is controlled by the tension T exerted on the control cable which passes around the two circular pegs fixed to the carriage. Determine the value of T required to limit the downward acceleration of the carriage to 1.2 m/s2 if the coefficient of friction between the cable and the pegs is 0.20. (Recall the relation between the tensions in a flexible cable which is slipping on a fixed peg: T₂ = T₁e ^μβ.