The acceleration of the bucket is required.
The acceleration of the bucket is \(1.793\ \text{m/s}^2\) upwards.
\(F_1\) = 115 N
\(F_2\) = 105 N
\(F_g\) = Weight of bucket = 186 N
\(g\) = Acceleration due to gravity = \(9.81\ \text{m/s}^2\)
\(m\) = Mass of bucket
\(a\) = Acceleration of bucket
Mass of the bucket is
\(F_g=mg\\\Rightarrow m=\dfrac{F_g}{g}\\\Rightarrow m=\dfrac{186}{9.81}\)
The force balance of the system is
\(F_1+F_2=F_g+F\\\Rightarrow F_1+F_2=F_g+ma\\\Rightarrow a=\dfrac{F_1+F_2-F_g}{m}\\\Rightarrow a=\dfrac{115+105-186}{\dfrac{186}{9.81}}\\\Rightarrow a=1.793\ \text{m/s}^2\)
The acceleration of the bucket is \(1.793\ \text{m/s}^2\) upwards.
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