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