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The weight of a bucket is 186 N. The bucket is being raised by two ropes. The free-body diagram shows the forces acting on the bucket.


The acceleration of the bucket, to the nearest tenth, is
___ m/s2.

The weight of a bucket is 186 N. The bucket is being raised by two ropes. The free-body diagram shows the forces acting on the bucket. The acceleration of the b class=

Answer :

pooptart
Fnet=(115+106)-186= 34 N

mass=Force/g= 186N/9.8m/s^2 = 18.98 kg

a=fnet/mass => 34N/18.98kg = 1.79 m/s^2

so A= 1.8m/s^2
boffeemadrid

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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