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a bucket of mass 2kg is whirled in a vertical circle of radius 1.20M. at the lowest point of its motion the tension in the rope supporting the bucket is 25N. find the speed of the bucket

Respuesta :

skyluke89

The speed of the bucket is 1.8 m/s

Explanation:

The bucket is in circular motion, therefore the net force acting on it is equal to the centripetal force:

[tex]F=m\frac{v^2}{r}[/tex]

where

m = 2 kg is the mass of the bucket

v is its speed

r = 1.20 m is the radius of the circle

At the lowest point of motion, there are two forces acting on the bucket:

  • The tension in the rope, T = 25 N, upward (same direction as the centripetal force, acting towards the centre of the circle)
  • The force of gravity, [tex]mg[/tex], where [tex]g=9.8 m/s^2[/tex] is the acceleration of gravity

Therefore the equation of motion for the bucket is:

[tex]T-mg=m\frac{v^2}{r}[/tex]

And solving for v, we find the speed of the bucket:

[tex]v=\sqrt{r(\frac{T}{m}-g)}=\sqrt{(1.20)(\frac{25}{2}-9.8)}=1.8 m/s[/tex]

Learn more about circular motion:

brainly.com/question/2562955

brainly.com/question/6372960

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