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5. Sandor fills a bucket with water and whirls it in a vertical circle to demonstrate that the
water will not spill from the bucket at the top of the loop. If the length of the rope from his
hand to the centre of the bucket is 1.24 m, what is the minimum tension in the rope (at the
top of the swing)? How slow can he swing the bucket? Explain your answer.

Respuesta :

Given that,

radius = 1.24 m

According to question,

The rope cannot push outwards. It must always have some slight tension or the bucket will fall.

We need to calculate the tension in the rope

At the top the force of gravity is

[tex]F=mg[/tex]

The force needed to move the bucket in a circle is centripetal force.

So, if mg is ever greater than centripetal force then the bucket and the contents will start to fall.

The rope have a tension of less than zero.

We need to calculate the velocity of swing bucket

Using centripetal force

[tex]F=\dfrac{mv^2}{r}[/tex]

[tex]mg=\dfrac{mv^2}{r}[/tex]

[tex]g=\dfrac{v^2}{r}[/tex]

[tex]v^2=gr[/tex]

[tex]v=\sqrt{gr}[/tex]

Put the value into the formula

[tex]v=\sqrt{9.8\times1.24}[/tex]

[tex]v=3.49\ m/s[/tex]

Hence, The minimum tension in the rope is less than zero .

The bucket swings with the velocity of 3.49 m/s.

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