Uniform Circular Motion

[MDwannabe7]

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A 1kg ball is swung around in a 90 cm circle at an angle of 10 degrees below the horizontal. What is the tension in the string?

How would you go about solving this problem?

 

[andafoo]

Taking a quick look I'd say you use the formula:

F=mv^2/r

That will give you one component (the horizontal), and the vertical is just the weight.

If that ain't clear lemme know!

 

[lixxx669]

T=mg/sin10degree

draw force diagram, there are only two force on the object: T and G
the total force F (combine vector T and vector G) would be pointing to the center of the circle, then you can find that T, G and F form a right triangle, with G/F=tg10, G/T=sin10

 

[andafoo]

.

 

[silverlion]

Is the answer mgsin10?

 

[silverlion]

I dont think there is any need for mv^2./r for this. A simple resolution of the mg vector should give the answer. one component of the vector is opposite to T and the other is perpendicular to it. The one that is opposite is equal to the Tension.

And if the centripetal force was asked in the question then again you would have to use the component of T that would be responsible for it and not the entire value of T. I hope you see this. It is because the circular path is not actually one that has a radius of 90 cms (the length of the string) but a smaller circle because the rotation is 10 degrees below the horizontal.

The value of r of the smaller circle would be less than the length of the string (less than 90 cms). So, r = (90*cos10) cms.

I'm not sure if I am right because physics is not my forte...Do you have the answer to the question though. Is T=mgsin10?