# Physics Tetherball Problem.?

I am given the mass of the ball, the length of the rope, and the speed the ball travels. I am asked for the angle and the tension force. I'm not sure how to do this question without the radius.

Any help is appreciated!

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• for the moving object, force acting will be centripetal force which is given by f = mv’2 /r, where “r” is the radius of the circle and it will be equal to length of the string in this case. Further what is the angle you asked for,Iam not sure.

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• If θ is string’s angle to vertical, the radius (of ball’s horizontal circular path) is Lsinθ.

In vertical direction: Tcosθ = mg (equation 1)

In horizontal direction: Tsinθ = mv²/r = mv²/(Lsinθ)

Tsin²θ =  mv²/L (equation 2)

Then do some messy algebra to solve for θ and T.

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• Anonymous
1 month ago

(m v^2 / r) sin@ = m g cos@

where

r = L cos@

then

(m v^2 / L) tan@ = m g cos@

or

A tan@ = B cos@

where

A = m v^2 / L

B = m g

then

(A/B)^2 tan@^2 = cos@^2

taking into account that

cos@^2 = 1 / (1+ tan@^2)

on obtain

(A/B)^2 tan@^2 = 1 / (1 + tan@^2)

tan@^2 + (A/B)^2 tan@^4 - 1 = 0

or

x + (A/B) x^2 - 1 = 0

where

x = tan@^2

solve for x and find tan@^2 and then tan@ and @

tension is

T = (m v^2 / r) cos@ = m g sin@

r = L cos@

then

T = m v^2 / L + m g sin@

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