A tetherball weighing 1 lb is pulled outward from the pole by a horizontal force u until the rope makes an angle of theta degrees with the pole
1. Determine the resulting tension in the rope and magnitude of u when theta = 30 degrees
2. Write the tension T in the rope and the magnitude of u as functions of theta
3. Determine the domains of the functions
4. Compare T and ||u|| as theta increases
I know that ||u|| = sqrt a^2+b^2 but I just don't know what the values of a and b are.
Thanks in advance!!!
Jennifer
I don't know if I understand.
I am assuming the magnitude of w is = 1??
If that is the case then in order to get the value of t (which is the tension) when angle is 30 degrees, I would use
t = 1/cos(30)
So now I have the t = 1.15.
Next -
Is this the formula to determine the magnitude of u??
If so, again assuming the magnitude of w is = 1 and the angle is 30 degrees, would it be
i * tan(30) = .58
so |u| = .58 ??
I think I am missing something but I'm not sure what....
Thanks,
Jennifer
The fact that w's magnitude is 1 is given in the problem (the ball is 1 pound). Look again at the diagram posted by earboth. The only assumption is that we are disregarding the weight of the rope itself.
Other than that, your work is correct. It is all right-triangle ratios (SOH, CAH, TOA).
At angle , tension T, in pounds, the horizontal force on the ball is [tex]Tsin(\theta)[/itex] and that must be u. The vertical force is and that must be the balls weight, 1 lb. Solve the equations and for T and .
Notice that if you square each equation and add you get . If you divide the first equation by the second, you get .