What is the ratio between radius and string length in a revolving mass system?

[zhenyazh]

hi,
can some one please tell me where am i wrong?

A mass of 9.50 kg is suspended from a 1.19 m long string. It revolves in a horizontal circle.
The tangential speed of the mass is 2.28 m/s. Calculate the angle between the string and the vertical.

so what i need is the ratio between radius and string length. to find the radius i use v and the fact it equals wr. w is the square of ration between g and l.

thanks

 

[alexmahone]

Let the angle between the string and the vertical be $\theta$

$Tcos\theta=mg$ ------ (1)

$Tsin\theta=\frac{mv^2}{r}$ ------ (2)

Dividing (1) by (2),

$tan\theta=\frac{v^2}{rg}$

$r=lsin\theta$

So,

$tan\theta=\frac{v^2}{lsin\theta g}$

$\frac{sin^2\theta}{cos\theta}=\frac{(2.28)^2}{1.19*9.8}=0.45$

$1-cos^2\theta=0.45cos\theta$

$cos^2\theta+0.45cos\theta-1=0$

$cos\theta=\frac{-0.45\pm\sqrt{(0.45)^2+4}}{2}$

$cos\theta=\frac{-0.45\pm2.05}{2}$

$cos\theta=0.8$ or $cos\theta=-1.25$

Rejecting $cos\theta=-1.25$, we get

$cos\theta=0.8$

$\theta=36.87^0$

 

[PhanthomJay]

I respectfully ask in the future that you do not post full solutions to problems. Provide help and guidance only, per Forum rules. Thanks.