- #1

jfnn

## Homework Statement

A 700g ball rotates around a vertical shaft supported by two strings. If the tension in the upper string is 20.0 N, determine (I have attached the file)

a. The tension in the lower string.

b. The rotation rate in rpm of the system.

## Homework Equations

[/B]

F=ma

F= m v^2/r

## The Attempt at a Solution

Sum of forces in y direction = 0 (again, I am not sure if this is zero, but I assume zero acceleration in y direction)

Tension in the y direction of 1 (T1y) - tension in the y direction of 2 (T2y) - weight (mg) = 0

T1sin theta - T2sin theta - mg = 0

20sin(theta) - T2sin(theta) = mg

sin(theta) * (20 - T2) = mg

T2 = 20 - mg/sin(theta)

theta = tan^-1 (0.35/0.50) --> Theta = 35

T2 = 20N - 11.96 N

T2 = 8.04 N ---> Can anyone verify if this is right?

b) w = v^2/r but I need v

sum of forces in x direction = mv^2/r

-T1cos(theta) - T2cos(theta) --> Theta is 35

T1 = 20 N

T2 = 8.04 N

F = -20cos(35) - 8.04cos(35)

F = -22.969 N

-22.969 N = mv^2/r --> -22.969 = (0.7) v^2/(0.5)

V^2 = -16.406 (not sure why this is negative/where to go from here...) I am stuck.

Any help is greatly appreciated! Thank you!