Circular Motion Problem: Finding Angular Velocity with Maximum Tension of 50 N

[anonymous820]

Homework Statement

A ball of mass .5 kg is attached to the end of a cord whose length is 1.5 m. The ball is whirled in a horizontal circle. If the cord can withstand a maximum tension of 50 N, what is the angular speed the ball can have before the cord breaks?

Homework Equations

------

The Attempt at a Solution

m (mass) = .5 kg
r (radius) = 1.5 m
Ft (tension force) = 50 N
w (angular velocity) = ?

w = v/r
Ft = Fg
m v^2/r = mg
v^2/r = g
v^2/1.5 = 9.81
v^2 = 14.715
v = 3.836 m/s

w = 3.836/1.5
w = 2.557

so my question is..what am i doing wrong? because the answer is [angular velocity (w) = 8.16 rad/s]

 

[Dick]

What you are doing wrong is equating mv^2/r to mg. The tension force is mv^2/r. You want to equate that to the 50N string strength.

 

[Dick]

Uh, v=w*r NOT w=v*r! Pay attention to units! v=m/sec, w=1/sec, r=m.

 

[Dick]

S'ok. Don't EVER do that again. It the sort of mistake that allows people to laugh at you and it's easily avoided. Carry the units along and you can easily see where you've goofed big time. Just trying to save you future humiliation.