Help with physics tension in the string

[phillip98]

Homework Statement

A 180 g ball on a 60-cm-long string is swung in a vertical circle about a point 200 cm above the floor. The tension in the string when the ball is at the very bottom of the circle is 5.6 N. At the very bottom of the circle, a very sharp knife is suddenly inserted, as shown in the figure View Figure , to cut the string directly below the point of support.

Homework Equations

V=sqrt(a R)
a=(F-W)/m = (F - mg)/m=F/m -g

The Attempt at a Solution

R=.6m

For a free fall
t=sqrt(2h/g)
S=Vt=
S=sqrt(a R) sqrt(2h/g)
S=sqrt(a R 2h/g)
S=sqrt(2[F/m -g] R h /g)
S=sqrt(2 [ 5.6N/ .180 - 9.81] 0.6 x 0.200 /9.81)
S=0.72m

I keep getting this answer. I'm unsure of what I'm doing wrong.

 

[Snazzy]

What exactly are you solving for? There's no question.

 

[Dick]

I can only guess, but is the question "how far does the ball travel before it hits the floor"? If so you haven't used the tension correctly to compute the initial velocity of the ball. You need to use an equation for circular motion like a=v^2/r and relate that to the tension.

 

[phillip98]

sorry lol

How far to the right of where the string was cut does the ball hit the floor?

 

[phillip98]

Hi Dick, I've tried it that way. I keep getting 2.3. Which seems to be wrong as well.

 

[Snazzy]

Free body diagram, you have a force of tension and a force due to gravity. You can relate this to the velocity, and this velocity will be in the x-direction. From there, use parabolic motion analysis.

 

[Dick]

Show Snazzy how you got the initial x velocity using v^2/r and a free body diagram. Because it's the right thing to do. Don't wait for me, I'm going zzzzzzzz.