What is the Maximum Speed at Point Q Without Breaking the String?

[tdreceiver17]

Homework Statement

The maximum tension the string can have without breaking is Tmax. Derive an expression for Vmax, the maximum speed the ball can have at point Q without breaking the string.

Homework Equations

F=ma
Vc=(mv^2)/r
T=mg+ma

The Attempt at a Solution

I thought I could do T+mg=mv^2/r because mv^2/r-mg would give you the max speed to keep the same tension and anything great would produce a greater tension that the string doesn't have causing it to break. So, I pulled out a common factor in m and got a common denominator giving me m((v^2-gr)/r)=T

 

[tdreceiver17]

Sorry for the size of the pic. If you click on it it will expand.

 

[jackarms]

Careful, the equation you have is incorrect -- tension and weight force act in opposite directions at point Q, so this needs to be reflected in their signs.

 

[tdreceiver17]

Sorry for the size of the pic. If you click on it it will expand.

Thats what I thought at first but wanted to try something new. So is it the same thing I have put down but with a plus sign?

 

[jackarms]

What I mean is that you have this:

T+mg=mv^2/r

but T and mg cannot have the same sign. There has to be a negative somewhere on the left.

 

[tdreceiver17]

What I mean is that you have this:



but T and mg cannot have the same sign. There has to be a negative somewhere on the left.

-T+mg=mv^2/r ?

 

[jackarms]

No, you're mixing up your signs. Start with this:

At Q, which way do both forces point, and which way does the acceleration point?