Using tensions to find maximum velocity

[MathewsMD]

An object is constrained by a cord to move in a circular path of radius 0.5m on a horizontal frictionless surface. The cord will break if its tension exceeds 16N. The maximum kinetic energy the object can have is:

Attempt at solution:

Well if tension can only be constant, then velocity is maximum when:

T = mv²/r - mg, right?

since v must be subtracted from to equal T, and this is the case at the bottom of the circle when it is motion.

So then I isolate m,

m = 16 / (2v² - 9.8)

Then I use K = [8/(2v² - 9.8)]v²

Now when I get here, I run out of equations to use. I am thinking I have forgotten something, but when I keep trying to isolate for v in other equations, I just keep getting the same answer.

Any help would be greatly appreciated! :)

 

[physics&math]

Tension is just mv²/r. Gravity is acting perpendicular to the tension force.

Don't try isolate m or v separately. Remember, kinetic energy is .5 mv².