Centripetal force problem with tension

[BrainMan]

Homework Statement

In a test of machine-part reliability, a specimen of mass m is swung in a vertical circle of constant radius .75 m. When the object is at the bottom the circular path, the tension in the supporting wire is found to be six times the weight of the object. Determine the rotation rate in revolutions per minute

Homework Equations

Fc = mv^2/r
ω = v/r

The Attempt at a Solution

I drew a free body diagram and realized that the only forces acting on the system is the centripetal force, which is composed of the weight of the object and the tension so
Fc = T - W
mv^2 = 6(9.8)(M) - (9.8)(M)
v^2 = 5(9.8)
v^2 = 49
v = 7 m/s

ω = v/r
ω = 7/.75
ω = 9 and 1/3 radians per second

So in 1 min there will be 560 radians
560/ 2 pi
So there will be 89.126 rotations per minute.
This answer is wrong the correct answer is 77.2 rev/min

 

[AlephZero]

Homework Equations

Fc = mv^2/r
ω = v/r

The Attempt at a Solution

Fc = T - W

Correct.

mv^2 = 6(9.8)(M) - (9.8)(M)

Oops!

The method is OK, except for that one mistake.

 

[BrainMan]

Correct.


Oops!

The method is OK, except for that one mistake.

Thanks!