Find Tension for Centripetal Motion

[petern]

[SOLVED] Find Tension for Centripetal Motion

George of the Jungle swings on a vine 6.5 meters long. What is the tension in the vine if George, whose mass is 75 kg, is moving at 2.4 m/s when the the vine is vertical?

I tried using the equation F = ma and a = v^2/r. I plugged the 2nd one into the first but it didn't come out with the right answer.

F = (75)(2.4^2)/(6.5) = 66.46 N when the answer should actually be 801.46 N. I know gravity should go somewhere in there too but I'm not sure where. I tried multiplying 66.46 by 9.8 m/s^2 and ended up with 651.32. What am I doing wrong?

 

[hage567]

There is tension in the rope and gravity. Draw a diagram if that helps. Both of these contribute to the centripetal force. Sum the forces up like you would any other force problem.

 

[petern]

Solved! Thanks a lot!