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Find the tension?

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2 Answers

Hey Sun -- at bottom, the string feels V*V/r plus g ... at top, V*V/r minus g ...
 
V*V ~ 3.5*4.0 ~ 14 m-m/s/s ... V*V/r ~ 14/0.82 ~ 16.8/0.98 ~ 17 m/s/s ...
 
BOTTOM: 3/4 kg with 27 m/s/s ~ 21N ... TOP: 3/4 kg with 7 m/s/s ~ 5N  :)
The tension is largest at the bottom, equals to the sum of gravitational and centripetal forces. At the top the tension is the difference between the centripetal force and the gravitational one. Centripetal force is Fc=mv2/R. Here R is the radius, which is the length of the string.