Find the tension?

Question

Luke Autbeloe twirls a 750 gram mass on the end of a 0.82 meter string. Find the tension at the top and bottom of the orbit. Assume the mass's velocity at both top and bottom is 3.7 m/s.

Answer 1

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  :)

Answer 2

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 F_c=mv²/R. Here R is the radius, which is the length of the string.