the man hanging upside down is holding a partner who weighs 491 N. Assume that the partner moves on a circle that has a radius of 5.09 m. At a swinging speed of 4.20 m/s, what force must the man apply to his partner in the straight-down position?

Answer 1

Weight =W= mg
m=W/g =491 / 9.8 =50.1 kg

F = mv²/ r=173.6
=50.1•4.2²/5.09 = 173.6 N
since his partner is in the straight-down position, the man also has to apply force to keep his partner from falling down due to gravity, so you have to add the partner's weight:
Force total = 173.6 + 491 = 664.6 N