| Sally Stoutheart
and her cat, Shivers, have just become airborne thanks to the lift from
some helium-filled balloons.
Sally, who weighs 400 N, is sitting 2 m from the left end of the 6-m pole. Shivers weighs 100 N and is sitting in the middle (3 m from either end). The pole weighs 500 N and its center of gravity is 2 m from the right end. Assume the balloons are attached to the ends of the pole and that Sally and her crew are not accelerating. How much lift are the balloons providing at each end? |
Both conditions for equilibrium must
be met; net force and net torque must equal zero. The total downward force
is 1000 N.
Setting a fulcrum at the right end, the balloons at the left end must exert a c.w. torque to balance the c.c.w. torques from Sally, her cat, and the pole. So, (FL)(6 m) = (400 N)(4 m) + (100 N)(3 m) + (500 N)(2 m) + (FR)(0 m) FLeft = 483 N therefore FRight = 1000 N - 483 N = 517 N Thanks to Ashvin Kohle for suggestions! |