Radius 3m, length of chain and chair 2.5m.Mass of rider and chair 100kg. (8 chairs riders)a)Determine rotational speed when chair is at 30 degrees to the verticalb)How many g's does a rider feel?I have the final answers, but don't know how to get to them.Using trig I get a total radius of 4.25m then I get stuck!Please help! Thanks
I assume the top of the chain is anchored to a point which is at radius 3m Let the force in the chain when in the 30? position be F then vertically downward force on rider chair = Fv = 981 N = F s30? so that F = 981/0.866 = 1133 N The horizontal component of force on the rider = Fh = F.sin30? = 566.4 N Radius or rider at the 30? position = 3 + 2.5sin30? = 4.25 m Fh is the force produced by rotation and = m.ω?.r giving ω = √[F/(m.r)] = 1.1544 where ω is the rotational angular frequency. So rotational frequency = ω/(2.π) = 0.18373 revs/sec = 11.024 r.p.m.. The rider experiences total force F = 1133N. If he were standing still he would experience 981 N, so g force is 1133/981 = 1.155g. This is the total force on the rider, including his own weight. The extra force he experiences due to rotation is 566.4/981 = 0.577 g – the answer you are given.
