Question

Problem 2 (25 pts) A new child's toy is made of a circular hoop of radius 25 cm and has a small bead of mass 20 grams attached to the hoop. The bead is free to move around the hoop without any friction. The hoop is oriented vertically and spins around at 10 revolutions per second about a pole which passes through the center of the circular hoop. As the hoop is rotating the bead slides up the hoop to an angle of B and sits there stationary going around in a circle. (A) Find the relation of the radius of the circle in which the bead is moving () to the radius of the circular hoop (R) in terms of the angle β? (Note: In this step of the problem your solution should only involve the variables R, r, β.no numbers (8 pts) (B) Find the angle β at which the bead is sitting stationary as the hoop is rotating (This should be a numeric solution)? (9 pts) (C) Is it possible for the bead to sit stationary at the center of the hoop (β = 90), explain your reasoning? (8 pts) 10 revlsec

Can someone show me not just the answers, but how it's solved?

Answer 1

A)   Here,   r/R = sinβ

             => r = R * sinβ

B)     Here,    (w² * cosβ - g/R) * sinβ = 0

   =>     (62.8² * cosβ   - 9.8/0.25) * sinβ = 0

=>     (62.8² * cosβ   - 9.8/0.25)   = 0

=>   cosβ   =   9.8/(62.8² * 0.25)

=>   β   = 89.43   degree

C)   No, it is not possible for β   =90   .This is because for this to happen according to formula , angular velocity have to be infinity .