Question

Fall 2017 Henry Ford College/ Physics 231-71 Problem 3 (30 points) The 10 mg bead in Figure 2 is free to slide on a frictionless wire loop. The loop rotates about a vertical axis with angular velocity ?. If ? is less than some critical value uc, the bead sits at the bottom of the spinning loop, when ? > ac, the bead moves out to some angle 0. a) b) What is wc, in rpm for the loop shown in the figure? At what value of u, in rpm, is ?-307 5.0 cm Fig.2

Answer 1

The mass of the bead is in equilibrium under gravitational force and centrifugal force let us say horizantal direction is along x - axis let T be the force of bead acting on wire F-Tsino F 0... 1) E-centrifugal force on bead due to angular velocity ( F-mr002 ) the total force along vertical direction..let us sayy - direction mg cos0 mr'ω from)sine cos(0) mg COS effective radial distance of bead from axis of rotation-r-r sinθ rcos θ when 0-0 rad Sec m- mass of ball-10e - 3kg g-9.8 m/s2 ω angular velocity of the ball r- rdius of the loop-5.0cm whe n0-30° rcos θ when plug the values in the relation ω-15.044 rad / sec-| | 43.66 RPM