Question

Problem 5 (15 points) A small bead can slide without friction on a circular hoop that is a vertical plane and has a radius of 0.100 m. The hoop rotates at a constant rate of 4.00 rev/sec (recall 1 rev = 2π rad) about a vertical diameter as shown in the figure below (a) Find the angle β at which the bead is in vertical equilibrium. (It has a radial acceleration toward the axis.) (b) Is it possible for the bead to "ride" at the same elevation as the center of the hoop? (c) What will happen if the hoop rotates at 1.00 rev/sec? 0.100 m Problem 6 (25 points) An object of mass m, hangs from a string that passes over affixed massless pulley Pi as shown below. The string connects to a second massless pulley Pz. A second string passes around this pulley with one end attached to a wall and the other to an object of mass m on a frictionless and horizontal table. (a) If a and az are the accelerations of mi and m2, respectively, derive an equation to relate these two accelerations. (b) Find an expression for the tensions in the strings in terms of the masses mi, m, and g (c) Find the accelerations a and a2 in terms of the masses mi, m2 and g my

Answer 1

Sigma F_y = 0 (a) N cos beta = m g Sigma F_c = m a_c N sin beta = m r w^2 sin beta/cos beta = r w^2/g = (0.1) sin beta (2 pi f)^2/g cos beta = g/0.4 pi^2 f^2 = 9.8/0.4 pi^2 4^2 beta = 81.07 degree (b) No, because there is an unbalanced �m g� force moving the bead down. (c) If hoop rotates at 1 rev/s Bead moves down due to (m g) force