Physics Minor problem

Problem #1 The small mass m1 is going around the funnel as shown. A second mass, m2, is attached by a frictionless string. In this setup, the first mass experiences friction, but only along the up/down direction. NOT along the tangential direction. In this problem, you need to find a relationship between the coefficient of static friction and the mass m2. This expression should only contain theta, R, omega, g, m1, and m2. No other variables. Then, you need to plot this relationship identifying key points on the plot (there are three key points: mu = -1, 0, 1 and the corresponding expressions for m2). Problem#2 A marble of mass m is going around the funnel slowly making its way down to the bottom hole (which is negligibly small). As this marble goes around it experiences kinetic friction mu_k only in the up/down direction (NOT the tangential direction). You need to find the time tau it will take for the marble to make its way down, and the full magnitude of the final velocity on exit (NOT only the vertical component, but the horizontal one as well). Your final expressions should only have g, R, omega, theta, and mu_k as variables. For the solution, assume that angle theta is large, so that the radial acceleration is approximately v^2/R. PLEASE LOOK AT THE FILES ATTACHED