A carnival ride consists of a vertical wheel of radius r rotating at angular velocity w around a horizontal axin. There is a horizontal platform attached to it; a penson stands on the platform. (This platform stays horizontal, and does not rotate; the person remains upright during the whole ride.) This person has mass m, and stands on a scale. The coefficient of static friction between their feet and the scale is 4, = 0.5. (a) Draw force diagrams for the person at the top of the circle, the bottom of the circle, and the position at the same height as the middle of the circle. (You will need to think carefully about the third one of these.) (b) How does the scale reading relate to the forces that act on the person standing on the platform? (c) In terms of m, g, r, pa, and w, what is the scale reading at the top? (Your answer may not depend on all of these.) (d) In terms of m, 9, r, Ha, and w, what is the scale reading at the bottom? (Your answer may not depend on all of these.) (e) What coefficient of static friction is required for the person not to slide at the position at the same height as the middle, in terms of m, g, r, and w? (E) Extra credit: If the angular velocity w is gradually increased, eventually the person will slide off of the platform. At what location will the person slide off? (Hint: It's not any of the three positions marked.)