You have lovingly restored a red 1964 Ford Falcon two-door sedan, complete with a pair of red fuzzy dice hanging from the rear-view mirror. When you go down a straight road at 26.0 m/s, the dice hang straight down, but when you enter a flat circular turn with radius 97.0 m at the same speed, they hang at an angle θ from the vertical. What is θ?
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draw a diagram of the forces acting on the dice; you should have a triangle whose vertex angle is theta, the vertical side represents gravity and the horizontal base is the centripetal force, therefore we can write
tan(theta) = mv^2/r / mg = v^2/rg
tan(theta) = (26m/s)^2 / (97m x 9.8m/s/s) => theta = 35.4 deg
tan(theta) = mv^2/r / mg = v^2/rg
tan(theta) = (26m/s)^2 / (97m x 9.8m/s/s) => theta = 35.4 deg