FE/EIT - Static analysis of a wheel (spool) pulled by a rope (See spool dynamics in Hw 15.5). The figure to the right shows a rigid body B consisting of an axle and wheel. One end of a thin (massless) rope is wrapped around B's axle and the other end is pulled so the rope is taut. B is in contact with a rough horizontal plane N at contact point By of B. Complete B's free-body diagram and the description of Fx and Fy in the following table. Draw useful points, unit vectors, etc. B Capp-right:40 2813 Paul Miligus. All rights reserved. FT R Description Earth's gravitational constant Mass of B Coefficient of static friction between B and N Radius of B's inner axle and outer wheel Rope's angle with the horizontal Symbol g m Tension in rope measure of force on measure of force on from from r, R Draw FBD 0 FT F Fy Note: This problem was motivated by the old-fashioned penny farthing bicycle. This "Which Way Will It Roll" puzzle was the Sept. 19, 2011 Wordplay (New York Times crossword blog). Video: Search YouTube with "Veritasium spool" or visit http://www.youtube.com/watch?v=Bwf3msm7rqM Assuming there is sufficient friction to prevent the wheel's sliding on N, calculate the angle static for B to be in static equilibrium. Result: (in terms of r, R) Ostatic acos(-) When When 0 < < static, static < 0 90, the wheel rolls left/right. the wheel rolls left/right. Determine the minimum s for B to be in static equilibrium. Result: (in terms of Fr, 0, m, g) sminimum - FT sin(0)