222_Dynamics 11ed Manual

222_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Engineering Mechanics - Dynamics Chapter 13 *Problem 13-100 Using a forked rod, a smooth cylinder C having a mass M is forced to move along the vertical slotted path r = a θ . If the angular position of the arm is = bt 2 , determine the force of the rod on the cylinder and the normal force of the slot on the cylinder at the instant t . The cylinder is in contact with only one edge of the rod and slot at any instant. Given: M 0.5 kg = a 0.5 m = b 0.5 1 s 2 = t 1 2s = Solution: tt 1 = Find the angle ψ using rectangular components. The velocity is parallel to the track therefore xr cos () = abt 2 cos bt 2 = x' 2 ( )cos 2 2 ab 2 t 3 sin 2 = yr sin = 2 sin 2 = y' 2 ( )sin 2 2 2 t 3 cos 2 + = atan y' x' 2 π + = 63.435 deg = Now do the dynamics using polar coordinates 2 = ' 2 = '' 2 b = ra = r' a ' = r'' a '' = Guesses F 1N = N C = Given N C sin Mg sin M r'' r ' 2 = FN C cos cos Mr '' 2 r' ' + = F N C Find
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