1 answer

Planar Kinetics of a Rigid Body

Question:

17—97. The truck carries the spool which has a weight of500 lb and a radius of gyration of k(g) = 2 ft. Determine theangular acceleration of the spool if it is nottied down on thetruck and the truck begins to accelerate at 3 ft/s^2. Assume thespool does not slip on the bed of the truck.

Answers

Calculate your InertiakG = 2ftkG = √(IG/m)IG = (m)(kG2)IG = (500/32.2)(22)IG = 62.11 lb ft2|Sum your forces:ΣFx = m(aG)xFA =(500/32.2)(aG)xΣFy = m(aG)yNa - 500 = 0ΣMG =(IG)(αG)-(FA)(3) =(62.11)(αG)|No slipping thereforeaG/T = αraG/T = 3α|The acceleration of the spoolis relative to that of thetruckaG = aT + aG/TaG =(3 ft/s2)+ 3α|SolveyourΣFx&ΣMGsimultaneously to find αGFA = (500/32.2)(aG)x-(FA)(3) = (62.11)(αG)|FA = (500/32.2)(3 + 3α)-(FA)(3) = (62.11)(α)|FA = (500/32.2)(3 + 3α)-FA = 20.70α|0= 46.584 + 67.287αα = -0.692α = 0.692 rotating counterclockwise.

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