Question

Given: The 80-kg rod is released from rest at 6=15 and moves to 8-45, while the spring remains vertical. The spring is unstretched when 8-0 Find: a) Are all forces acting on OA conservative? Why or why not? 0 k = 150 N/m 3 m А b) Find the angular velocity, w, of the rod. Show all work, and draw appropriate diagrams. rad/s c) What is the spring force when 6=45°? N d) Select one possible method to solve for angular acceleration.

Answer 1

Jo forces acts is k=150N/m gravitational force 3 spring force Both are conservathe Because werk done by these forces is independent of party Datum 10 Qigo 1.5 sinis 45° T 3 sin 45 3 sinis lossinas ✓ mg initial Position ng . P. Ei = mg xis siniso thk (3sinis) ² - -30 4.682 + 45.216 P.Eis -259.466 J P.Efa -mg x 1.5 sings' + tk (3 Sin45°) 2 832.406 337.5 J -494.gob = K. Ei0 system Stents from rest Kief < I wa + 2 muam 2 x me xw² + 1 xm xwe j² 2 x me 2 x w2 80x32 xw2 = 12ow 2 6 energy conser retion P-Ei + T. EL- P. Eftk. Ef -959.466 +0= -494.906 + 120W2 w2 335.44 120 Tw=lou Madis Spring force When 0 - 45° Fs - KX 3 sinas" 150 X 3x sinds 318.198 N

@ os כט וקרי וי דיק angulae acreleratia com be at any instant Ioa Słnet Just after release me a mg xles cosis -(ko 3 sin 15“) (36osis) 337-5 3.332 ra 1137.088 racy8² 2uo

Method used for angular acceleration is instantaneous center method at any instant