A particle of mass m is attached to one end of a light slender rod which pivots

Question

A particle of mass m is attached to one end of a light slender rod which pivots about a horizontal axis through point O. The spring constant k = 150 N/m and the distance b = 130 mm. If the system is released from rest in the position shown where the spring is unstretched, the bar is observed to deflect a maximum of 44 degree clockwise. Determine (a) the particle mass m and (b) the particle speed v after a displacement of 30 degree from the position shown. Neglect friction. Answers: m = kg when theta = 30 theta , v = m/s

Explanation / Answer

Extended length = (b/2) / (sin 46) + b*tan 44 = 1.66*b ;

Change in length = 1.66*b - 0.5*b = 1.16*b = 150.9 mm ;

Force = k*x = 150*150.9*10^-3 = 22.635 N ;

mg*2b* cos 44 = Force*b ;

m = 1.605 kg ;

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