Question

The slender uniform bar with a weight of 9 lb can rotate in a vertical plane with respect to a bolt B. A spring of constant k = 40 lb / ft and an undeformed length of 5 in is connected to the bar as shown . If the bar is released from rest in the position shown, determine after rotating 90 °:

A) The initial energy of the spring:
B) Final spring energy:
C) The velocity of the G point of the Bar
D) The angular velocity of the BD bar

A 24 in. D B 5 in. 아 14 in.

Answer 1

Position Position 2 A 1200 G 140 Yin C B D Gal B 7in sin ain 5in c 14 in positions ; 21 = CD - unstreetched length (V65)7(14)))-5 = 9.866 in x,=0.822 ft A The intial energy of spring, ve = 1 kali? ve - < (40 Lblf t)(0.82232 = 13.514 16-oft Ve = 13:514 lb-ft Gravity, ug = wh=19863 Ft) = 5.2516-ft Vi= Ve + Vg = 13514 +5.25 V,=18.764 26-ft energy : 7,0 Kinetic B) position 2 2 spyt: 22 = 9-5=4in=0.333 ft final energy of spring, ve=1 422 Ve=4140)(0:333)2 Ve=2.218 loft

N2= =W2= Gravity, Vg = wh=0 V2 = Ve + Vg = 2.21870 V2 = 2:218 lb-ft Kinetic erzegy Gift) W2 Jam +6034) (231 1-0.0932 Slug-ft T2 = m + 1 h I wa -*191) 4(0.0932) T2 = 0.09462% from conservation of energy c) The velocity of G Titvi = T2 + V2 0 +18764 -0.09462? + 2.218 W2=13.267 radls point of the bar Uz = (13.) (13.267) U2 = 7.74 ftls bare Irelocity of BD D) The angular W2=13.267 yad's