Bar ABC is attached to collars A and B that can move freely on the rods shown. T
ID: 1822869 • Letter: B
Question
Bar ABC is attached to collars A and B that can move freely on the rods shown. The constant of the spring is k, and the spring is unstretched when ? = 0. (a) Neglecting the mass of bar ABC, derive an equation in terms of , ? m, g, k, and l that is satisfied when bar ABC is in equilibrium. (b) Determine the value of ? corresponding to equilibrium when m = 5 kg, k = 800 N/m, and l = 250 mm, and check that the equilibrium is stable.
Bar ABC is attached to collars A and B that can move freely on the rods shown. The constant of the spring is k, and the spring is unstretched when ? = 0. (a) Neglecting the mass of bar ABC, derive an equation in terms of , ? m, g, k, and l that is satisfied when bar ABC is in equilibrium. (b) Determine the value of ? corresponding to equilibrium when m = 5 kg, k = 800 N/m, and l = 250 mm, and check that the equilibrium is stable.Explanation / Answer
Balancing momennts about B
mgcos .l = l.Kxsin
now when =0, x=0
when =
x = (l-lcos)
hence net eq
l.mgcos = l.k (l-lcos)sin
mgcos= l.k(1-cos)sin
now when m = 5 kg, k = 800 N/m, and l = 250 mm
5*10cos = 0.25*800*(1-cos)sin
tan = 4(1-cos)
=20 degree
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