- #1
RyanV
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Homework Statement
There are two collars hanging on a vertical frame made up of two smooth rods (see attached for figure). If the mass of collar A is 8 kg and the mass of collar B is 4 kg, determine the equilibrium angle [tex]\alpha[/tex] and the tension in the cable between the collars.
Homework Equations
When in equilibrium, [tex]\sum F[/tex] = 0
The Attempt at a Solution
The forces at Collar A,
x: T cos [tex]\alpha[/tex] - Na cos 30 = 0
y: T sin [tex]\alpha[/tex] + Na sin 30 - 8g = 0
The forces at Collar B,
x: -T cos [tex]\alpha[/tex] + Nb sin 45 = 0
y: - T sin [tex]\alpha[/tex] + Nb cos 45 - 4g = 0
where, Na and Nb are forces acting on the beams.
I've simplified the 4 equations to these two equations:
T = 4g / ( cos [tex]\alpha[/tex] - sin [tex]\alpha[/tex] ) ----- (1)
( sin [tex]\alpha[/tex] + cos [tex]\alpha[/tex] tan 30 ) = 2 ------- (2)
( cos [tex]\alpha[/tex] - sin [tex]\alpha[/tex] )
After that, I'm stumped. Any help?
Thanks =)