Two slender rods of length l and mass m, are released from rest in the positions

Question

Two slender rods of length l and mass m, are released from
rest in the positions shown. Knowing that a small knob at end
B of rod AB bears on rod CD, determine immediately after
release
a) the acceleration of end C of the rod CD
b) the force exerted on the knob
d) the angular acceleration of bar CD

Two slender rods of length l and mass m, are released from rest in the positions shown. Knowing that a small knob at end B of rod AB bears on rod CD, determine immediately after release a) the acceleration of end C of the rod CD b) the force exerted on the knob d) the angular acceleration of bar CD

Explanation / Answer

Suppose the force on the knob is N

Taking moment about A for rod AB:
mg(l/2)-N(l) = 1/3 ml2 AB

Taking moment about D for rod CD:

mg(l/2)+N(l/2) = 1/3 ml2 CD

Also immediately after release the acceleraion B on two rods is the same:

AB l = CD (l/2)

Now, by solving these set of equations, we get:

AB  = 9g/10l , CD = 9g/5l , and N=mg/5

So,

1) ac = CD (l) = 9g/5

2) N=mg/5

3) CD = 9g/5l

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