Playing with rods and sticks

We have two rods \(AB\) and \(CD\) touching each other and placed on the ground in the position as shown in the figure. At \(t=0\) the system is set free to move, find the normal force (in Newtons) between the two rods at this instant.

Details and Assumptions

  • Mass of rod \(AB=35\sqrt{3}\) kg , mass of rod \(CD = 26\sqrt{3}\) kg, \(\theta={30}^{\circ}\).
  • There is no friction between the ground and the rod and also there is no friction between the two rods, (In the diagram it may seem that the rods are stuck to the ground but it's not so, they can freely slip on the ground)
  • The ends of both the rods are perfectly curved and assume they are perfectly rigid and very thin.
  • Rod \(AB\) is perpendicular to \(CD\) (i.e \(\angle ADC={90}^{\circ}\)) and rod \(CD\) touches rod \(AB\) at its mid-point(i.e \(AD=DB\))
  • \(g=10 \text{m/s}^2\)

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