Two identical uniform bars are pinned together at one end, and each bar has a roller at it...

Two identical uniform bars are pinned together at one end, and each bar has a roller at its other end. The rollers can roll freely along the horizontal surface as shown. Each bar has mass m and length L, and a horizontal force P is applied to bar BC at B. Although the bars can rotate relative to each other, for a given value of P there exists a corresponding value of θ such that the system moves with θ constant.

(a) Find the forces on the bars at A and B and show that they are independent of P.

(b) Determine θ as a function of P and find θ0 as P → 0 and θ∞ as P → ∞.

Neglect the mass of the rollers and any friction in their bearings.

Figure P7.66