(20 1 1? The two ends of the right-angle bracket with negligible mass are respectively connected with balls A and B with the mass of m and 2m. The lengths of the two right-angled sides of the bracket are separated. According to the meaning of the question, the angular velocity of ball A and ball B is equal, and the ratio of linear velocity is equal to the ratio of rotating radius, which is 2: 1. In the system of ball A and ball B, only the potential energy and kinetic energy of gravity are transformed into each other, and the mechanical energy of the system is conserved. Suppose that the rotation is θ, the angle between OA rod and horizontal direction is θ, and the mechanical energy reduced by ball A is equal to the mechanical energy increased by ball B.

Mg? 2l？ sinθ-2mg？ (l-lcosθ)= 12mv2+ 12？ 2m？ (v2)2

solve

v=83gl(sinθ+cosθ？ 1)

According to mathematical knowledge, when θ = 45, sinθ+cosθ has the maximum value, so when θ = 45, the speed of ball A is the maximum;

Gravitational potential energy decreases by 23E0, so kinetic energy increases by 23E0, including

23e 0 = 12mv 2 1+ 12？ 2m？ (v 12)2

solve

v 1=8E09m

So the answer is: 8E09m. ..