Kvant Physics Problem 12
The only identified defect is the justification of the initial phases and velocity directions.
Verified: no
Verdicts: FAIL + FAIL
Solve time: 26m14s
Source on kvant.digital
Problem
Two identical heavy steel balls rotate on light rods of lengths $l$ and $2l$ about points $O_1$ and $O$, the distance between which is equal to $3l$ (Fig. 3). Initially, the balls are at points $A$ and $B$, having velocities $v$ and $2v$ respectively. How many times will the balls collide during the time $t$? After what time will the balls have collided $k$ times? Assume the collisions of the balls are perfectly elastic.
Fig. 3
G. L. Kotkin
The only identified defect is the justification of the initial phases and velocity directions. The algebraic derivation itself is correct. The fix is to replace the unsupported assumption by an explicit geometric verification from the figure and from the stated initial velocities.
Setup and Assumptions
Two identical steel