Spring vs thread: which ball hits the ground first?

Problem: Two identical balls are suspended at the same height, one by a spring and the other by a thread. If both supports are cut simultaneously, which ball will hit the ground first?

Answer: The ball on a thread (B).

Fig. 1. Two identical balls, one attached by a spring, the other by a thread, are released at the same time. Which will reach the ground first?

Solution. Suspended from a support, the balls exert a downward force of F = mg on their tethers, where m is their mass and g is the acceleration due to gravity. Although this force barely affects the thread's length, it significantly stretches the spring. Without the balls, the spring would contract to a shorter, relaxed length, with its lower end positioned higher above the ground. This difference is essential for understanding the outcome.

When the support is cut, as illustrated in Fig. 1, the balls and their tethers begin to fall with the same acceleration g. As they move at the same rate, the tension between them disappears, causing the spring and the thread to relax. The thread, having not stretched significantly in the first place, remains practically the same length. However, the relaxed spring contracts, thus briefly pulling the ball upward.

This pull effectively increases the distance to the ground. The increase is roughly equal to the amount the spring was originally stretched. So now, this ball must spend some extra time in motion. Although the balls accelerate at the same g, the spring will pull its ball upward first, creating a delay equivalent to starting from a higher position. This gives the second ball the advantage necessary to win the race. Consequently, the ball on the thread (B) will hit the ground first.