Question

Two small balls of the same size and of mass m₁ and m₂ (m₁ > m₂) are tied by a thin weightless thread and dropped from a balloon.

Determine the tension T of the thread during the flight after the motion of the balls has become steady-state.

Answer 1

The steady-state motion of the system in air will be the falling of the balls along the vertical at a constant velocity. The air drag F acting on the lower (heavier) and the upper ball is the same since the balls have the same velocity and size. Therefore, the equations of motion for the balls can be written in the form

Solving this system of equations, we obtain the tension of the thread: