The balloon descends at a constant speed. What mass m of ballast must be dropped so that then a ball

The balloon descends at a constant speed. What mass m of ballast must be dropped so that then a ball with a mass of M = 100 kg would move at the same speed, but upward? The lifting force F = 1.5 • 10 ^ 3 N of the ball is known; it is the same both during the descent and during the ascent of the ball.

Data: M (own mass of a given balloon) = 100 kg; Fod (lifting force) = 1.5 * 10 ^ 3 N.

Constants: by condition g (acceleration of gravity) = 10 m / s2.

1) Projection of forces (upward movement): Ft1 – Fd = (M + mb) * g – Fd.

2) Projection of forces (lifting up): Fpod – Fт2 = Fpod – M * g.

3) The resulting equality: (M + mb) * g – Fpod = Fpod – M * g.

(M + mb) * g – Fpod = Fpod – M * g.

2Fp = 2M * g + mb * g.

mb = (2Fpod – 2M * g) / g = (2 * 1.5 * 10 ^ 3 – 2 * 100 * 10) / 10 = 100 kg.

Answer: It is necessary to dump the ballast weighing 100 kg.