What mass m ballast must be dropped from a uniformly descending balloon so that it starts to rise uniformly

What mass m ballast must be dropped from a uniformly descending balloon so that it starts to rise uniformly at the same speed? The mass of the balloon with ballast m = 1600 kg, the lifting force of the aerostat F = 12 kN. Consider the resistance force F to be the same when going up and down.

m1 = 1600 kg.

g = 9.8 m / s ^ 2.

Fp = 12 kN = 12000 N.

mb -?

According to 1 Newton’s law, the condition for the uniform motion of a body is the compensation of the forces that act on it.

There are 2 forces acting on the balloon: the gravity force m * g, directed downward, and the lifting force Fd, directed vertically upward.

m * g = Fp.

The mass of the balloon with ballast m, which should be expressed by the formula: m = Fd / g.

m = 12000 N / 9.8 m / s ^ 2 = 1224.5 kg.

The mass of the ballast to be dropped is found by the formula: mb = m1 – m.

mb = 1600 kg – 1224.5 kg = 375.5 kg.

Answer: from the balloon you need to drop the load mb = 375.5 kg.