[Physics] Understanding the math behind a falling object attached to a parachute


I'm trying to understand the mathematics behind calculating the total speed and force of a $40 kg_f$ object hooked up to a parachute, falling to Earth.

From what I understand, the formula for this is
$$m \frac{dv}{dt} = (mass \times gravity) -Force_{deceleration}= 0 $$

Here's where I'm confused:
I understand that $m \frac{dv}{dt} = 0$ because once the parachute is deployed, the object reaches a constant speed at which it falls for the rest of the way down. However I also learned that $m \frac{dv}{dt} = F$, which is the total force of any moving mass. The object is falling to Earth and therefore it is moving, so how could the force, $F$, be equal to zero??

If you could help me get things straight, I'd really appreciate it.

Best Answer

There are actually 2 forces acting on the object . 1) Weight = mass * gravity 2) Air resistance

At first the object is accelerating because the Weight > Air resistance, until the object reaches its terminal velocity where Air resistance = Weight, meaning there is no more acceleration, or in other words, a Net Force of 0.