I don't understand why if the frictional force of air resistance is proportional to an object's cross sectional area, and not velocity, it would never reach terminal velocity. If the frictional force of air resistance is much smaller than the weight of the falling object, wouldn't it never reach terminal velocity anyways?
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If the frictional force is proportion to cross-sectional area, then the frictional force will always have the same value as an object falls (it's area isn't changing, right?). Thus, if the air resistance is smaller than the weight of the object, we will never reach translational equilibrium; the weight will always be larger than the drag force.
In real life, this isn't the case. Drag starts off at a very small value (smaller than the weight), but increases with the velocity of the falling object. Eventually, the drag force is equal to the weight, and that's when the object is in translational equilibrium -- at terminal velocity.
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