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When the buoyancy effects are taken into account, an object falling through a fluid under its own weight can reach a terminal velocity (settling velocity) if the net force acting on the object becomes zero.
When the skydiver has reached terminal speed and remains in a state of dynamic equilibrium, we know the size of the drag force must be equal to the skydiver’s weight, but in the opposite direction. This concept will allow us to determine how the skydiver’s mass should affect terminal speed.
The two main factors which affect the terminal velocity of an object falling through a fluid are the mass and the shape of the object. The larger the mass of the object, the greater the weight.
When the object moves through a liquid, Archimedes Principle and buoyancy play a key role in determining its terminal velocity. The expression for terminal velocity is modified by replacing the object’s mass with its reduced mass (m – ρ o V).
At this point, the person’s velocity remains constant and we say that the person has reached his terminal velocity (\(v_T\)). Since \(F_D\) is proportional to the speed squared, a heavier skydiver must go faster for F D to equal his weight.
Terminal velocity will depend on the mass, cross sectional area, and drag coefficient of the object as well as the density of the fluid through which the object is falling and gravitational accelleration.
When drag is equal to weight, there is no net external force on the object and the object will fall at a constant velocity as described by Newton's first law of motion. The constant velocity is called the terminal velocity .
At terminal velocity, air resistance equals in magnitude the weight of the falling object. Because the two are oppositely directed forces, the total force on the object is zero, and the speed of the object has become constant.
The terminal velocity is the same as the limiting velocity, which is the velocity of the falling object after a (relatively) long time has passed. Similarly, the limiting distance of the boat is the distance the boat will travel after a long amount of time has passed.
How does weight affect terminal velocity? For objects falling towards a body that attracts other bodies by gravitational interaction and that has a uniform fluid slowing them down, the terminal velocity depends linearly on the square root of the weight.