When an object moves through a fluid (such as water or air), it exerts a force o

Question

When an object moves through a fluid (such as water or air), it exerts a force on the fluid to push it out of the way. By Newton’s third law, the fluid pushes back on the object, in a direction opposite to the object’s velocity relative to the fluid, always opposing the object’s motion and usually increasing with speed. In high-speed motion through air, the resisting force is approximately proportional to the square of the object’s speed v; it’s called a drag force, or simply drag. We can represent its magnitude FD by FD=Dv2 where D is a proportionality constant that depends on the shape and size of the object and the density of air. When an object falls vertically through air, the drag force opposing the object’s motion increases and the downward acceleration decreases. Eventually, the object reaches a terminal velocity: Its acceleration approaches zero and the velocity becomes nearly constant. Derive an expression for the terminal-velocity magnitude vT in terms of D and the weight mg of the object.

Explanation / Answer

weight is balanced by D*v^2
so,
mg = D*v^2
5*9.8 = D*(22)^2
D = 0.10
Answer: 0.10 Ns^2/m^2

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