# drag forces are functions of velocity , rather than functions of time. drag forces:

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Drag Forces: Non-Constant Forces that are Functions of Velocity. Drag forces are functions of velocity , rather than functions of time. Drag Forces: slow an object down as it passes through a fluid act in opposite direction to velocity vary with velocity or velocity squared - PowerPoint PPT Presentation

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• Drag forces are functions of velocity, rather than functions of time. Drag Forces:slow an object down as it passes through a fluidact in opposite direction to velocityvary with velocity or velocity squareddepend upon the fluid and the projectile characteristicswill impose a terminal velocity if a falling object reaches a high enough speedDrag Forces: Non-Constant Forces that are Functions of Velocity

• Drag as a Function of VelocityIn general, a drag force acts like a velocity-dependent kinetic friction. The general expression isfD = bv + cv2b and c depend uponshape and size of objectproperties of fluidb is more important at low velocityc is more important at high velocity

• Drag Force in Free Fallwhen fD equals mg, terminal velocity has been reached

• Drag Force in Free FallFor fast moving objects:

FD = c v2

c = 1/2 D r A

WhereD = drag coefficientr = density of fluidA = cross-sectional area of projectileFD = bv + c v2For slow moving objects:

FD = b v

mgFD

• Practice Problem: For slow-moving objects, show that vT = mg/b, where vT is terminal velocity.

• Practice Problem:For slow-moving objects, show that prior to attaining terminal velocity, the velocity of an object subjected to the drag force varies as:

• Practice Problem: For fast-moving objects, show that terminal velocity is

• Practice Problem: Derive an expression for the velocity of a falling fast-moving object as a function of time. The expression you derive should be valid prior to attainment of terminal velocity, as well as after terminal velocity is attained.

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