Terminal Velocity, Weight & Area

As v increases, so does air friction…

…until F = W-f =0.Now a=0, and the maximum or “terminal” velocity is achieved

Curveballs

Lab: Coffee Filter, Air Drag & Terminal Velocity with Motion Detector

Ailerons

Motion in the presence of resistive forces

Motion in viscous media.

Objects interact with the medium through which they are moving.

- Air

- Water, oil, liquids.

The resistive forces depend on the speed of the object.

F ~ v: Objects falling in liquid, tiny objects falling in air.

F ~ v2: Large objects moving in air.

Terminal velocity.

When the resistive force of the falling object is equal to the gravitational force on the object.

Examples:

- skydivers

- soap bubbles falling in air

- small spheres dropping in liquid.

Air drag at high speeds.

For objects moving at high speeds through air:

Resistive force:

2

2

1vADR

Where:

D… Drag coefficient of object (depends on shape)

…density of air

A… cross-sectional area of object

v… velocity of object

CC Sabathia fires a baseball (m = 0.145 kg) past you at 100 miles/hr (45 m/s).

(a) Calculate the resistive force acting on the ball at that speed.

D… Drag coefficient = 0.284

…density of air = 1.29 kg/m3

r… radius of baseball = 0.037 m

v… velocity of object

Example

Air Drag a.k.a. Fluid Drag

Fluid friction = ½ CAv2

@ V terminal,

F = W – f = 0Solve for v:

mg - ½ CAv2 = 0

V terminal = (2mg/ CA)½

©2008 by W.H. Freeman and Company

Drag Forces

• Shape of the object.– Cars and planes are given aerodynamic shape to

reduce drag.

• Properties of the fluid.– Denser fluids increase drag.

• Speed of the object relative to the fluid.

What factors influence drag?

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speeds. lowat 1

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Terminal Velocity

• Because the drag force increases with increasing velocity, an object in free fall will reach a speed where the drag force balances the force of gravity.

• This speed is called terminal velocity.

Terminal Velocity

•

• At terminal velocity

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Getting to Terminal Velocity

• Because the drag force depends on velocity, at first the drag force is small and the motion is like free fall.

• At terminal velocity the velocity is constant.

• The graph is exponential growth. )1( BteAv

Getting to Terminal Velocity

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