5-3 Drag Forces

1
5-3 Drag Forces

• Drag forces come from fluids gas or liquid
  and are generally proportional to the square of
  the speed of the object

• So, as falling object accelerates, drag force
  gets bigger and bigger, until it is equal to
  accelerating force

• At this point, the net force on the object is
  zero, and it moves at a constant velocity from
  then on this is called the terminal velocity

2
5-3 Drag Forces
(5-30)
Here, FD is the drag force ? the density of
the medium A the cross-sectional area of the
object CD the drag coefficient.
3
Terminal Speed

• The terminal velocity is found from the
  condition that the forces of gravity and the drag
  are equal and opposite

• We solve for terminal speed

(5-31)
4
A Better Approximation to Drag Force

• Precise experiments reveal that the force law
  for the drag force depends in a more complicated
  way on the medium through which the object moves
  and on the shape and size of the moving object
  than Eq 5-30 suggests. In fact, at low speeds,
  the drag force is proportional to v, not v2.

• It is only after the speed has increased enough
  to produce turbulence in the medium that the v2
  term comes in.

5
A Better Approximation to Drag Force

• Thus a better approximation to the drag force
  magnitude than Eq (5-30) is

(5-32)

• The coefficients b and c contain information on
  the shape of the moving object as well as on the
  medium in which it moves. The first term
  dominates for sufficiently low speeds, while the
  second term dominates for higher speeds.