Download Dag Force and Terminal Speed

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
5-3 Drag Forces
(5-30)
Here,
FD is the drag force;
ρ the density of the
medium;
A the cross-sectional
area of the object;
CD the drag
coefficient.
Terminal Speed
• The terminal velocity is found from the
condition that the forces of gravity and the
drag are equal and opposite:
1
2
mg   ACD vt
2
• We solve for terminal speed
vt 
2mg
 ACD
(5-31)
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.
A Better Approximation to Drag Force
• Thus a better approximation to the drag
force magnitude than Eq (5-30) is
FD  bv  cv
2
(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.