1. Fundamentals of Physics School of Physical Science and Technology
Mechanics
(Bilingual Teaching)
张昆实
School of Physical Science and Technology
Yangtze University

2. Chapter 6 Force and Motion-II
6-1 Friction
6-2 Properties of Friction
6-3 The Drag Force and
Terminal speed
6-4 Uniform Circular Motion

3. 6-1 Friction
Friction: When a force tends to slide a body along a surface, a frictional force from the surface acts on the body.
The frictional force is parallel to the surface and directed so as to oppose the sliding. It is due to bonding between the body and the surface.
If the body does not slide, the frictional force is a static frictional force
If there is sliding, the frictional force is a kinetic frictional force

4. 6-2 Properties of Friction
When a dry and unlubricated body presses
against a surface, a force attempts to slide the
body along the surface, the frictional force has:
Property1. If the body does not move, then the
static frictional force and the component of
that is parallel to the surface balance each
other.
Property2. The magnitude of has a maximum velue :
is the coefficient of static friction
If , the body begins to slide.
(6-1)

5. 6-2 Properties of Friction
Property3. If the body begins to slide along the surface, the magnitude of the frictional force rapidly decreases to a value
is the coefficient of kinetic friction.
The coefficient and are dimensionless and
must be determined experimentlly.
漆安慎书 :P75 table 3.2
(6-2)

6. 6-3 The Drag Force and Terminal speed
When there is a relative motion between air
( or some other fluid ) and a body, the body
experiences a drag force that opposes
the relative motion and points in the direction
In which the fluit flows relative to the body.
The magnitude of is related to the
relative speed by an experimentlly
determined drag coefficient C according to
(6-14)
(6-14)

7. 6-3 The Drag Force and Terminal speed
(6-14)
Where is the air density; is the
effective cross-sectional area of the body
( the area of a cross section taken
perpendicular to the velocity ).
The drag coefficient C can vary with the
variation of , For simplicity, take it
as a constant.

8. 6-3 The Drag Force and Terminal speed
(6-14)
Falling
body
During the falling, Newton’s second law for a vertical y axis:
If the body falls long enough, eventually equals the body’s speed no longer increases.
(6-15)

9. 6-3 The Drag Force and Terminal speed
If the body falls long enough,
eventually equals
the body’s speed no longer
increases. The body then falls at
a constant speed, called the
terminal speed
Find :
(6-15)
terminal speed
(6-16)

10. 6-3 The Drag Force and Terminal speed
Skydiving

11. 6-3 The Drag Force and Terminal speed
Group Skydiving

12. 6-4 Uniform Circular Motion
★ Uniform circular Motion : ( Section 4-7 )
A particle travel around a circle or a circular arc
at constant (uniform) speed , it is said to be in
Uniform circular Motion.
The body has a centripetal acceleration.
direction: toward the center of the circle;
magnitude:
(4-32)
Example: Fig.6-9 , P107
A centripetalforce accelerates a body by
changing the direction of the body’s velocity
without changing the body’s speed.

13. 6-4 Uniform Circular Motion
★ From Newton’s second law and
(4-32)
(magnitude of centripetal force)
The directions of the centripetal acceleration and
force are not constant, they vary continuously so
as to always point toword the center of the circle
along a radial axis The positive direction of
the axis is radially outward, but the acceleration
and force vectors point radially inward.
Sample problem 6-9 : P110