# Applications of Newton Laws

Document Sample

```					Chapter 5
Applications of
Newton’s Laws
5-1
Friction
Static Friction

The force of static friction
increases until it
reaches a maximum
value

fs      s Fn
f s ,max  s Fn
Kinetic Friction

The object begins to
slide and the force of
friction that is now
acting is called
the force of
kinetic friction

f k  k Fn
k
Example 5-2
Example 5-2 (1)
Free-Body Diagram

Fn  w  f S  ma
ˆ
Fn  0i  Fn ˆ
j
ˆ
w  mg sin  i  mg cos  ˆ
j
ˆ
f S   f si  0 ˆ
j
ˆ
a  0i  0 ˆ
j
Example 5-2 (2)
Free-Body Diagram

Fn  w  f S  ma
Equate x and y
components
Fn  mg cos   0  0
0  mg sin   f s  0
Example 5-2 (3)
Free-Body Diagram

Fn  w  f S  ma
mg sin    fs

mg cos  Fn
tan   s
5-2
Motion Along a
Curved Path
Circular Motion                      (1)

ˆ
r  r (cos  i  sin  ˆ )
j
( x, y )             constant

r
      ˆ
j
O                        x
iˆ
Circular Motion                  (2)

dr
v      Velocity
y                      dt
d
( x, y )               ˆ
 r (cos  i  sin  ˆ)
j
dt
r
      ˆ
j
O                     x
iˆ
Circular Motion                     (3)
d          ˆ
v  r (cos  i  sin  ˆ) j
dt
y                        d d
r                  ˆ
(cos  i  sin  ˆ)
j
( x, y )         d t d
d
r                 r               ˆ
( sin  i  cos  ˆ)
j
dt
      ˆ
j        d/dt is the
O                     x angular velocity
iˆ
Circular Motion                     (4)

dv
a    Acceleration
y                      dt
( x, y )         v (t  t )
r                v (t )               v (t )
      ˆ
j
O
v (t  t )  v (t )
x
iˆ                            t
Circular Motion                     (5)
dv
a      Acceleration
dt
y                    d  d           ˆ  cos  ˆ) 
 r      ( sin  i         j 
( x, y )    dt  dt                       
 d 
2

r              r              ˆ
( cos  i  sin  ˆ)
j
 dt 
     ˆ
j          Assume
O                     x d/dt is constant
iˆ
Circular Motion                     (6)
 d 
2

a  r             ˆ
(cos  i  sin  ˆ)
j
 dt 
y
 d 
2

( x, y )     r      ˆ
 r
 dt 
r                          Centripetal
      ˆ
j                  Acceleration
O                       x
iˆ
Circular Motion               (7)
Magnitudes of velocity
and centripetal
y                       acceleration are
( x, y )           related
as follows
r                             2
v
O
      ˆ
j              a
iˆ
x         r
Circular Motion                (8)
Magnitude of velocity
and period T related as
y                           follows
( x, y )
2 r
r                      v
ˆ
T
      j
O                     x
iˆ
Example 5-10     (1)
Turning corners
Example 5-10       (2)

The static friction force
the car causes the car to
accelerate towards the
center of the circle;

that is, to turn!
Example 5-11      (1)
Rounding a Banked Curve
Example 5-11      (2)
Free-Body Diagram

Vertically
Fn cos   mg  0

Horizontally
Fn sin   ma
v2
m              v2
r    tan  
rg
5-3
Drag Forces
Problems

To go…
Ch. 5, Problem 43
Ch. 5, Problem 51
Ch. 5, Problem 53
Ch. 5, Problem 70

```
DOCUMENT INFO
Shared By:
Categories:
Stats:
 views: 196 posted: 4/10/2011 language: English pages: 31