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Applications of Newton Laws

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					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
y                         r = radius is
         ( 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
      exerted by the road on
      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