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Free Fall Motion

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					Free fall motion
1   Three objects are let go from the same
    level.
A   The 1-kg object falls fastest.
B   The 3-kg object falls fastest.

C   The combined
                                     1 kg
    object falls
    fastest.
D   None of the
                      1 kg    3 kg   3 kg
    above.
2       Car A is moving to the left and
        decelerating...
        … car B is moving to the right and
        accelerating.

    A   decelerating          B    accelerating
A    decelerating                  B     accelerating
    Take left as positive direction, give the
    sign of the following quantities:

                       Car A         Car B
        Velocity         +             
     Acceleration                     
  1    Falling objects
In air, a coin falls faster than a piece of paper.
In a vacuum, they fall at the same rate.
The difference, in air, is due to air
resistance...
having a greater effect on light bodies than on
heavier bodies.
       2             Reading graphs
0.8                    s-t graph of free fall
                              motion
      Position (m)

0.6

0.4

0.2


             0.20      0.30      0.4   0.50   0.60   0.70
                              time (s)
                v-t graph of free fall motion
3.5
      velocity (m/s)   Linear Fit

3.0                    m ( Slope )
                       b ( Y Intercept )
                                              9.4174
                                              3.0252
                       r                      0.9975
                       Standard Deviation m   0.1836
                       Standard Deviation b   0.0945
2.0
                                                       slope <9.8 m s–2
1.0                                                      Due to air
                                                         resistance.

              0.20      0.30          0.4   0.50            0.60   0.70
                                   time (s)
Q1 In our daily life, the lighter...
     In our daily life, the lighter objects
     usually fall slower because
     A     it is a physical law.
     B     it is an illusion.
     C     there is air resistance.
     D     there is measuring error.
   Q2    True or false...
The acceleration of a free falling object
increases as it falls faster and faster. (T/F)
   Q3 True or false...
The acceleration due to gravity is larger for
heavier objects on Moon.                 (T/F)
Q4   Draw the s-t, v-t and...
Draw the s-t, v-t and a-t graphs of a freely
falling object from rest. (downwards: +ve.)
           s




                                  t
    Q4    Draw the s-t, v-t and...
    Draw the s-t, v-t and a-t graphs of a freely
    falling object from rest. (downwards: +ve.)
s                   v



         slope t

                           point
                                           t
    Q4   Draw the s-t, v-t and...
    Draw the s-t, v-t and a-t graphs of a freely
    falling object from rest. (downwards: +ve.)
v
                    a
            slope
                        point
                t



                                           t
2   Acceleration due to gravity
     If resistance is negligible...
     … a body falls freely under gravity with
     uniform acceleration.

      acceleration due to gravity g

       Accepted value = 9.8 m s–2

      Take g  10 m s–2 for simplicity
2     Acceleration due to gravity
    momentarily at rest
    a = –10 m s–2
          rises up, speed 
            a = –10 m s–2
          The ball is thrown
          vertically upwards
            u = 40 m s–1
            a = –10 m s–2
2   Acceleration due to gravity

       When the ball falls,
       its speed  at the
         rate of 10 m s–2




    Video           Simulation
3     Solving free fall problems
    The equations of motion...

          for uniformly accelerated motions...

                        … apply to falling objects.
         g  10 m s-2
      Example 10
(a)    How long does the stone     Central Plaza
       take to reach the ground?




                                       374 m
  Example 10
        u=0      s = 374 m
        a = g = 10 m s–2
        t=?

(a)   Applying s = ut + 1 at 2
                        2
                           1
            374 = 0  t +  10  t   2
                           2
              t = 8.65 s
      Example 10
(b)    With what speed does        Central Plaza
       the stone hit the ground?



                                       374 m
   Example 10
      u=0        s = 374 m
      a = g = 10 m s–2
      v=?
(b) Applying v 2  u 2 = 2as
               v 2  0 = 2  10  374

                   v = 86.5 m s1
   Example 10
        u=0      s = 374 m
        a = g = 10 m s–2
        v=?

                       The stone hits the
 What happens
if the stone hits      ground with a
    your head?         speed of 86.5 m s-1
                       (or 311 km h-1)!
   Example 11
Peter throws a stone vertically upwards
from the ground with a speed of 20 m s–1.
(a) How high does the stone rise?
      Example 11
(a)    How high does the stone rise?
       Upward journey:
       u = 2 m s–1
                         momentarily at rest
       v=0                (at highest point)

       a = 10 m s–2 (downwards ve)
       s=?

                            decelerates
                           as it rises up
      Example 11
(a)    How high does the stone rise?
       Applying v 2 – u 2 = 2as
                            v 2
                                 u2 02  (2) 2
                        s=          =
                               2a     2  (10)
                          = 0.2 m (upwards)
      Example 11
(b)    How long does it take to rise up & to
       return to the ground?
            Applying s = ut + 1 at 2
                              2
                                  1
                      0 = 5  t +  (–10)  t     2
                                  2
                    t = 0 or t = 0.4 s
       The stone is at s = 0 twice initially at 0 s
       and on its return to the ground
       after 0.4 s.
      Example 11
(c)    With what speed does the stone hit the
       ground?

       Applying v = u + gt
                  = 2 + (–10)  0.4
                  = –2 m s1

        The stone hits the ground on its return
        with a speed of 2 m s-1.
      Example 11
(d)    Sketch the (i) s-t graph
                  (ii) v-t graph
                  (iii) a-t graph
                  of the stone’s motion.
   Example 11
s-t graph

   displacement/m

      0.2




                           time/s
               0.2   0.4
   Example 11
v-t graph

   velocity/m s-1

        2

                                time/s


       –2
                    0.2   0.4
   Example 11
a-t graph

   acceleration/m s-2



                        time/s

     –10
   (For questions 1 to 5.) A ball is fired upwards
   with u = 5 m s1 from the top of a building...
   Q1 When the ball goes up...
 When the ball goes up, the speed it loses in
                  10 m s–1
 each second is __________.
A ball is fired upwards with u = 5 m s–1
       from the top of a building.

          It hits the ground 2 s later.
                      (Take g = 10 m s–2.
                     Neglect air resistance.)
    Q2 When the ball falls down...
 When the ball falls down, the speed it gains in
                   10 m s–1
 each second is _________.



A ball is fired upwards with u = 5 m s–1
       from the top of a building.

          It hits the ground 2 s later.
                      (Take g = 10 m s–2.
                     Neglect air resistance.)
    Q3 True or false...
 True or false: Its velocity changes direction as
 it passes the highest point.             (T/F)



A ball is fired upwards with u = 5 m s–1
       from the top of a building.

          It hits the ground 2 s later.
                      (Take g = 10 m s–2.
                     Neglect air resistance.)
    Q4 True or false…
 True or false: Its acceleration is zero at the
 highest point.                             (T/F)



A ball is fired upwards with u = 5 m s–1
       from the top of a building.

          It hits the ground 2 s later.
                      (Take g = 10 m s–2.
                     Neglect air resistance.)
Q5 What is the velocity...
What is the velocity of the ball when it hits the
ground? (Take upward direction as +ve)



A    s = 0 as it hits the ground.
     v2 = u2 + 2as = 52 + 0 = 25
     v = 5 m s-1 downwards
Q5 What is the velocity...
What is the velocity of the ball when it hits the
ground? (Take upward direction as +ve)



B     v = u + gt
        = 5 + 10  2 = 25 m s1
      The velocity is 25 m s1 downwards.
Q5 What is the velocity...
What is the velocity of the ball when it hits the
ground? (Take upward direction as +ve)

C   First, consider the rise.
    It momentarily stops at the highest point:
    t = (0  u)/a = (0  5)/(10) = 0.5 s
    Then, consider the fall.
    v = 0 + at = 0 + a  (2  t)
       = 0 + (10)  (2  0.5) = 15 m s1
    The velocity is 15 m s1.
Q5 What is the velocity...
What is the velocity of the ball when it hits the
ground (Take upward direction as +ve)


A    s = 0 as it hits the ground...
B    v = u + gt...
C    First, consider the rise.
     It momentarily stops...

				
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posted:11/17/2011
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