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					3.3 Carousels
and Roller Coasters
                 THE VIPER
                 (Six Flags Over
                 Magic Mountain)

                 188 feet high
                 70 mph
                 One of the largest
                 looping roller
                 coasters in the world
Top Thrill Dragster
(Cedar Point)
420 feet tall
120 mph
0 to 120 mph in 4 sec

“ …free-falls back to
Earth, reaching a
speed of 120 mph for
the second time…”

$ 25 million
Amusement park rides
are fun when they make
us accelerate around
loops, twists, turns, etc.

        WHY?
New ideas for today
•Feeling of acceleration
•Circular motion
•Roller coaster physics!
At the start of a NASCAR race… Office chair
                                            Cart




                            Feeling of
                            acceleration

                        F

   •Which direction is the force on the driver?
   •Which way is the feeling of acceleration?
What about at the end of a race?




                       F


        Feeling of
        acceleration
Which way do you feel the
acceleration for circular motion?
                         Feeling of
                         acceleration
                      Force




But the cables pull you inward!
A “stupid human trick”




  The human carousel
Feeling of
acceleration
               F
Feeling of       F
acceleration

Circular motion:
       force is toward center of circle
Note: the kid in the middle feels no acceleration!
      v                     Tennis ball on string




                                   at




Try this at home – acceleration always
points toward the middle of the circle
Uniform circular motion – constant speed
       2         Ice table, record player
    v
ac    r Centripetal
        2

     r     acceleration
                   2
             v
Fc  mac  m           Centripetal
             r
    m r
        2              force

•Always points to center of circle
•As you move to the edge of the
 carousel:
   is constant, force increases,
  speed increases         Xmas lights
So far:
 •Feeling of acceleration always
  opposite to acceleration:
      FOA = -ma
 •Uniform circular motion involves
  force toward center of circle
The experience of weight


               The force of your
               weight causes a
               series of support
               forces between
               parts of your body
  Your body senses
  changes in these
  support forces as a
  change in weight!

Force from
accelerating elevator
The Feeling of
Acceleration
      and
Apparent Weight

  AW = W + FOA
Acceleration and Weight
• Feeling of acceleration
   – Feeling is caused by your support forces
     acting on your body
   – It points in the direction opposite the
     acceleration
   – It has a strength proportional to the
     acceleration
• “Apparent weight” is felt due to the combined
  effects of gravitational acceleration and the
  feeling of acceleration
• Your body really can’t tell the different
  between acceleration and weight!
• Neither can anything else…this idea led to
  theory of general relativity by Einstein
“g-forces” are what         Inside the Numbers

make roller coasters        G
                            Force
                                     Example



and carousels fun!
                              1      Standing.
                              1.2    Normal elevator acceleration (up).
                             1.5-2   Walking down stairs.
                              2-3    Hopping down stairs.
                              1.5    Commercial airliner during takeoff run.
                              2      Commercial airliner at rotation.
                              3.5    Maximum acceleration in amusement park rides
                                     (design guidelines).
                              4      Indy cars in the second turn at Disney World (side
                                     and down force).
                              10     Threshold for blackout during violent maneuvers in
                                     high performance aircraft.
                              10     The NASA g-force simulator is limited to 10 g for
                                     astronaut training.
                              11     Alan Shepard in his historic sub orbital Mercury
                                     flight experience a maximum force of 11 g. During
                                     this time he was unable to speak because he could
                                     not move his jaw.
                              20     The Colonel Stapp experiments on acceleration in

 Measure acceleration                rocket sleds indicated that in the 10 to 20 g range
                                     there was the possibility of injury because of
                                     organs moving inside the body.

 in units of g = 9.8 m/s2     30     The design maximum for sleds used to test
                                     dummies with commercial restraint and air bag
                                     systems is 30 g.
     g-force = -a
Clicker Question                              Rotating stool


A woman is
riding one of
those “barrel of
fun” rides at the
amusement park.                Feeling of
                               acceleration
Which one of the
diagrams best
shows the forces
acting on the
woman?              Apparent
                    weight A           B      C    D     E
                 Leaky cup, bean bag

NASA’s vomit comet




     look at the passengers!
Clicker Question
What has to be true about
the acceleration a of the
vomit comet (if the
apparent weight of the
passengers is zero)?

A. a points upward
B. a points downward
C. a points towards the
   center of their
   circular trajectory
Roller coasters
  You better believe in conservation
  of energy if you want to live!
                    “Most people find this   Loop
                    sudden reduction in
                    apparent weight
                    terrifying.”




Note: this is not uniform circular motion!
Roller Coaster Loops
At top of loop:
   – acceleration is large and downward
   – so feeling of acceleration is large and
     upward
   – apparent weight is therefore much less
     than equilibrium weight:
     can feel weightless or even feel force
     upward.
Roller Coasters Hills
  • Just over the top of hill
    (think about descent),
     – acceleration is mostly downward
     – so feeling of acceleration is mostly upward
     – apparent weight is therefore less than
       equilibrium weight, and into the track.
  • Just past the bottom of hill
    (think about ascent),
     – acceleration is mostly upward
     – So feeling of acceleration is mostly
       downward
     – apparent weight is therefore more than
       equilibrium weight, and into the track.
Why we want the
last seat on the
roller coaster
The weight of the first cars
 combined accelerates the
 last cars over the hill
For next class: Read Section 4.1




     See you next class!

				
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