The Physics of Phun: Roller Coaster Science

1
The Physics of PhunRoller Coaster Science

• Steve CaseNSF NMGK-8December 2005

2
Mississippi Frameworks Addressed

• 9a Explore, measure, and graph the motion of an
  object.
• 9b Explore and measure the effect of force on
  an object.

National Standards

• Content Standard A Science as Inquiry
• Content Standard B Physical Science

3

• The Hill Conservation of Energy
• The Drop Free-fall
• The Curves Inertia
• The Loop Centripetal Force
• The Big Picture Newtons Laws of Motion

4
Some Important Terms

• Velocity how fast something is traveling
  measured in distance per time
• Acceleration how quickly something is changing
  velocity measured in change in velocity per time

5
The Hill Conservation of Energy
Why is the first hill of the roller coaster
always the highest?
6
Conservation of Energy

• Energy can never be created or destroyed. The
  amount of energy in a system will always be the
  same.
• Once a coaster starts, the system cannot gain any
  more energy.
• However, energy can be transformed from one form
  to another.
• Energy is transformed from potential energy to
  kinetic energy and back again and from kinetic
  energy to heat energy by friction.

7

• Potential Energy-
• stored energy
• related to an objects height above the ground
• the higher something is, the more potential
  energy it has
• Kinetic Energy-
• energy of motion
• related to an objects velocity
• the faster something is traveling, the more
  kinetic energy it has

8

• Conservation of energy says that the amount of
  energy the coaster has will always be constant.
  This means the potential energy of the car plus
  the kinetic energy of the car must always be the
  same. If the potential goes up, the kinetic must
  come down if the kinetic goes up, the potential
  must come down.

9
At the top of the first hill

• Kinetic Energy?
• The coasters velocity is zero . . .
• Kinetic energy 0
• Potential Energy?
• The coaster is very high . . .
• Potential energy high
• All of the coasters energy is in the form of
  potential energy.

10
At the bottom of the hill

• Kinetic Energy?
• The coaster is moving at a high velocity.
• Kinetic energy high
• Potential Energy?
• The height of the coaster is zero . . .
• Potential energy 0
• By the time the coaster reaches the bottom of the
  hill, all potential energy has been transformed
  to kinetic energy.

11
What about half-way down the hill?

• Potential Energy?
• The coaster is only half as high as it was at the
  top . . .
• The coaster has half the potential energy it did
  at the top. (Where did the rest go?)
• Kinetic Energy?
• Half the potential energy has been transformed
  into kinetic energy.
• The coaster has half the kinetic energy it will
  have at the bottom of the hill, which means its
  traveling half as fast as it will be at the
  bottom of the hill.

12
But why is the first hill highest?

• When the coaster reaches the bottom of the first
  hill, all its energy has been transformed from
  potential to kinetic energy.
• As it goes up the next hill, that kinetic energy
  must be transformed back into potential energy so
  the process can repeat.
• But dont forget friction the coaster is always
  losing energy to friction between the car and the
  tracks, so each time it goes up a hill it will
  have less kinetic energy to transform back into
  potential.

13

• The first hill of a roller coaster always must be
  the highest, otherwise the coaster wont have
  enough energy to get up the other hills.

14
The Drop Free-Fall
The feeling you get when you go down the first
hill of a roller coaster, when your stomach seems
to drop, is called free-fall. Free-fall is what
you experience when the only force you feel is
from your own weight.
15
But dont I always feel my own weight?

• Yes, but you dont always feel JUST your own
  weight. As much as your weight is pressing
  downward, there is usually another force pressing
  upward.
• If youre walking, the ground pushes up against
  you with a force equal to your weight. If youre
  sitting on your chair, your chair is pressing
  upward with a force equal your weight.
• This is what it means for two forces to be
  balanced (equal and opposite).

16
What Happens When the Floor Is Gone?

• If someone were to remove the floor or your
  chair, there would no longer be a force pressing
  upward against you. There would be nothing to
  balance the force of your weight.
• The force on your body would be unbalanced and
  you would fall.
• This is what happens on the sharp drops on a
  coaster, and you experience a brief sense of
  weightlessness.

17
The Curves Inertia

• What squishes you into your seat around the
  corners?

18
To answer this question, we must define inertia.

• Inertia is the tendency of all matter to resist
  changes in motion. (Change in motion can include
  change in speed or change in direction.)

19

• All matter wants to keep moving in the same
  direction and at the same speed unless a force
  acts upon it.
• When the coaster rounds a curve, your body wants
  to keep traveling in a straight line.
• The force of the seat or straps pressing against
  you change your direction and make you move along
  with the coaster.
• This is also why you feel pressed back into the
  seat when the coaster accelerates. The coaster
  is changing speeds while your body wants to
  remain still. The force of the seat against your
  back acts against your bodys inertia to change
  your velocity.

20
Another example of inertia

• If youre in a car and the driver slams on the
  brakes, what happens?
• The inertia of your body keeps you moving forward
  until the force of your seatbelt stops you.

21
The Loop Centripetal Force
Why dont you fall out of your seat when the
coaster goes up-side-down?
22
Centripetal Force

• Centripetal force is a force that keeps something
  moving in circular motion.
• If you imagine swinging a yo-yo in a loop, the
  tension in the string that keeps the yo-yo
  traveling in a circle is centripetal force.
• The yo-yo wants to keep traveling in a straight
  line (remember inertia), but the force of the
  string keeps pulling it inward.

23
What if you swung the yo-yo over your head?

• The yo-yo would keep traveling in a circle (if
  you swung it fast enough), because the inertia of
  the yo-yo wanting to fly outward would balance
  the gravity and centripetal force pulling it
  downward.

24
What about loops on a coaster?

• Instead of the centripetal force of a string, the
  centripetal force around a loop in a coaster acts
  through the tracks pushing on the cars.
• The inertia of the cars and passengers at the top
  of the loop is great enough to overcome the
  centripetal force of the track pushing and
  gravity pulling downward.

25
What if the coaster breaks down at the top of a
loop?

• Most coasters have safety features to keep this
  from happening, but if it does happen . . .
• Once the car and passengers are stopped, inertia
  is no longer pushing them out of the loop nor is
  centripetal force pushing them into the loop.
• The only force active in this situation is
  gravity. (Better hope those straps are secure.)

26
Newtons Laws of Motion Bringing It All Together

• Long before roller coasters were invented, Sir
  Isaac Newton devised three laws to explain the
  way things move.

27
Newtons First Law

• An object moving at a certain speed in a certain
  direction will continue moving at that same speed
  and direction unless acted upon by an outside
  force.
• This is known as the Law of Inertia
• Where can we see it on a coaster?
• Curves
• Loops
• Any time the coaster changes speed or direction

28
Newtons Second Law

• Force is equal to mass times acceleration.
• (F ma)
• This means that the larger something is or the
  faster it is changing speed or direction, the
  more force it has.
• When do we experience greatest force on a
  coaster?
• Whenever the coaster is changing speed very
  quickly or going around sharp curves (changing
  direction quickly).

29
Newtons Third Law

• For every action, there is an equal and opposite
  reaction.
• Remember what we said about your weight pressing
  downward and the floor pressing upward with equal
  force.
• As the coaster speeds up or rounds curves, your
  body presses against the seat or straps and they
  press against you with equal and opposite force.

30
Quick Review

• Conservation of Energy
• Can energy be created or destroyed?
• Between what two forms can energy be transformed
  back and forth?
• Free-fall
• If youre sitting in your chair, what two forces
  are acting on your body?
• Inertia
• What does a body moving at a certain speed and
  direction want to continue to do?
• What is needed to change the speed or direction
  of an objects motion?
• Centripetal Force
• Centripetal force keeps a body moving in what
  kind of motion?

31
Newtons Laws of Motion

• Newtons First Law explains that you are pressed
  up against the side of the car when the coaster
  rounds sharp bends because your body possesses
  what?
• Newtons Second Law says that something larger
  will have more or less force than something
  smaller?
• Newtons Third Law says that if you press against
  the straps of the coaster with a certain force,
  with what force do the straps press back against
  you?

32
For more information . . .

• Amusement Park Physics Links .com/cbakken/pga/links.html
• Britannica Online Roller Coaster Physics
  
• Funderstanding Roller Coaster tanding.com/k12/coaster/
• Amusement Park Physics hibits/parkphysics/coaster.html

33
Photograph Sources

• Daves Roller Coaster Page. 2 May 2002.
  Accessed December 8, 2005. m/drounds/
• Wikipedia, Loop (roller coaster). 7 September
  2005. Accessed December 8, 2005.
  ster29
• RealCoasters.com Roller Coaster Photography. 23
  October, 2005. Accessed December 8, 2005.