The Physics of Phun:
Roller Coaster Science
Steve Case
NSF NMGK-8
December 2005
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
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The Hill:
Conservation of
Energy
The Drop:
Free-fall
The Curves:
Inertia
The Loop:
Centripetal Force
The Big Picture:
Newton’s Laws of
Motion
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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
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The Hill: Conservation of
Energy
Why is the first hill of the
roller coaster always the
highest?
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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.
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 Potential Energy “stored” energy
 related to an object’s height above the
ground
 the higher something is, the more
potential energy it has
 Kinetic Energy “energy of motion”
 related to an object’s velocity
 the faster something is traveling, the
more kinetic energy it has
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 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.
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At the top of the first hill:
 Kinetic Energy?
 The coaster’s velocity is zero . . .
 Kinetic energy = 0
 Potential Energy?
 The coaster is very high . . .
 Potential energy = high
 All of the coaster’s energy is in the
form of potential energy.
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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.
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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 it’s traveling
half as fast as it will be at the bottom of the hill.
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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 don’t 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.
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The first hill of a roller coaster always
must be the highest, otherwise the
coaster won’t have enough energy to get
up the other hills.
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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.
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But don’t I always feel my own
weight?
Yes, but you don’t always feel JUST
your own weight. As much as
your weight is pressing
downward, there is usually
another force pressing upward.
If you’re walking, the ground pushes
up against you with a force equal
to your weight. If you’re 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).
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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.
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The Curves: Inertia
What squishes you into your seat
around the corners?
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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.)
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 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 body’s inertia to change your velocity.
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Another example of inertia:
 If you’re 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.
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The Loop: Centripetal Force
Why don’t you fall out
of your seat when the
coaster goes up-sidedown?
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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.
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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.
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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.
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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.)
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Newton’s 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.
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Newton’s 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
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Newton’s 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).
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Newton’s 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.
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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 you’re 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
object’s motion?
 Centripetal Force
 Centripetal force keeps a body moving in what kind of
motion?
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Newton’s Laws of Motion:
 Newton’s 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?
 Newton’s Second Law says that something
larger will have more or less force than
something smaller?
 Newton’s 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?
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For more information . . .
 Amusement Park Physics Links:
<http://homepage.mac.com/cbakken/pga/links.ht
ml>
 Britannica Online: Roller Coaster Physics:
<http://www.britannica.com/coasters/ride.html>
 Funderstanding Roller Coaster:
<http://www.funderstanding.com/k12/coaster/>
 Amusement Park Physics:
<http://www.learner.org/exhibits/parkphysics/coa
ster.html>
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Photograph Sources:
 Dave’s Roller Coaster Page. 2 May 2002.
Accessed December 8, 2005.
<http://www.jvlnet.com/~drounds/>
 Wikipedia, “Loop (roller coaster)”. 7 September
2005. Accessed December 8, 2005.
<http://en.wikipedia.org/wiki/Loop_%2
8roller_coaster%29>
 RealCoasters.com: Roller Coaster Photography. 23
October, 2005. Accessed December 8, 2005.
<http://www.realcoasters.com/>
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