The Physics of Phun:Roller Coaster ScienceThe Physics of Phun:

Roller Coaster Science

Steve CaseNSF NMGK-8

December 2005

Steve CaseNSF NMGK-8

December 2005

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Mississippi Frameworks Addressed:Mississippi Frameworks Addressed: 9a – Explore, measure, and graph the

motion of an object. 9b – Explore and measure the effect of

force on an object.

9a – Explore, measure, and graph the motion of an object.

9b – Explore and measure the effect of force on an object.

National Standards:National Standards: Content Standard A: Science as Inquiry Content Standard B: Physical Science

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

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: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

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

The Hill: Conservation of Energy

Why is the first hill of the roller coaster always the

highest?

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Conservation of EnergyConservation 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.

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

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.

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: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.

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: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.

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?

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.

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?

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.

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.

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-FallThe 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?

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).

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?

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.

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: InertiaThe Curves: Inertia

What squishes you into your seat around the corners?

What squishes you into your seat around the corners?

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To answer this question, we must define inertia.

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.)

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.

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:

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.

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

The Loop: Centripetal Force

Why don’t you fall out of your seat when the coaster goes up-side-

down?

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Centripetal ForceCentripetal 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.

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?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.

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?

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.

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?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.)

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

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.

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 LawNewton’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

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 LawNewton’s Second LawForce 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).

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 LawNewton’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.

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: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?

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 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?

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 . . .For more information . . .

Amusement Park Physics Links: <http://homepage.mac.com/cbakken/pga/links.html>

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/coaster.html>

Amusement Park Physics Links: <http://homepage.mac.com/cbakken/pga/links.html>

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/coaster.html>

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Photograph Sources: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/>

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/>