The Physics of Phun: Roller Coaster Science The Physics of Phun: Roller Coaster Science Steve Case NSF NMGK-8 December 2005

North Mississippi GK-8 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 :  Content Standard A: Science as Inquiry  Content Standard B: Physical Science  Content Standard A: Science as Inquiry  Content Standard B: Physical Science

North Mississippi GK-8 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

North Mississippi GK-8 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

North Mississippi GK-8 The Hill: Conservation of Energy Why is the first hill of the roller coaster always the highest?

North Mississippi GK-8 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.  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.

North Mississippi GK-8  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

North Mississippi GK-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.

North Mississippi GK-8 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.

North Mississippi GK-8 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.

North Mississippi GK-8 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.

North Mississippi GK-8 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.

North Mississippi GK-8 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.

North Mississippi GK-8 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.

North Mississippi GK-8 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).

North Mississippi GK-8 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.

North Mississippi GK-8 The Curves: Inertia What squishes you into your seat around the corners?

North Mississippi GK-8 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.)

North Mississippi GK-8  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.

North Mississippi GK-8 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.

North Mississippi GK-8 The Loop: Centripetal Force Why don’t you fall out of your seat when the coaster goes up-side- down?

North Mississippi GK-8 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.  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.

North Mississippi GK-8 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.

North Mississippi GK-8 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.

North Mississippi GK-8 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.)

North Mississippi GK-8 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.

North Mississippi GK-8 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 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

North Mississippi GK-8 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). 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).

North Mississippi GK-8 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. 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.

North Mississippi GK-8 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?

North Mississippi GK-8 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 ?

North Mississippi GK-8 For more information...  Amusement Park Physics Links:  Britannica Online: Roller Coaster Physics:  Funderstanding Roller Coaster:  Amusement Park Physics:  Amusement Park Physics Links:  Britannica Online: Roller Coaster Physics:  Funderstanding Roller Coaster:  Amusement Park Physics:

North Mississippi GK-8 Photograph Sources:  Dave’s Roller Coaster Page. 2 May Accessed December 8,  Wikipedia, “Loop (roller coaster)”. 7 September Accessed December 8,  RealCoasters.com: Roller Coaster Photography. 23 October, Accessed December 8,  Dave’s Roller Coaster Page. 2 May Accessed December 8,  Wikipedia, “Loop (roller coaster)”. 7 September Accessed December 8,  RealCoasters.com: Roller Coaster Photography. 23 October, Accessed December 8, 2005.