UPWARD BOUND 2016 THE PHYSICS OF ROLLER COASTERS

UPWARD BOUND 2016 THE PHYSICS OF ROLLER COASTERS UNIVERSITY OF SAN DIEGO TOM SKELTON CONNER HOUGHTBY

WHAT DO YOU HOPE TO LEARN?

MY TWO QUESTIONS: 1. WHAT PULLS THE TRAIN? 2. WHY NOT CIRCLES FOR THE LOOPS?

COURSE GOAL: BASICS OF ROLLER COASTERS COURSE LEVEL: MOST OF PHYSICS SOME OF THE MATH OUTLINE: DEFINITIONS NEWTON’S LAWS APPLICATIONS (!)

DEFINITIONS WE WILL NEED VECTOR: HAS MAGNITUDE AND DIRECTION SPEED: HOW FAST IT’S MOVING VELOCITY: SPEED AND DIRECTION ACCELERATION: HOW FAST VELOCITY IS CHANGING - A VECTOR THIS MEANS THAT A CAR IS ACCELERATING IF IT IS SPEEDING UP, SLOWING DOWN, OR ROUNDING A CURVE YOU NEED TO REMEMBER THESE

NEWTON’S LAWS 1. An object at rest tends to remain at rest, and an object in motion tends to remain in motion in a line, unless acted on by a NET force. 2. Net Force equals mass x acceleration 3. If Object A exerts a force on Object B, then Object B exerts a force on Object A which is equal and opposite. The second law is written F NET = m a or a = F NET / m

The NET FORCE is the VECTOR SUM of all forces

Examples of forces Fg = Gravitational force – weight, pointed downwards FN = Normal Force – support force from tabletop, rails, etc. “normal” means the direction is perpendicular. Ff = Friction force – direction is along surface, rails, etc. FD = Drag force – opposite direction as velocity FT = Tension force – pull by a string, rope, etc.

A FREE BODY DIAGRAM HELPS ANALYSIS What force or forces act on the box (car)?

A FREE BODY DIAGRAM HELPS ANALYSIS F g is fixed; and F NET = F g + FN must point in the direction as a

MOTION IN A CIRCLE AT CONSTANT SPEED: Is it accelerating?

MOTION IN A CIRCLE AT CONSTANT SPEED: Is it accelerating? YES!! THE VELOCITY IS CHANGING!

MOTION IN A CIRCLE AT CONSTANT SPEED: Is it accelerating? THE ACCELERATION IS TOWARDS THE CENTER OF THE CIRCLE

MOTION IN A CIRCLE AT CONSTANT SPEED: Is it accelerating? YES; | a | = v 2/R v = speed R = radius THE ACCELERATION IS TOWARDS THE CENTER OF THE CIRCLE

APPLY WHAT WE HAVE LEARNED TO DRIVING IN CIRCLE ON A BANKED ROAD SKETCH TOP VIEW. TRACK IS BANKED. SKETCH HORIZONTAL VIEW. CAR COMING AT YOU. NO FRICTION. FREE-BODY DIAGRAM FN a d Fg F NET IN NORMAL DRIVING, FRICTION WOULD MEAN THAT SPEED v DOESN’T HAVE TO BE EXACT.

APPLY WHAT WE HAVE SO FAR TO TOP OF LOOP: SKETCH FREE-BODY DIAGRAM FN a F NET Fg What you feel is FN , the force on your body F NET = m a F NET = m v 2/ R F NET = Fg + FN =d m v 2/ R FN = m v 2/ R - Fg FN MIGHT BE NEAR ZERO; IF NEGATIVE …

APPLY WHAT WE HAVE SO FAR TO BOTTOM OF LOOP: SKETCH FREE-BODY DIAGRAM FN a F NET Fg F NET = m a F NET = m v 2/ R F NET = FN - Fg d= m v 2/ R FN = m v 2/ R + Fg FN WILL BE MUCH GREATER THAN Fg; FURTHERMORE… …

ENERGY IN A ROLLER COASTER GENERAL REMARKS ON ENERGY: ALWAYS CONSERVED – ONLY CONVERTED FROM ONE FORM TO ANOTHER SEVERAL FORMS: KINETIC – ASSOCIATED WITH MOTION GRAVITATIONAL POTENTIAL – HEIGHT THERMAL – BASICALLY SAME AS HEAT ELECTRIC CHEMICAL – SUCH AS A BATTERY OTHERS

ENERGY IN A ROLLER COASTER THE TOTAL ENERGY STAYS CONSTANT. POTENTIAL ENERGY CHANGES FORM TO KINETIC ENERGY P K K P P K

ENERGY IN A ROLLER COASTER K = ½ mv 2 P = mgh ETOT = K + P = constant Since there is really some friction, some energy is converted to heat. Ignore… P K K P P K

K = ½ m v 2 m = mass; often confused with weight, since they are similar in everyday life. Mass is the total amount of material. Weight is the gravitational pull on it, Fg. Fg = m g g is the acceleration due to gravity; same for any object. v is the speed, as before. P = mgh h is height above baseline. ETOT = K + P = constant (ignoring loss to heat)

ENERGY IN A ROLLER COASTER K = ½ mv 2 P = mgh ETOT = K + P = constant Since there is really some friction, some energy is converted to heat. Ignore… P K K P P K

A CAR IS TO BE RELEASED AT POINT “A. ” WHICH TRACK DESIGN WILL HAVE IT GOING THE FASTEST AT “B? ” A B

A CAR IS TO BE RELEASED AT POINT “A. ” WHICH TRACK DESIGN WILL HAVE IT GOING THE FASTEST AT “B? ” A B ALL THE SAME! SINCE THE CHANGE IN HEIGHT IS THE SAME, THE CHANGE IN POTENTIAL ENERGY IS THE SAME, AND SO IS THE CHANGE IN KINETIC ENERGY

B A WILL THE CAR MAKE IT OVER HILL B, WHICH IS HIGHER THAN HILL A?

K K K B P A P P WILL THE CAR MAKE IT OVER HILL B, WHICH IS HIGHER THAN HILL A? YES; IT HAS PLENTY OF TOTAL ENERGY.

GO BACK TO THE TOP OF LOOP: SKETCH FREE-BODY DIAGRAM FN a F NET Fg What you feel is FN , the force on your body F NET = m a F NET = m v 2/ R F NET = Fg + FN =d m v 2/ R FN = m v 2/ R - Fg If FN = 0, then Fg = m v 2 top / R. A little more algebra and v 2 top = Rg

GO BACK TO BOTTOM OF LOOP: K K P A LITTLE ALGEBRA, AND FN = 6 Fg AT THE BOTTOM

BIOLOGICAL CONSIDERATIONS Increased blood pressure Can rupture weak spots in arteries, etc Can damage arteries Brain Damage 6 g’s is the limit for many people; too much for some

ENGINEERING CONSIDERATIONS There is friction – and it varies with wear, lubrication There is air drag – and it varies with wind Safety in keeping car on the track Structural strength of the support Speed adjustment – compensate for variations

MY TWO QUESTIONS: 1. WHAT PULLS THE TRAIN? 2. Nothing, after the original lift … Energy 2. WHY NOT CIRCLES FOR THE LOOPS? Too many g’s …