Slide 2 Roller Coasters: The Clothoid Loop
http://upload.wikimedia.org/wikipedia/commons/f/f7/Rollercoaster_dragon_khan_universal_port_aventura_spain.jpg
Slide 3 Why the tears??? Have you ever examined a roller coasters
loop? They will always look more like a tear drop than a circle.
This tear drop shape is called a clothoid loop. A clothoid loop is
essentially a loop where the radius of curvature changes. Why a
clothoid loop? The answer lies in the engineers desire to make the
ride thrilling, but SAFE. How does physics relate to the safety of
a rider?? gees!!!! Over the next several slides, we will see why
this shape has to be. Slide 4 Circular Loop vs. Clothoid Loop Two
different shaped loops same total height R = 6.0 m h = 12.0 m R BOT
= 8.0 m R TOP = 4.0 m h = 12.0 m Note: We will consider a
simplified version of a clothoid loop one in which the clothoid is
made up of two different radii. In this case, both the entrance and
exit have radii = 8.0 m. The top has a radius = 4.0 m. Slide 5
Circular Loop Calculation Our ultimate goal is to figure out how
many gees a rider would experience in a circular loop and compare
this to a clothoid loop. Work through this series of questions
without looking at the solution. If you get stuck, try clicking on
the speaker graphic next to the question for a hint. (Try it on
your own first.) When you are finished, you may look at the next
few page for the solution. 1)A rider will always feel the largest
number of gees at the bottom of a loop. Why? 2)Assume that the mass
of the rider is 75 kg and use g = 10.0 m/s 2. Find the minimum
speed that the roller coaster can go at the top of the loop without
relying on the seat belt to hold the person up. 3) Find the speed
at the bottom of the loop (assuming no friction). 4) Find the
normal force at the bottom. 5) Find the # of gees the person
experiences at the bottom. R = 6.0 m h = 12.0 m Slide 6 Circular
Loop - Solution 1)A rider will always feel the largest number of
gees at the bottom of a loop. Why? The # of gees we feel is related
to the normal force that is acting on us. At the bottom of a loop,
the normal force must overcome gravity to create an upward
acceleration. At the top of the loop, the normal force and gravity
are both acting downward so the normal force will be smaller.
2)Assume that the mass of the rider is 75 kg and use g = 10.0 m/s
2. Find the minimum speed that the roller coaster can go at the top
of the loop without relying on the seat belt to hold the person up.
R = 6.0 m h = 12.0 m Slide 7 Circular Loop Solution Cont R = 6.0 m
h = 12.0 m 3) Find the speed at the bottom of the loop (assuming no
friction). Slide 8 Circular Loop Solution Cont R = 6.0 m h = 12.0 m
4)Find the normal force at the bottom. 5) Find the # of gees the
person experiences at the bottom. Slide 9 Clothoid Calculation Now,
we would like you to answer the same set of questions except for
the clothoid loop. You will compare your solutions at the start of
class with your partner(s). Make sure you use the appropriate
radius for each question. 1)Again, assume that the mass of the
rider is 75 kg and use g = 10.0 m/s 2. Find the minimum speed that
the roller coaster can go at the top of the loop without relying on
the seat belt to hold the person up. 3) Find the speed at the
bottom of the loop (assuming no friction). 4) Find the normal force
at the bottom, just as the rider is entering the loop. 5) Find the
# of gees the person experiences as they enter the loop. R BOT =
8.0 m R TOP = 4.0 m h = 12.0 m Slide 10 A first approximation of
friction Lets return to the circular loop problem. Lets assume that
a car 550 kg car enters the circular loop going 17 m/s and exits
the loop going 16.5 m/s. What is the average frictional force
acting on the car? Listen to this speaker graphic. R = 6.0 m h =
12.0 m
