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Knex 78890 - Education Amusement Park Experience Teachers Guide Manual

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LESSON 11
11: C
11: C
OASTING
OASTING
TO
TO
THE
THE
E
E
ND
ND
- A
- A
PPLYING
PPLYING
THE
THE
C
C
ONCEPTS
ONCEPTS
LEARNED
LEARNED
www.knexeducation.com
ACTIVITY 4: WHY THE TEARS
Teacher’s Notes
• The loop was the illusive element for a long time during the modern coaster era. Loops formed
from perfect circles were used during the late 1800s, but few people rode such rides because of the
intensity of the g-forces. Finally, in 1976, engineers discovered that there was a shape that could be
used to turn riders upside down and not impose extreme g-forces on them and the first modern
looping coaster was constructed at the then Magic Mountain in California. The shape of the loop
resembled a teardrop and was known as a clothoid. The clothoid was actually a mathematical
function that was studied extensively by Euler. The clothoid was effective at reducing the g-forces
because of the changing radius of the loop.
• The g-forces on the riders at the bottom of the loop have centripetal force as a component.
To calculate the centripetal force, one uses the formula
where m is the mass, v is the speed, and r is the radius of the circle. At the bottom of the loop, where
the g-forces are greatest the radius is larger. This means that the centripetal force is reduced, since
the divisor in the expression, r, will be larger. Likewise, the centripetal force at the top of the loop and
other locations where the loop is tighter will be greater since the radius, r, is smaller.
C =
mv
2
r
PROCESS
Whole Class
1. Explain to the students that in this activity they will investigate the characteristics of the clothoid
(tear drop shape) loop and why it is used on a coaster.
In Groups
2. Students could use the following procedure for their investigation:
a. Use masking tape to connect the left track at the two supports that climb half way up the loop
on both sides.
b. Use masking tape to connect the left track at the very top of the loop to the bottom of the loop.
This will create a plus sign made of masking tape. The crossing represents the center of the
circle. This central point should be marked by a small dot.
c. Mark the top of the loop on the left track, using a water-based marker, and measure six 5 cm
increments in each direction from the left and right of the mark at the top.
d. Label each of the marks in order, starting with the mark that is closest to the lift hill on
the track.
3. Ask the students to:
a. Construct a 2-column table in their journals, with the labels that they have chosen in the
left column.
b. Measure and record (in the right column of the table) the distance from each of the labeled
points to the center of the circle (the dot on the masking tape). In other words, find the radius.
,
… 78


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