Bedienungsanleitung Knex 78890 - Education Amusement Park Experience Teachers Guide (Seite 78 von 80) (Alle Sprachen)

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LESSON 11

11: C

OASTING

THE

- A

PPLYING

THE

ONCEPTS

LEARNED

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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 =

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.

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Knex 78890 - Education Amusement Park Experience Teachers Guide Seite 78

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