This speed is the maximum possible speed attained by the roller coaster, or the
“theoretical speed”. Roller coasters are carefully designed to minimize frictional forces
so that they approach these theoretical speeds. The efficiency of a roller coaster design
can be found by comparing the actual speed attained with this theoretical speed...

% efficiency = (actual v / theoretical v ) x 100
The table below gives reported values for height (y) and maximum speed attained by
actual roller coasters. Determine the theoretical speed and the % efficiency for each

Y(m) actual speed (m/s) theoretical speed(m/s) % efficiency

Roller Coaster
Rattler 54.7 32.6
Texas Giant 41.8 29.1
Mean Streak 49.1 29.1
Hercules 45.1 29.1
American Eagle 44.8 29.5
Son of Beast 66.4 35.0
Colossus 59.7 33.3
Steel Phantom 68.6 35.8
Steel Force 62.6 33.5
Wild Thing 59.7 33.1
Raging Bull 63.4 32.6
Steel Dragon 2000 96.9 42.5
Millennium Force 94.5 41.1
Goliath 77.7 38.0
Fujiyama 78.9 37.1

Which roller coaster has an actual speed that cannot be true? How do you know?

Which roller coaster has the least friction?

Which roller coaster has the most friction?

The first seven roller coasters listed are made of wood and the last eight are made of
steel. Use your table to compare the wooden and steel roller coasters. How are they
different? Consider heights, speeds, and efficiencies.

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