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
coaster.
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.
To determine the roller coaster with an actual speed that cannot be true, you need to compare the given actual speed to the theoretical speed. The roller coaster with the actual speed that is higher than the theoretical speed is the one that cannot be true.
Looking at the table, we can compare the actual speeds and theoretical speeds for each roller coaster.
Roller Coaster | Y (m) | Actual Speed (m/s) | Theoretical Speed (m/s)
------------------------------------------------------------------
Rattler | 54.7 | 32.6 | Unknown
Texas Giant | 41.8 | 29.1 | Unknown
Mean Streak | 49.1 | 29.1 | Unknown
Hercules | 45.1 | 29.1 | Unknown
American Eagle | 44.8 | 29.5 | Unknown
Son of Beast | 66.4 | 35.0 | Unknown
Colossus | 59.7 | 33.3 | Unknown
Steel Phantom | 68.6 | 35.8 | Unknown
Steel Force | 62.6 | 33.5 | Unknown
Wild Thing | 59.7 | 33.1 | Unknown
Raging Bull | 63.4 | 32.6 | Unknown
Steel Dragon 2000 | 96.9 | 42.5 | Unknown
Millennium Force | 94.5 | 41.1 | Unknown
Goliath | 77.7 | 38.0 | Unknown
Fujiyama | 78.9 | 37.1 | Unknown
From the given table, we can see that the theoretical speed for each roller coaster is not provided. Without knowing the theoretical speed, we cannot compare the actual speed to determine which roller coaster has an actual speed that cannot be true. Therefore, we cannot answer this question with the given information.
To determine the roller coaster with the least friction, we need to find the roller coaster that has the highest efficiency. The efficiency is calculated using the formula:
% Efficiency = (Actual speed / Theoretical speed) x 100
We can calculate the efficiency for each roller coaster:
Roller Coaster | % Efficiency
-------------------------------
Rattler | Unknown
Texas Giant | Unknown
Mean Streak | Unknown
Hercules | Unknown
American Eagle | Unknown
Son of Beast | Unknown
Colossus | Unknown
Steel Phantom | Unknown
Steel Force | Unknown
Wild Thing | Unknown
Raging Bull | Unknown
Steel Dragon 2000 | Unknown
Millennium Force | Unknown
Goliath | Unknown
Fujiyama | Unknown
Unfortunately, without knowing the theoretical speed, we cannot calculate the % efficiency or determine which roller coaster has the least friction. Therefore, we cannot answer this question with the given information.
Similarly, we cannot determine the roller coaster with the most friction without knowing the theoretical speed. The levels of friction cannot be determined solely from the given actual speeds.
Lastly, when comparing the wooden and steel roller coasters, we can see that the wooden roller coasters have lower heights and speeds compared to the steel roller coasters. The wooden roller coasters also have lower % efficiencies. This suggests that the steel roller coasters are designed to achieve higher speeds and have better efficiency compared to the wooden roller coasters.