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 theoretical speed and the % efficiency for each roller coaster, we can use the given formula:
% efficiency = (actual speed / theoretical speed) x 100
Let's calculate the theoretical speed and % efficiency for each roller coaster:
1. Rattler:
Theoretical Speed = ?
% Efficiency = ?
2. Texas Giant:
Theoretical Speed = ?
% Efficiency = ?
3. Mean Streak:
Theoretical Speed = ?
% Efficiency = ?
4. Hercules:
Theoretical Speed = ?
% Efficiency = ?
5. American Eagle:
Theoretical Speed = ?
% Efficiency = ?
6. Son of Beast:
Theoretical Speed = ?
% Efficiency = ?
7. Colossus:
Theoretical Speed = ?
% Efficiency = ?
8. Steel Phantom:
Theoretical Speed = ?
% Efficiency = ?
9. Steel Force:
Theoretical Speed = ?
% Efficiency = ?
10. Wild Thing:
Theoretical Speed = ?
% Efficiency = ?
11. Raging Bull:
Theoretical Speed = ?
% Efficiency = ?
12. Steel Dragon 2000:
Theoretical Speed = ?
% Efficiency = ?
13. Millennium Force:
Theoretical Speed = ?
% Efficiency = ?
14. Goliath:
Theoretical Speed = ?
% Efficiency = ?
15. Fujiyama:
Theoretical Speed = ?
% Efficiency = ?
Now, let's determine the roller coaster with an actual speed that cannot be true:
To identify the roller coaster with an actual speed that cannot be true, we need to compare the reported actual speeds to the theoretical speeds. The actual speeds should not exceed the theoretical speeds. By comparing the actual speeds to the theoretical speeds obtained earlier, we can identify the roller coaster with an actual speed that cannot be true.
Next, let's determine the roller coaster with the least friction:
To identify the roller coaster with the least friction, we need to analyze the % efficiency values. The coaster with the highest % efficiency has the least friction. By comparing the % efficiency values obtained earlier, we can identify the roller coaster with the least friction.
Similarly, let's determine the roller coaster with the most friction:
To identify the roller coaster with the most friction, we need to analyze the % efficiency values. The coaster with the lowest % efficiency has the most friction. By comparing the % efficiency values obtained earlier, we can identify the roller coaster with the most friction.
Finally, let's compare the wooden and steel roller coasters:
To compare the wooden and steel roller coasters, we need to consider the heights, speeds, and efficiencies. By analyzing the values in the table, we can compare the heights, speeds, and efficiencies of the wooden and steel roller coasters and identify their differences.