Six flags physics?
American Eagle Specifications
Description: A double-track, racing wooden roller coaster.
Introduced 1981
Top Speed 66.32 mph
Ride Duration 2 minutes, 35 seconds
Number of Trains, Cars, and Passengers 6 trains
5 cars per train
30 passengers per train
Passengers per Hour 1,800
Height Restriction Must be at least 48" tall
Manufacturer Figley-Wright Contractors For Intamin
Height of Lift 127 feet
Length of First Lift 330 feet
Chain Speed = 9 feet/sec
Degree of First Drop 55o
Length of First Drop 147 feet
Length of Track 4,650 feet per track
9,300 total feet of track
Number of Helix 3
Gravity Forces Do not exceed 1.65 gees in the dips
Weight of Each Car 2,300 pounds
Drive Motor 200 horsepower
Other Interesting Facts 2,000 concrete footings (average of 18" diameter, 4.5' deep)
1,360,000 board feet of lumber used
129,720 bol
Answer:
Average speed = length of track (ft) / ride duration (sec)
= 4650 ft / 155 sec = 30 ft/sec
Average velocity = 0 (train stops at same location it starts)
Weight (not mass) of train (empty) = 5 cars / train * 2300 lb/car = 11500 lb. To this, add weight of 30 passengers for weight of a full train.
Potential energy of train at top of first lift (compared to beginning/end of ride) = weight of train * height of lift = 11500 lb (empty) * 127 ft = 1.46e6 lb-ft. (Note: weight is mg, not just m.)
Centripetal acceleration - does not exceed 0.65 gee (1.65 gee - 1 gee for gravity); 0.65 gee * 9.81 m/sec^2 / gee * 1 in/2.54e-2 m * 1 ft/12 in = 20.9 ft/sec^2
Cannot use F = ma to find corresponding centripetal force because not all five cars would be at the bottom of the loop at the same time; can only get a rough estimate of the upper bound this way. Assuming an average of 150 lb per passenger, this would add 4500 lb to the 11500 lb weight of the empty train for 16000 lb. Divide by g = 32.17 ft/sec^2 and multiply by 20.9 ft/sec^2 (or simply multiply 16000 lb by 0.65 gee) to get a maximum centripetal force of 10400 lb.
Approx speed at bottom of first drop:
Energy at top (empty)
= potential energy at top - potential energy at bottom + kenetic energy at top
= (mg)*delta h + 1/2*m*(vo)^2
delta h = 147 ft * sin (55 deg)
vo = 9 ft/sec
g = 32.17 ft/sec^2
Energy at bottom (empty)
= 1/2*m*v^2
1/2*m*v^2 = (mg)*delta h + 1/2*m*vo^2
v = sqrt (2*g*delta h + vo^2)
= 88.5 ft/sec
Rated top speed of 66.32 mi/hr
* 5280 ft/mi * 1 hr/3600 sec
= 97.3 ft/sec
You cannot find centripital force given the information provided.
speed? "Top Speed 66.32 mph"
velocity? "Top Speed 66.32 mph. down"
potential energy (empty) is mass x gravity x height = 2300 x (# of cars) x 9.8 x 127
I dont think you understand what you're asking. The top speed is given in your information and velocity is just speed with a direction. Potential energy varies largely depending on if the cars have people in them and how much those people weigh. Also you need to how how many cars weighing 2300 lbs there are.
If you perhaps revise the information provided I could help more.
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