Centripetal force of a roller coaster car

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SUMMARY

The discussion centers on calculating the speed of a roller coaster car at the top of a 30-meter diameter loop, where the apparent weight equals the true weight. The relevant formula is F=mv²/r, where the radius is 15 meters. Since the apparent weight equals the true weight, the net force at the top of the loop is zero, indicating that the centripetal force required for circular motion is provided entirely by gravitational force. The conclusion is that the speed can be derived from the relationship between gravitational force and centripetal force without needing the mass of the car.

PREREQUISITES
  • Understanding of centripetal force and its formula F=mv²/r
  • Knowledge of gravitational force, expressed as F=mg
  • Basic principles of circular motion
  • Familiarity with the concept of apparent weight
NEXT STEPS
  • Calculate the speed of an object in circular motion using F=mv²/r
  • Explore the relationship between gravitational force and centripetal force
  • Study the effects of radius on the speed of roller coasters
  • Investigate the concept of apparent weight in different gravitational contexts
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in the dynamics of roller coasters and circular motion principles.

sdskater15
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I got all the other centripetal force questions but this one has me stumped...

As a roller coaster car crosses the top of a 30m-diameter loop-the-loop, its apparent weight is the same as its true weight. What is the car's speed at the top?

The formula I used for all of the other questions was F=mv^2/r. The problem is the only number I have is the diameter (therefore radius). I'm guessing because the apparent weight is the same as true weight the net force is zero? There's also no way to get mass. Maybe there's another formula? Any assistance with this problem would be much appreciated!
 
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The true weight of something is F=mg, so then you don't need to figure out the mass.
 
Last edited:
If the apparent weight is the same as the true weight, then the passengers at the top of the loop are experiencing the equivalent of 1 g of force from their seats.
 

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