Centripetal force motorcycle problem

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SUMMARY

The discussion focuses on calculating the maximum speed of a motorcycle traveling over the crest of a hill with a circular arc radius of 45.0 meters without losing contact with the road. The key concept is understanding the forces acting on the motorcycle at the zenith, specifically the relationship between gravitational force (mg) and the normal force (FN). The conclusion is that when the motorcycle is at the point of losing contact, the normal force must be zero, leading to the equation FC = mv² / r = mg - FN = 0, which simplifies to FN = mg when the motorcycle is in contact.

PREREQUISITES
  • Understanding of centripetal force and its equation FC = mv² / r
  • Knowledge of free body diagrams and force analysis
  • Familiarity with gravitational force (mg) and normal force (FN)
  • Basic principles of circular motion
NEXT STEPS
  • Study the concept of centripetal acceleration and its implications in circular motion
  • Learn about free body diagram construction for various scenarios
  • Explore the effects of varying radius on maximum speed in circular motion
  • Investigate real-world applications of centripetal force in vehicles and roller coasters
USEFUL FOR

This discussion is beneficial for physics students, motorcycle enthusiasts, and anyone interested in the dynamics of vehicles in circular motion.

bulbasaur88
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A motorcycle is traveling up one side of a hill and down the other side. The crest of the hill is a circular arc with a radius of 45.0 meters. Determine the maximum speed that the cycle can have while moving over the crest without losing contact with the road.

Will somebody sound this problem out with me please? I think I am missing an important concept that I am missing...

Given
r = 45 m
Vmax = ____ m/s

What I Gather
We do not want the motorcycle to lose contact with the road, especially at the zenith.

At the very top of the hill, we have mg pointing down towards the center of the circle. We also have FN, which points up and away from the center of the circle.

***I hope the above forces have been set up correctly in my free body diagram.***

My question is: Doesn't FN = mg ?

That would give me: FC = mv2 / r = mg - FN = 0

? I get lost here...I am sure there is something wrong with either my FBD or my reasoning. Can I get a hint please?
 
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bulbasaur88 said:
At the very top of the hill, we have mg pointing down towards the center of the circle. We also have FN, which points up and away from the center of the circle.

***I hope the above forces have been set up correctly in my free body diagram.***
Looks good.

My question is: Doesn't FN = mg ?
No. If FN = mg, then the net force on the motorcycle would be zero--no acceleration at all.

Hint: What must FN be when the motorcycle just loses contact with the road?
 
Zero! - thank you :))))
 

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