Motion in a Circle: Find Slowest Speed for Roller Coaster

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SUMMARY

The discussion focuses on calculating the slowest speed for a roller coaster at the top of a vertical loop with a radius of 300 meters. The correct answer is established as 5.86 m/s, which ensures that all centripetal force is provided by the roller coaster's weight. The user initially miscalculated the speed using the formula for centripetal force, leading to confusion. The correct relationship is derived from setting centripetal force equal to gravitational force, confirming the answer found in the textbook.

PREREQUISITES
  • Understanding of centripetal force and acceleration
  • Familiarity with gravitational force equations
  • Basic knowledge of physics concepts related to motion in a circle
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Study the derivation of centripetal acceleration formulas
  • Learn about gravitational force calculations in physics
  • Explore examples of motion in circular paths
  • Investigate real-world applications of centripetal force in amusement park rides
USEFUL FOR

Students studying physics, educators teaching motion concepts, and anyone interested in the mechanics of roller coasters and circular motion dynamics.

fern
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heh! this is my first post!
ok... I've been trying to do this for ages, i think I am just doing it the wrong way... its holiday homework so i couldn't ask my teacher
i drew a diagram but i think i did it wrong... I am just not getting the right answer!
ok here it is
part of a roller coster track is in the shape of a vertical circle of radius 300m. what is the slowest speed the roller coster can have at the top of the loop so that all the centripetal force is supplied by the roller coaster's weight?
answer:5.86 m/s
could someone please explain how to do this!
stank you! :smile:
 
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Allright:
Given velocity and radius of the circle you're moving on; what's the centripetal ACCELERATION you experience?
 
As far as I know the answer is
centripetal force=weight
mv^2 /r= mg
v=54.221 m/s
 
Looks good to me; the answer is wrong.
 
argh! thank you! heheh that answer (5,86) was in the back of the book! i hate it when they make mistakes it just confuses me!
i propbaly would have got it if the answer was right!
thank you so much! :smile:
 

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