Motion in a Circle: Find Slowest Speed for Roller Coaster

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To find the slowest speed for a roller coaster at the top of a vertical loop with a radius of 300m, the centripetal force must equal the weight of the coaster. The correct formula is mv²/r = mg, leading to the calculation of centripetal acceleration. The expected answer for the slowest speed is 5.86 m/s, which was confirmed to be correct. The initial confusion arose from a miscalculation that suggested a much higher speed of 54.221 m/s. Accurate understanding of the relationship between centripetal force and gravitational weight is essential for solving such problems.
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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