Circular motion
Monday, March 9, 2009 This post is for helping people with problems in vertical circular motion!!!After much heated discussion with KaiYi ......
MUAHAHAHAHA I SAW THE LIGHT! (we both saw it actually)
As one of the ICs of class blog, I decided to put it here to benefit the whole class
Animation--> http://webphysics.davidson.edu/physlet_resources/bu_semester1/c8_vertical.html
Raw Maths/Logic -->http://www.physicsforums.com/showthread.php?t=121314
In case u wondering wads all that normal reaction force crap --> http://www.physicsforums.com/library.php?do=view_item&itemid=73
A summary of ideas that are 100% true(so you guys can use them as guide instead of cracking ur head over it):
- In case u are wondering why reaction force can be smaller or bigger than mg (it goes against newton's 3rd law), it is because in circular motion, this rule "dosen't" apply(layman terms, actually it does in some way).
- No such thing as centrifugal force
- For Bucket w/ Water, F(c) at top = Mg(pointing down) + Normal(pointing down) = m(v^2/r)
- For different situations, the "2nd" component determining F(c) will vary. (eg Normal reaction, Tension, Gravity ect.) But gravity will always be there.
- All the forces we consider are forces that ACT on the thing eg Gravity, normal reaction force(because its pushing outwards and normal reaction force is keeping it in) not forces that the thing act on other stuff
- Tip on minimum/maximum speed: Minimum speed and Maximum speed only applicable for certain situation. So far the vertical circular motion situations i encountered only either has minimum speed or maximum speed. I haven't met a situation where there is a limit on both.
1. For maximum speed, try this train of thought:
Hypothetical situation for explaining: Car ON top of a hill
Forces on the car: Mg (downwards) , Normal Reaction Force(Upwards)
F(c) = Mg - N = m(v^2/r)
If speed goes up, F(c) has to increase also. But mg is a constant, so N has to become smaller. As N tends towards 0, F(c) = mg. At maximum speed, centripetal force is mg. Now u got the maximum centripetal force, u can calculate maximum velocity[m(v^2/r) remember?]
A bit of extension. Now, what if velocity gets higher than maximum? In order for v to be higher, F(c) must be higher, but it is not possible since mg is constant, therefore because centripetal force is not enough to keep the car in current radius, the car will just start flying like ET :D
2. For minimum speed, try this train of thought
Hypothetical situation to explain: Water + Pail (muahahaha familiar?)
Considering Pail,
Forces at top: Mg(downwards), Tension(downwards)
F(c) = Mg + Tension = m(v^2/r)
The Train of thought(choo choo):
If the velocity is minimum, then the string will be slack(not taut) right? not taut implies that the tension = 0
Therefore F(c) = mg = m(v^2/r)
sub in values then get answer! :D
Considering Water,
Forces on the water at top: Mg(downwards), Normal reaction force(downwards)
F(c) = Mg + N
water at minimum speed in bucket w/o flying out imply that must be barely touching the pail. Which means that normal reaction force is approximately zero (dosen't press on bucket)
Therefore
F(c) = Mg = m(v^2/r)
sub and get speed :D
Hopefully this post is helpful in clarifying those circular motion doubts.
I wanted to add pictures badly but very lazy and short of time so..... D:
Special thanks to KaiYi for trying to teach me
lolx the class blog became my physics notebook...