PHYSICS: centripetal force

[snoopypoo]

I find my understanding of this problem seemingly contradictory of centripetal force.

Aren't these two always true about Fc
1. Objects moving at circle have net force = mv^2/r
2. that this net force points towards the center

However in doing Berkeley and the problem with roller coasters, I am confused. The problem states poorly paraphrased as such :what is the direction of the net force when a roller coaster is at lets say point B traveling through a loop. If the loop is a clock point B is 3 o clock.

Solution states that with mg pointing down and normal force pointing towrad the center, that the net force is pointing toward 6oclock. This answer must contradict statements 1 or 2 above. Right?

Looking at this picture point B refers to "right side of the loop"
http://www.physicsclassroom.com/mmedia/circmot/rcd1.gif

Picture from a somewhat related topic:
http://forums.studentdoctor.net/showthread.php?t=685186

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[Handinhand]

I have always thought circular motion was the hardest to grasp, because it's hard to visualize the problems. Instead of normal force, try and imagine a string is attached to a ball going around in a circle. When the ball is at 6 o' clock, gravity is acting fully against the ball. When the ball is at 8 o' clock. gravity is still acting straight down, but now the ball isn't completely in the plane of gravity, so it only acts on the ball partially (like a box on a slope, gravity only works on the box at the sin(theta))

So, you are right when you way Fc = constant throughout the entire motion, because radius, mass, and velocity aren't changing. However, this doesn't ask about Fc, it asks about Fnet. Hopefully after reading above, you can see that Fnorm and Fgrav are infact NOT constant throughout motion.

I do think you have your time positions on a clock wrong though. The only way Fnet would be pointing toward 6 is if the mass is at 12.

 

[snoopypoo]

I have always thought circular motion was the hardest to grasp, because it's hard to visualize the problems. Instead of normal force, try and imagine a string is attached to a ball going around in a circle. When the ball is at 6 o' clock, gravity is acting fully against the ball. When the ball is at 8 o' clock. gravity is still acting straight down, but now the ball isn't completely in the plane of gravity, so it only acts on the ball partially (like a box on a slope, gravity only works on the box at the sin(theta))

So, you are right when you way Fc = constant throughout the entire motion, because radius, mass, and velocity aren't changing. However, this doesn't ask about Fc, it asks about Fnet. Hopefully after reading above, you can see that Fnorm and Fgrav are infact NOT constant throughout motion.

I do think you have your time positions on a clock wrong though. The only way Fnet would be pointing toward 6 is if the mass is at 12.

I unfortunately posted this in another thread because I though this thread couldnt be created. hmm, but lets see.

Yes, the positions metioned above are correct. The net force points towards 6oclock when the coaster is at the 3oclock position. This is also true when the coaster is at 12oclock. Is Fc the net force or not? After seeing the solution Iwas thinking the normal force was Fc and that Fc does not have to be the net force

 

[godcyning]

Fc and the net force are 2 different things. Fc has the characteristics you mentioned: Fc = mvv/r, and points to the center of the circular path. Net force on the other hand, is just the sum of all the forces acting on the object.

Fc = centripetal force. So the key to rotational motion is that anything going in a circle at a constant speed must have a force on it that points toward the center of the circle. This can be counterintuitive, because that's perpendicular to the velocity. But think about it this way: a ball....in space (no other forces, namely gravity). Suppose you'd like the ball to move in a circle at a constant speed of 10mph. If the ball is going 10mph it will want to continue straight the way it's going. You have to do something to it to make it turn, to make it curve. You have to put a force on it. If you don't want it to speed up or slow down, your force has to be perpendicular to its velocity vector. But wait, the instant you put that force on it, you've changed the velocity direction, and so you've got to change your force to be perpendicular to THAT direction, otherwise the ball will change speed. At every INSTANT the force you need to apply has to be perpendicular to the velocity, and so your force is also always changing. Note, this is a very qualitative way of viewing rotational motion. To take the next step, you can show (or just have faith that) the MAGNITUDE of the force has to be mvv/r.

So what's this got to do with like, real life? How do you get this "force that constantly changes to be perpendicular to velocity"? A string attached to a ball does just that. So does gravity, to a satellite. So does the normal force of a rollercoaster rail on the rollercoaster car in a circular loop-de-loop. This is the centripetal force, ZOMG.

So in the rollercoaster problem you have, it asks for the net force at B. The only forces acting on the car are a) normal (from the track) and b) gravity. Gravity is simple enough, it's always mg. You know the direction of the normal force, but to get its magnitude you have to know how fast the car is going and how much it weighs. Treating the loop-de-loop as a circular path, you've got a car of known mass and speed going in a circle of known radius. So you can calculate what the centripetal force would have to be to produce that kind of circular motion. You know that Fc = Fnormal in this case, because well, the car's going in a circle and the only force that's always pointed at the center is Fnormal. Knowing Fnormal and Fgrav, Fnet is just the vector sum of those.

Oh, an added complication is that due to gravity, the car slows down as it goes up, so you gotta somehow factor that in too (potential and kinetic energy). Just be thankful that unlike in real life, friction doesn't exist in physics problems that aren't about friction.

 

[Seraph 84]

Centripetal motion become a tricky topic when the speed of the object is not constant.

For objects moving at constant speed like twirling a ball on a string, the net force is directed towards the center.

In this problem, however, the net force is not directed toward the center because the speed of the coaster is not constant. In all the figures, the coaster has the force F(cent) directed toward the center and a tangential force to increase or decrease it's speed. The tangential force is only gravity - or a component of gravity.

This should make sense because the coaster will have the greatest magnitude of tangential acceleration at 9 and 3 o' clock and no tangential acceleration at noon or 6 o' clock. This is why coasters speed up and slow down in a loop - the net force isn't always directed toward the center.

 

[Insulinshock]

Centripetal motion become a tricky topic when the speed of the object is not constant.

For objects moving at constant speed like twirling a ball on a string, the net force is directed towards the center.

In this problem, however, the net force is not directed toward the center because the speed of the coaster is not constant. In all the figures, the coaster has the force F(cent) directed toward the center and a tangential force to increase or decrease it's speed. The tangential force is only gravity - or a component of gravity.

This should make sense because the coaster will have the greatest magnitude of tangential acceleration at 9 and 3 o' clock and no tangential acceleration at noon or 6 o' clock. This is why coasters speed up and slow down in a loop - the net force isn't always directed toward the center.

Ok, now I'm confused. If the object is constantly, say, accelarating, which direction does the force point?

 

[Seraph 84]

Ok, now I'm confused. If the object is constantly, say, accelarating, which direction does the force point?

For constant acceleration, the net force is toward the center.

In the roller coaster example the acceleration is changing and is dependent on the car's position in the loop; therefore, the direction and magnitude of the net force must be variable, which it is.

 

[godcyning]

Ok, now I'm confused. If the object is constantly, say, accelarating, which direction does the force point?

I'm not 100% sure, but are you asking about if an object goes in a circle and changes speed as it does? Technically anything going in a circle is constantly accelerating (changing velocity because it's changing direction, but speed is constant).

For an object going in a circle at constant speed, the net force is the centripetal force: a force pointed at the center equal to mvv/r.

If the object wants to change speed (but move in the same circular path), then it needs to get some force in the tangential direction. So the net force would just be the sum of the centripetal + tangential forces. It would not point toward the center.