why a person do not fall form the loop of highest point of roller coaster since the centripetal acceleration and gravitational acceleration is point inward to the circle? According to my textbook, when the centripetal acceleration is greater than the gravitational acceleration, the person do not fall from roller coaster. Therefore, the centripetal should point outward to balance the gravitational acceleration, right?
-
One thing to be clarified in this aspect, is that velocity and acceleration vectors are not in the same direction always. In the case of the vertical circle (or so to say, the top of the loop of a roller coaster), we observe that the net acceleration is downwards. But 'motion' is not always in the direction of 'acceleration'. These are two different things.
If you have done the vertical circle problem, you would know that even though at the top most point both mg and N forces are directed downward to the center of the circle, yet the stone you have whirled will complete the circle if given a minimum velocity. The stone there, does not fall down straight at the top most point (as is ur claim in this question).
The reason: At the top most point, net acceleration is downwards no doubt, but the object going in a vertical circle has attained a certain velocity on its journey upwards. Hence, at the top most point, it has a certain component of velocity along X and Y directions, hence it does not "fall from the top" of the loop. Instead it shoots on in the direction of its velocity vector, thus completing the circle.
I hope this is clear; especially the point that acceleration and velocity need not be in the same direction always!
If you have done the vertical circle problem, you would know that even though at the top most point both mg and N forces are directed downward to the center of the circle, yet the stone you have whirled will complete the circle if given a minimum velocity. The stone there, does not fall down straight at the top most point (as is ur claim in this question).
The reason: At the top most point, net acceleration is downwards no doubt, but the object going in a vertical circle has attained a certain velocity on its journey upwards. Hence, at the top most point, it has a certain component of velocity along X and Y directions, hence it does not "fall from the top" of the loop. Instead it shoots on in the direction of its velocity vector, thus completing the circle.
I hope this is clear; especially the point that acceleration and velocity need not be in the same direction always!
-
You may be making confusion on centrifugal and centripetal forces (or accelerations). The centrifugal acceleration forces you to the roller coaster seat, thus has to be more than gravity for you not fall (at the top of the loop). have a look on the source I indicated that there are sketches that make it clear.