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What is causing the normal force in circular motion?

  1. Feb 16, 2015 #1
    TQC1j0N.jpg

    In the picture, at point 2 (the bottom of the ramp) the normal force of the object has a greater magnitude than weight. I understand that the normal force has to be greater than the weight since the acceleration points towards the center of the circle and the net force is in the same direction as the acceleration. However, that doesn't explain what causes the normal force to be greater than weight.

    If the object was placed at point 2 without the prior motion (sliding down the ramp) in the diagram, the normal force would equal weight. But why does sliding down the ramp increase the magnitude of the normal force at point 2? Here's another way to phrase it: since normal force is the reactionary force of the force the object exerts on the surface, why is the force of the object on surface greater than the weight at point two?
     
  2. jcsd
  3. Feb 16, 2015 #2

    tony873004

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    At point 2, his instantaneous velocity is completely in the horizontal direction. An infinitesimal amount of time after he reaches point 2, he will no longer be traveling horizontal. What's causing this deviation from the straight line he would otherwise travel along? It's the ground pushing up. This is true of all the points from point 1 to point 2. In each point, draw his instantaneous velocity vector. The curved ground prevents him from traveling on this straight line. His motion along the curved path causes him to push against the ground. The ground pushes back. The force the ground exerts on him is a a normal force acting as a centripetal force. It is added to the normal force he would have if he were stationary on the incline: N=mg cosθ.
     
  4. Feb 20, 2015 #3

    CWatters

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    Perhaps compare this problem with the tension in a pendulum. The track is preventing him travelling in a straight line and is accelerating him towards the centre point O. So there are two forces which sum to give the normal force.. that resulting from gravity and that required to make him move in a circle.
     
  5. Feb 22, 2015 #4
    Ah, I see you are actually trying to UNDERSTAND what's going on, the "mechanics" behind the mechanics, the why's and whereabouts, how things work. You're trying to actually FEEL the forces, you want to actually be able to intuitively FEEL that ground force pushing back at you. And you're on the right track, thinking in terms of action and reaction. Let me explain:
    As you've pointed out, the normal force is just a reaction force. Friction is another example of a reaction force. Such forces don't just come out of nowhere, they don't initiate by themselves; there has to be some external "action", some external agent, creating an "action", to which such forces can oppose or "react". So the question then becomes, why is the object pushing into the ground in the first place? Or equivalently, if we wish to know why there is tension in the pendulum, since tension is a reaction force, we should ask : "why is the bob pulling on the string? And why so strongly (at the bottom)?"

    Well, Newton's first law tells us that objects have tendency to move in a STRAIGHT LINE. If they are at rest, they will stay there untouched. If they are moving, they will keep moving along a straight line. They have INERTIA, tendency to remain the same, or resistance to external change. The greater the mass of the object, the greater this inertia. Also, the greater the velocity of the object, the greater it's inertia, meaning that it would require greater force to affect its motion. In a nutshell, the greater the momentum of the object, the harder it is to change its mind as to where it's going.

    Which one do you think is harder to keep put , a wild beast or a tiny chihuahua? The beast can pull stronger on the leash, so it would require greater force to keep it "on track". On the other hand, it also depends on its speed; for instance if the beast ain't moving at all, you don't need to exert any force to keep it put. On the other hand if our little friend's on the run, and with lightning speed...well you get the drift ;)

    So it really depends on the momentum of the object how hard it is to keep it on track. The greater the momentum, the greater the force (or impulse) required to change it's momentum for some given amount. In our case, the mass of the object is constant, but like I said, it has tendency to move in a straight line due to its velocity. If it's attached to an essentially unstretchable string, it will pull on the string, causing it to micro-lengthen until the string can bear no more and becomes taught. The greater the speed (or mass) of the rotating object, the greater its tendency to "escape" the central force (due to Newton's first law), and thus the harder it will be to tame the beast. Ultimately, if the object is really heavy, or moving super fast, it will pull so hard that the string may break.

    At the bottom of the ramp, the skater has the greatest speed ( you could use Newton's second law to prove this, or consider that it has maximum kinetic energy at the lowest level). He's got the greatest tendency to move along a straight line at the bottom, hence he's pushing into the ground hardest at the bottom, and the normal force, being normal to the surface, is doing its thing keeping the guy on track.

    Also keep in mind that sometimes reaction forces can serve as "action" forces acting on other objects. For instance, If you have a moving object DRAGGING another object on top of it with itself, here the static friction force becomes action force for the top object. In the pendulum example, even though the tension in string is in reaction to the force from the bob, it is an action force when considering the ceiling to which it is attached. In this case, it will be the force from the ceiling which is reacting to the tension force.
     
    Last edited: Feb 22, 2015
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