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Centrifugal Force At Work? 
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#1
Dec1212, 07:48 AM

P: 937

Hello, the problem I am working on is:
"A puck of mass [itex]m = 51.0 g [/itex]is attached to a taut cord passing through a small hole in a frictionless, horizontal surface (see figure below). The puck is initially orbiting with speed [itex]v_i = 1.30 m/s[/itex] in a circle of radius [itex]r_i = 0.310 m[/itex]. The cord is then slowly pulled from below, decreasing the radius of the circle to [itex]r = 0.120 m[/itex]." In the problem, it states that the surface is frictionless, so what would counterbalance the tension force in the string, so that the puck wouldn't be pulled completely towards the hole in the center of the table? Is it the centrifugal force (or, inertial force)? If so, could someone give me a descriptive answer as to why it is the centrifugal acting. 


#2
Dec1212, 09:57 AM

Mentor
P: 11,589

Centrifugal force, in a rotating coordinate system.
Centripetal force, in an inertial system. The puck is changing its direction of motion all the time  and this acceleration is always "towards the center". It is the same concept as in planetary orbits: They are accelerated towards the sun all the time, which leads to a circular motion around the sun. Here, you change the force a bit, this changes the radius. 


#3
Dec1212, 10:38 AM

P: 937

Yes, I know the acceleration is directed towards the center. But what keeps the puck from moving towards the center of the table under the tension force?



#4
Dec1212, 10:53 AM

Mentor
P: 11,589

Centrifugal Force At Work?
The force is not sufficient to pull it in (it would have to be more than the centripetal force, but that is not limited). It moves closer to the center, this increases centripetal force until the system is in equilibrium again.



#5
Dec1212, 11:33 AM

P: 937

Is it not sufficient because of the puck's inertia?



#6
Dec1212, 12:02 PM

Mentor
P: 11,589

The puck's inertia is one of the concepts used to describe the system. It does not exist in a meaningful way with a theory what inertia does, and that is classical mechanics.



#7
Dec1212, 03:17 PM

HW Helper
P: 7,034

http://en.wikipedia.org/wiki/Reactive_centrifugal_force During the time the string is being pulled inwards, the path of the puck is a spiral, and a component of the tension in the string is in the direction of the inwards spiraling puck, increasing it's speed. Angular momentum will be conserved, while kinetic energy will be increased due to the work done by pulling the string inwards. 


#8
Dec1312, 07:40 AM

P: 937

rcgldr, so are you, and the wikipedia article, essentially saying that though the centrifugal force isn't real, its effects are?



#9
Dec1312, 05:09 PM

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Thanks
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#10
Dec1312, 06:22 PM

HW Helper
P: 7,034

http://en.wikipedia.org/wiki/Rotating_reference_frame wiki_centrifugal_force_(rotating_reference_frame) Note that all of these rotating frame fictitious forces appear to be forces exerted onto an object within the rotating frame. For your example, all of these rotating frarme fictitious forces would appear to act on the puck. This is different than the term "reactive centrifugal force". For your example, the "reactive centrifugal force" is exerted onto the string (not the puck). There is a net centripetal force exerted by the string onto the puck that accelerates the puck so that it follows a circular path. The puck reacts to this acceleration by exerting an outwards "reactive centrifugal force" onto the string. This "reactive centrifugal force" would correspond to the tension in the string. http://en.wikipedia.org/wiki/Reactive_centrifugal_force The wiki article on centrifugal force includes a section that explains the difference between fictitious and reactive forces: wiki_fictitious_vs_reactive_force.htm 


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