Circular Motion: What's the Source of Centripetal force in this?

  • #26
haruspex
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Nothing. The force of gravity will 'keep the truck moving' in a parabola
It moves in a circle. It never ceases moving in a circle. Therefore, at all times, there is a centripetal force.
Even if an object moves in a parabola it has, at each instant, a centre of arc, so there is a centripetal force.
The centripetal force is the component normal to the velocity of the resultant of applied forces.
The only applied force at the apex is gravity. Ergo, gravity is providing the centripetal force.
 
  • #27
hmmm27
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Even if an object moves in a parabola it has, at each instant, a centre of arc, so there is a centripetal force.

So you're contending that any force is "centripetal" in nature when it acts on an object ?

Otherwise, the only centripetal force in the problem is the normal force - gravity affects that, but is not a centripetal force in its own right.
 
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  • #28
haruspex
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So you're contending that any force is "centripetal" in nature when it acts on an object ?

The only centripetal force in the problem is the normal force. Gravity affects that, but is not a centripetal force in its own right.
A centripetal force is not an applied force, it is a resultant of applied forces. It is only the component normal to the velocity, so no, I am not saying any force is centripetal in nature.
Beyond that, I don't think there is universal agreement on its definition. Some would only use the term in circular motion, while others accept it in any motion where there is an instantaneous centre of arc. Others reject the term altogether, only referring to centripetal acceleration.

Certainly for a satellite in a circular orbit you would have to accept gravity as providing the centripetal force.
 
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  • #29
hmmm27
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Certainly for a satellite in a circular orbit you would have to accept gravity as providing the centripetal force.

Yes, and I accept that a point or line source force has an integral "centripetality"
 
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  • #30
andrewkirk
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@haruspex I'm not sure whether we are in agreement or disagreement. My opinion is that the question is not a proper science question, and should be relegated to the philosophy department. Physics questions are about formulas, equations and measurements, not about causes. 'Cause' is a rubbery term that can mean almost anything. I think your comparison of the question to Zeno is apt, because the question is like Zeno's paradox statements - a confusion that arises from using imprecise words instead of precise equations. But unlike whoever wrote this question, Zeno had the excuse that calculus had not been invented yet.

When I am finally emperor of the world (why is it taking so long!) it will be forbidden for science lecturers to ask questions like 'what is keeping the truck moving in a circular path' as opposed to 'identify all objects that exert a force on the truck and find the magnitude of each such force'. The answer to the first question, as with all other such questions, is 'the Big Bang'.
 
  • #31
hmmm27
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So, at the end of the day, all the help we can give the OP is

When answering 'b', be sure to specify the domain, ie: "at the apex" or "within the circle".
 
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  • #32
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I think this all raises more questions than there already were. I am going to go with 'gravity' while answering this and hope they just don't bring this question in the exam.(Too many confusions, specifically because of this part 'When the truck is at the position shown there is no reaction force between the wheels of the truck and the track.')
 
  • #33
andrewkirk
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(Too many confusions, specifically because of this part 'When the truck is at the position shown there is no reaction force between the wheels of the truck and the track.'
There's actually no problem with that statement. It is a clear, meaningful, scientific statement, because it talks about the forces that two bodies exert on one another. Further, it is correct.

The problem is question (a), which is unclear. A good exam strategy when faced with unclear questions is to just write down your understanding of the situation. For example here you could write something like:

Excluding friction and air resistance, the net force on the truck can be decomposed into components normal and parallel to the track.

The parallel component varies over time according to this formula <write formula> and causes the speed of the truck to vary. That component is equal to the component of the gravitational force on the truck that is parallel to the track. It is zero when the truck is at the point shown.

The normal component is always equal to <insert formula> and is a centripetal force as a result of which the truck moves in a circle. It is the sum of the normal force exerted by the track and the component of the gravitational force on the truck that is normal to the track. The former varies over time and is equal to <insert formula>. It is zero at the point shown, so the magnitude of the gravitational force is equal to that of the centripetal force.​

It would be hard for them to mark you down with an answer like that.
 
  • #34
hmmm27
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Too many confusions, specifically because of this part 'When the truck is at the position shown there is no reaction force between the wheels of the truck and the track.'

I don't get the confusion. It would be redundant to add "and only at that position" since, if at any other point there is "no reaction force" (due to the interaction with gravity), then the truck never reaches the apex.

At the apex the truck's motion is parallel to the track, at a distance of zero. Gravity's pull has cancelled rotation's push. 'b' solves for the velocity necessary to achieve that.

Do feel free to worry about if it's actually "on" or "off" the track, though. Is the glass half empty or half full ? Is zero a positive or negative number ? Yes, we have no bananas.

Everybody else is annoyed at 'a', to which I propose...

Gravity provides a pseudocentripetal force to the truck at the apex. While the vector is equal to that of the track and the force is perpendicular to velocity, the motion due to gravity is elliptical at that velocity, and is not contributing to circular motion.

Curious what your prof/teach says about it.
 
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