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 Aug 19th 2017, 03:12 AM #1 Junior Member   Join Date: Aug 2017 Posts: 2 Circular Motion Question. A particle of mass m oscillates along arc AB on the inside of a smooth circular hoop of radius 'a' fixed in a vertical. The force on the hoop at any point is : ? (a) k/a (b) k/3a (c) 2k/a (d) 3k/a
 Aug 19th 2017, 07:00 AM #2 Senior Member   Join Date: Aug 2010 Posts: 264 The downward gravitational force on the object at any time is, of course, mg. The object does not go downward because the hoop is applying a force on it. That force is equal to the component of gravitational force perpendicular to the hoop. Let $\displaystyle \theta$ be the angle the line from the center of the hoop makes with the vertical. The component of gravitational force perpendicular to the hoop is $\displaystyle mg cos(\theta)$ and is also the force the object applies to the hoop. That does not appear to be any of the options you give. In particular, that force is not a constant- it is greatest at the bottom and least at the end points of the arc.
Aug 19th 2017, 08:30 AM   #3
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 Originally Posted by HallsofIvy The downward gravitational force on the object at any time is, of course, mg. The object does not go downward because the hoop is applying a force on it. That force is equal to the component of gravitational force perpendicular to the hoop. Let $\displaystyle \theta$ be the angle the line from the center of the hoop makes with the vertical. The component of gravitational force perpendicular to the hoop is $\displaystyle mg cos(\theta)$ and is also the force the object applies to the hoop. That does not appear to be any of the options you give. In particular, that force is not a constant- it is greatest at the bottom and least at the end points of the arc.

I managed to solve it when i tried again. Check it out.

Aug 20th 2017, 10:14 AM   #4
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 Originally Posted by HallsofIvy The downward gravitational force on the object at any time is, of course, mg. The object does not go downward because the hoop is applying a force on it. That force is equal to the component of gravitational force perpendicular to the hoop. Let $\displaystyle \theta$ be the angle the line from the center of the hoop makes with the vertical. The component of gravitational force perpendicular to the hoop is $\displaystyle mg cos(\theta)$ and is also the force the object applies to the hoop. That does not appear to be any of the options you give. In particular, that force is not a constant- it is greatest at the bottom and least at the end points of the arc.

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