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TonyCross

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**Summary::**Theoretical reaction force due to ball traveling in a semi-circle circum

Hi,

Can anyone please help me with the following question:

Setup...

1 x length of pipe bent 180 degrees with an inner diameter of 22mm, it's radius is 2mtrs, the mass of this object is 100kg. Total length of pipe (4*3.14/2) = 6.28 mtr.

1 x Metal ball (sphere) with a Diameter of 20mm and a mass of 1kg.

Question:

Assuming there is no gravity and the tube and the ball are in the vacuum of space, no other forces come to bear such as friction from the pipe sitting on the ground, or tangental friction forces from the rolling ball.

The ball rolls around the pipe causing friction, however I would like to ignore friction for the sake of this problem.

I introduce the 1kg metal ball into the tube at a constant velocity of 5m/s.

What is the total reactive force acting on the pipe?

A followup question is what direction (x/y) is this force acting on the pipe. (Assuming the pipe lays x/y direction with the ball introduced into the x direction and exits -x) What is the linear displacement vector for the tube. I would think that the y force on the tube cancels out.

My confusion lays in the centripetal force equation

**(**Fc = m v² / r ) which gives the figure 25/2 = 12.5N. If the 100kgm pipe is at rest there is inertia to also consider.

My question is what formula would I use to calculate the reactive force in the x direction shown in my diagram, given the time the ball is traveling which is just over 1 second as the pipe is just over 6m long and the ball is traveling at 5m/s. I am trying to workout the acceleration and the displacement of the 100kg pipe, as in Newtons 3rd law.

I hope this makes sense as I am very much trying to find my feet with this problem.

Thanks Tony

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