Help please, Newtons 3rd law.

[tonycross]

Hi,
Not sure which area to post this question...
My last Maths class was 50 years ago, can anyone please help me I have 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 10kg. 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.
I introduce the metal ball into the tube at a velocity of 5m/s with a force of 5N (F=ma)
Friction inside the tube, causes the ball to exit the pipe with a velocity of 4m/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) What is the linear displacement vector for the tube.
My confusion lays in the centrifugal force (F = m v² / r ) which gives the figure 25/2 = 12.5N.

Many thanks
Tony Cross

 

[Deleted member 4993]

Hi,
Not sure which area to post this question...
My last Maths class was 50 years ago, can anyone please help me I have 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 10kg. 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.
I introduce the metal ball into the tube at a velocity of 5m/s with a force of 5N (F=ma)
Friction inside the tube, causes the ball to exit the pipe with a velocity of 4m/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) What is the linear displacement vector for the tube.
My confusion lays in the centrifugal force (F = m v² / r ) which gives the figure 25/2 = 12.5N.

Many thanks
Tony Cross

Is there a picture/figure associated with this problem? How is the pipe supported?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

 

[tonycross]

Further,
I have attached a picture to help visualise the problem.

Please assume that the two objects are floating in the vacuum of space, i.e. there are no external forces acting on the objects such as gravity or ground friction.
My thoughts are that the there is a loss of momentum (energy) = 1m/s this translates to a transfer of 1N to the pipe if the pipe has a mass of 10kg then I would assume that the reactive force is = 10N in the +x direction, the remaining energy 4N continues in -x, however I am certain this is incorrect.
I would be happy to give any other information I can to solve this query.

Cheers Tony

 

[Deleted member 4993]

Further,
I have attached a picture to help visualise the problem.

Please assume that the two objects are floating in the vacuum of space, i.e. there are no external forces acting on the objects such as gravity or ground friction.
My thoughts are that the there is a loss of momentum (energy) = 1m/s this translates to a transfer of 1N to the pipe if the pipe has a mass of 10kg then I would assume that the reactive force is = 10N in the +x direction, the remaining energy 4N continues in -x, however I am certain this is incorrect.
I would be happy to give any other information I can to solve this query.

Cheers Tony

Is this a problem assigned to you - or is it made up?

If the pipe is floating in space - why would not it "start to rotate" as the ball applies friction force (tangential) to the pipe?

 

[tonycross]

This is a theoretical problem made up by me. However it's part of a bigger project which I have already developed.

Indeed the ball may well rotate like a pinball machine ball going around an obstacle, however the mass of the pipe is 10x the
ball. I assume that tangential forces will be applied at each point of the arc, from the point at the centre of the radius vectoring out. We could assume the pipe is any mass as the Force-Mass would factor in it's linear displacement.

The velocity vector must be constantly changing at each point on the arc.
I assume that the displacement in space of the pipe must be somehow tied to angular velocity and the radius of the half circle.

What really confuses me is that centripetal force is calculated from { F = m v² / r} so in our case F(Newtons)=1x25/2=12.5N
does this mean that 12.5N is applied to the tube?

If so what would be the linear displacement of the pipe when the ball leaves the tube. Would it be simply Newtons law
F=ma or a=F/m so the pipe from a standstill would experience (Force)12.5/(Mass)10=1.25m/s acceleration in my example.

As you can see it's not a simple answer, well not for me..
I have tried to simulate this problem using Solidworks and Motion Study using Force with Action and Reaction enabled, but I doubt the result is gives is accurate.

I was hoping someone might just say, here is the equation which would show the acceleration of a mass when subjected to a centripetal force.

I hope this gives a better understanding of my thought process.

Cheers Tony