Bouncing Height of Cylindrical Tube: Equation & Properties

[Tech Guy]

What is the equation to find the bouncing height of a cylindrical tube when the flat surface is falling on the floor under Earth's gravity? I know the mass, drop height and material properties of the cylindrical tube.

 

[256bits]

And the floor properties too.

 

[Tech Guy]

C

And the floor properties too.

Considering it as a concrete floor.

and Material of the tube is high-density polyethylene: Density 960 kg/m3, Tensile modulus 1500MPa Tensile strength at yield 31 MPa Charpy Imp strength 4.0 kJ/m2

 

[jbriggs444]

What is the equation to find the bouncing height of a cylindrical tube when the flat surface is falling on the floor under Earth's gravity? I know the mass, drop height and material properties of the cylindrical tube.

Do you know the rotation rate and impact angle?

 

[Tech Guy]

Tube is falling normal to the ground without rotation.

 

[256bits]

Have you tried a simple spring -mass analysis to begin with, and then work your way up to the variable compression of the tube ( the part hitting the ground compresses the most )
Of course we don't know the energy loss.
It would be something like
E_p = E_{k at impact} = E_{k at rebound} + E_losses

 

[Tech Guy]

Have you tried a simple spring -mass analysis to begin with, and then work your way up to the variable compression of the tube ( the part hitting the ground compresses the most )
Of course we don't know the energy loss.
It would be something like
E_p = E_{k at impact} = E_{k at rebound} + E_losses

I did not understand. It would be great if you can explain.

Actually I am trying to calculate the impact force due to freefall. As I know the KE due to fall, I need the impact distance to calculate the force (1/2 mv²/d).
If this is difficult to calculate theoretically, any equation to calculate impact time to use Newtons second law to calculate the Impact force?

 

[256bits]

Oh ok then.
You write an equation comparing the kinetic energy to the elastic deformation of the cylinder with the assumption that the concrete is rigid. ( which is not true but it gives you that worst case, I think ).
And solve for deformation of the cylinder.

Note:
1.You have a continuous force acting on the cylinder during deformation. This force is the weight of the cylinder. This adds work to the deformation.
2. The kinetic energy of the falling cylinder is absorbed by elastic energy within a reduced length less than the full length of the cylinder. This tends to increase the stress and deformation nearer the impact area.