Bouncing Height of Cylindrical Tube: Equation & Properties

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Discussion Overview

The discussion revolves around the calculation of the bouncing height of a cylindrical tube when it impacts a flat surface under Earth's gravity. Participants explore the necessary equations and factors influencing the outcome, including material properties and impact dynamics.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant inquires about the equation needed to determine the bouncing height of a cylindrical tube, given its mass, drop height, and material properties.
  • Another participant emphasizes the importance of considering the properties of the floor, specifically mentioning a concrete surface.
  • Details about the material properties of the cylindrical tube are provided, including density, tensile modulus, tensile strength, and impact strength.
  • A question is raised regarding the rotation rate and impact angle of the tube during the fall.
  • It is clarified that the tube falls normally to the ground without rotation.
  • One participant suggests starting with a spring-mass analysis to understand the variable compression of the tube upon impact, noting the uncertainty of energy loss during the process.
  • Another participant expresses confusion about the spring-mass analysis and seeks clarification on calculating impact force, given the kinetic energy from the fall and the impact distance.
  • A later reply proposes comparing kinetic energy to the elastic deformation of the cylinder, assuming the concrete is rigid, and discusses the continuous force acting on the cylinder during deformation.
  • It is noted that the kinetic energy is absorbed by elastic energy within a reduced length of the cylinder, which may increase stress and deformation near the impact area.

Areas of Agreement / Disagreement

The discussion contains multiple viewpoints and approaches regarding the calculation of bouncing height and impact force. There is no consensus on a single method or equation, and participants express varying degrees of uncertainty about the assumptions involved.

Contextual Notes

Participants highlight limitations such as the unknown energy loss during impact and the assumption of a rigid concrete surface, which may not accurately reflect real-world conditions.

Tech Guy
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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.
 
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And the floor properties too.
 
C
256bits said:
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
 
Last edited:
Tech Guy said:
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?
 
Tube is falling normal to the ground without rotation.
 
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
Ep = Ek at impact = Ek at rebound + Elosses
 
256bits said:
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
Ep = Ek at impact = Ek at rebound + Elosses
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?
 
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.
 

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