Impact Energy of Toppling Cuboid

[NickG09]

I want to calculate the impact energy of a toppling cuboid striking a vertical surface.

Once the cuboid is brought just past it's toppling point the only force acting will be it's weight.

Will the energy of the impact be equal to the transfer of gravitational potential energy to kinetic energy if we assume no energy is lost due to heat or sound? i.e. Will the transferred to the surface simply be mg∆h?

Thanks

 

[MJCronin]

Nick:

Thank goodness that this is a real world engineering problem and not a homework problem !!!

(I also have had challenging problems when cuboids tumbling along my power plant !)

You see, Nick... some less-than-honest young people try to get us old geezers to do their problems for them !!!

There is a Student Engineering General Forum for such people

MJCronin
Sr. Process Engineer

 

[NickG09]

*Correction

∆h should be the difference in heights of the COM (not the corner as shown in the picture)

 

[NickG09]

Hi MJCronin,

It is a real problem, albeit heavily simplified. I just want to know if my thought process is correct or if there's any published work on this because i cant find much.

thanks,
Nick

 

[JStephen]

Neglecting energy losses, it will bounce right back up on that far corner then rock back and forth.
Don't forget rotational energy.

 

[NickG09]

Hi JStephen,

Thanks, thinking about the moment of inertia is why I've simplified it as a cuboid.

In reality it's frame assembly with many members, so it got me thinking would i even need to consider inertia before spending the time figuring it out.

I will look further into rotational energy.

thanks,
Nick

 

[Compositepro]

The "impact energy" is simply the change in potential energy of the object. The usefulness of this number is very doubtful, however. Impacts are complex events, and have been discussed in many threads here, usually with no clear answer. What is it that you really want to ultimately figure out?

 

[NRP99]

Mostly your approach (mgh=linear kinetic energy=(1/2)mv^2 converted to rotational kinetic energy = (1/2)Iω^2) is correct if you want preliminary calculation for the amount of energy absorbed by the cuboid while free falling. But It has some limitation like it does not consider the rebound plus energy lost in friction between the surface and cuboid.

 

[NickG09]

Thanks, the real world scenario was that a cylinder bundle toppled and struck a single gas cylinder.

I want to estimate the likely energy of the collision and compare it to the energy required to fracture the cylinder material.

I have modelled the system as an inverted pendulum and assumed that all of the rotational energy was transferred into the cylinder at the point of impact, neglecting the initial angular velocity which caused the bundle to topple in the first place.

 

[rb1957]

I'd say PE is converted to rotational KE. You're assuming a rigid contact surface (zero coefficient of restitution, no bounce; no strain energy absorbed by the surface).

then the impact force is, as in all other impact problems, dependent on the time interval (to bring the cuboid to rest).

two other "issues" ...

1) what force initiates the topple ? This could help your real world problem ... how likely/unlikely is it ?

2) this would also add the input work (impulse?) to the initial PE ... so probably can't be overlooked ?

3) how does friction play into this ? friction on the ground resisting the initial overturning force ? friction on the pivoting corner (when would the cuboid slip and slide out from underneath itself ?

another day in paradise, or is paradise one day closer ?

 

[NickG09]

Thanks rb1957, the topple was initiated when a vehicle carrying these cylinders/bundles manoeuvred around a corner. So it's difficult to predict the actual initial force, i have considered assuming some value of g-force in the horizontal plane.

I understand that whatever value i come out with is going to be very rough estimate given all the idealised assumptions.

 

[rb1957]

1) these shouldn't be free standing in a vehicle, but strapped down (so they don't topple) !

2) the vehicle inertial load to initial a topple would be one where the cuboid's resultant (with weight) is outside the base of the cuboid. Anything less can't, won't, topple the cuboid.

3) for very small excesses (beyond the stable load) the cuboid is rotating about the corner, raising the CG. So there is some load that are safe beyond the base of the cuboid. The critical load is one where the input energy causes the cuboid to rotate so that the CG motion is no longer upward. Now it'll topple over.

another day in paradise, or is paradise one day closer ?