Strain energy on impact

[yashsinghla]

A prismatic bar of cross section A, length L and mass m falls from a height h. What is the impact force on the bar? and also stress generated in the bar?
Feel free to use any other parameter or variable that might've been missed.

 

[rb1957]

what is the stiffness of the "ground" ?

if it is "rigid" then the force is "infinite". the stiffness controls the duration of the impact, how the bar decelerates. If the ground is infinitely rigid, then the impact is "instantaneous".

If you know the force then you can calculate the stress ... no?

 

[Ron247]

Is this a homework problem?

 

[GregLocock]

Conceptually think of the bar as a series of springs and masses. As the mass hits the ground the spring above it compresses, and so on and so forth up the chain of springs and masses.

As you can see there's a series of compression and rarefaction waves set up in the system.

It looks like it would be fairly easy to set up a differential equation to describe the continuous system. Whether it is analytically solvable is another matter (I am confident it is). You need E as well.

It is almost directly equivalent to the axial oscillation of a column of air.

 

[yashsinghla]

what is the stiffness of the "ground" ?

if it is "rigid" then the force is "infinite". the stiffness controls the duration of the impact, how the bar decelerates. If the ground is infinitely rigid, then the impact is "instantaneous".

If you know the force then you can calculate the stress ... no?

What's the difference between the ground being rigid and infinitely rigid?

 

[goutam_freelance]

Assuming
1. Rigid floor
2 Elastic collision
3. Instantaneous propagation of stress (infinite speed of sound)