Calculating Time of Impact of Pendulum Bob on Cylindrical Bar

[grzz]

Homework Statement

A cylindrical metal bar of length L hangs by two strings in a horizontal position. The metal bob of a simple pendulum hits one end of this metal bar in a direction perpendicular to the crossection of the bar. Find an expression for the time t of contact during the impact of the bob with the bar.

Homework Equations

velocity v = 2L/t

The Attempt at a Solution

Can the velocity of longitudinal sound waves in the bar be used for v?

 

[I like Serena]

Hi grzz!

Well, I don't really have a clue how to splice sound waves into this problem.

I also don't understand your relevant equation v=2L/t.
Where does it come from?
What does it mean?Either way, the time of contact will depend on lots of unmentioned variables.
If the materials involved are softer, contact will be longer.
If the speed of the bob is greater, contact will be longer.

So the best I can think of, is to try to model it and see if we can find a couple of likely relationships.
Like how the time of contact depends on the masses involved, the initial speed, and the coefficient of elasticity.

When the bob hits the bar, both will be deformed and exert an elastic force on each other.
Due to Hooke's law this can be modeled with F=-kx.
If we give the bob an initial kinetic energy, we can calculate the time it takes for maximum deformation to occur, which would be half the time of the impact.

And so on...

 

[grzz]

I was thinking about a set of particles bound by springs as a model of the metal bar. When one end of the bar is hit by the pendulum bob, a pulse is sent along these particles. This gets reflected at the other end and when this pulse arrives back, the bob is pushed back.