Calculating Rod Strength: Help with Oak Rod Homework Problem

[johnlogie]

Homework Statement

An example in my problem set (homework help) An oak rod is hung from a rigid support.
The rod has a diameter = 12 mm, length = 9 m, and a catch plate at its base.
a) The maximum mass of a weight that each rod can support.
b) The minimum mass of a weight that will break the rod when dropped from the top of the rod.
Numbers I think can be used: E (stiffness) = 14000 MPa
Yield Tensile strength = 75 MPa
Ultimate tensile strength = 90 MPa

Homework Equations

I can not find a formula to calculate the following question, any help would be appreciated,
Thank you for your help!

The Attempt at a Solution

I solved A but struggling in b) these are all the information provided to us in the question.

 

[scottdave]

Drop a mass, it falls 9 meters. What is going to happen when it strikes the catch plate? How will the oak rod stretch (and eventually fail). That is the way I think to approach it. You will need to make some assumptions (and state them) about how the collision between the mass and catch plate occurs.

 

[johnlogie]

Thank you for your reply,

The thing is, I don't have a formula in mind in which I can plug the 9m and get the resulting force, I think it's pretty obvious but I can't recall it !

 

[scottdave]

So it has been awhile since I've done one of these. Is it possible that you could model the beam as sort of a spring? I'm not positive but I think it can be done. Then you could say that the mass has a certain amount of kinetic energy, this could be transferred into the spring (and figure out how far the "spring" stretches).
If you can figure the stretch distance necessary to break, then work backwards to see what mass will cause that amount.

 

[Dr.D]

The maximum mass of a weight that each rod can support.

The mention of "each rod" is confusing. Is there more than one wooden rod involved?

In many respects, this is a classic problem, and the OP has identified the nature of the problem when he said

I don't have a formula in mind in which I can plug the 9m and get the resulting force.

The problem is, nobody has such a formula that works in all cases. It depends upon what happens during the impact, and the time is too short for it to be well observed. What SCOTTDAVE has proposed is as good as anything for a homework problem with no further information given.

 

[Mark44]

a) The maximum mass of a weight that each rod can support.

The mention of "each rod" is confusing. Is there more than one wooden rod involved?

My take is that there is only one rod, and "each rod" means "each rod of this type."