Pedulum impact problem (tipping a screen over)

[crayons]

I have a problem that I'm having trouble cracking and was wondering if anybody has any ideas on it.

An impact test that we have to do involves swinging a pendulum of weight 50lbs into a rolling easel (for writing on, approximately 6ft high, with casters).
The wheels are blocked so the easel can tip over if it is not stable enough.
I want to be able to apply physics to this to be able to optimize the easel design without having to iterate prototypes more than 1x or 2x.

A simple force/moment calculation would be great to apply to this situation, but this is an impact problem so that won't work.
Also, I tried conservation of PE, but that doesn't take into account that the higher you impact the easel, the easier it is to tip it over.
I'm thinking a conservation of momentum application?
*It is also unrealistic to know how long the impact occurs for, given the lack of high speed cameras etc., so an F=ma calculation isn't going to be possible.

I'm a bit stuck here... I feel like the answer is on the tip of my tongue but I can't get to it... does anybody have any ideas?

 

[jbriggs444]

Conservation of PE? What's that? Why would you expect Potential Energy to be conserved?

I agree that conservation of angular momentum is a good starting point, along with the working assumption of a completely inelastic collision.

The pendulum will come to rest with respect to the easel as a result of the impact. The easel will then retain whatever angular momentum results from this interaction and either will or will not continue to rotate to and through its tipping point.

You will, of course, have decide upon an axis of rotation that is convenient to use for your analysis.

 

[crayons]

thanks for the notes...
sorry, I meant conservation of energy (KE/PE for whole system)... I was barking up the wrong tree there though...
I'm going to give this a try using the angular momentum format suggested... one question though...

Do I need to use the same axis of rotation for the pendulum and the easel?
The easel is rotating about it's blocked caster, while the pendulum rotates about it's pivot above and to the side... I guess I need to use the parallel axis theorem here to get everything in the same co-ordinates?

 

[jbriggs444]

thanks for the notes...
sorry, I meant conservation of energy (KE/PE for whole system)... I was barking up the wrong tree there though...

On reflection after posting, I realized that there is a way to apply a conservation of energy argument to this problem...

Suppose the the pendulum starts at rest with the bob at some height h above the bottom-most point of its arc. Then it follows that the maximum kinetic energy that the pendulum bob can gain is equal to the mass of the bob (m) times h times the acceleration of gravity (g).

Now consider your easel. As it tips up to its tipping point (on any particular pair of legs), it will need to raise its center of gravity somewhat. Take the mass of the easel (m') times this increase in center of gravity (h') times the acceleration of gravity. If this figure exceeds the kinetic energy of the bob then it is physically impossible that any impact from the bob can possibly tip the easel over, even assuming the most unfavorable and elastic collision.

Do I need to use the same axis of rotation for the pendulum and the easel?

No, you don't. If you consider the mass of the pendulum to be entirely concentrated in its 50 pound bob then you can just consider the linear motion of that bob just prior to the instant of impact. Using your chosen axis of rotation you can compute the angular momentum that this linear motion represents

[This is a bit of angular momentum that not all students "get" or are even taught at first -- linear motion that does not intersect the chosen axis of rotation contributes to angular momentum]

 

[crayons]

re: angular momentum & parallel axis theorem... great! thanks for that.

re: energy methods... that was the first approach I took, which seemed so clean and tidy, but when you think about this physically, if you impact the easel near the top rather than near the bottom, the applied moment is going to be much more, be more likely to tip it over... but the energy method does not reflect this...not that I can see at least.??

thanks for your help on this problem eh!
I'll work on this over the weekend and post my results.

 

[jbriggs444]

As you start impacting farther and farther up, you'll eventually reach the point where the rotation rate imparted by the impacting pendulum becomes to small to amount to anything. There is a point of diminishing returns.

The conservation of energy argument survives this assault.