Impulse/momentum of cart rolling over a step

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Discussion Overview

The discussion revolves around the dynamics of a mobile cart attempting to roll over a 10mm step threshold at an initial velocity of 0.8m/s. Participants explore the implications of impulse, momentum, and energy equations in this context, particularly focusing on the tipping behavior of the cart and the forces involved during the maneuver.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant, Mike, describes the challenge of determining whether a mobile cart can successfully roll over a step without tipping, emphasizing the role of impulse and momentum.
  • Mike notes the complexity introduced by having two pivot points: the center of the wheel and the contact point with the step.
  • There is a suggestion that the vertical velocity required for the wheel to clear the step depends on the momentum of the cart's center of mass, which is positioned relatively high.
  • Another participant questions the clarity of the provided sketch and the absence of a cart representation, indicating a potential misunderstanding.
  • A later reply highlights the importance of torques on the front wheel if the rear wheel loses contact, suggesting that this could complicate the analysis further.
  • Mike confirms that the rear wheel will indeed lose contact during the maneuver and considers simulation or physical testing as potential methods to analyze the situation.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and clarity regarding the problem, with some uncertainty about the cart's dynamics and the implications of the pivot points. There is no consensus on a definitive approach or solution to the problem presented.

Contextual Notes

The discussion reveals limitations in the provided sketches and examples, as well as the need for further clarification on the forces and torques involved. The analysis appears to depend on several unknown parameters that have not been fully defined.

knokout5
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Hello everyone,

This is my first thread so thanks in advance for any help! I have been trying to figure out this problem, and though I've gotten close to an end solution (also with the help of motion analysis on Solidworks) I am not very confident.

So, in order to meet an IEC standard of a mobile cart, I am trying to figure out if a mobile cart can roll over a 10mm step threshold without tipping over going at an initial velocity of 0.8m/s. I have been basically using impulse, momentum, and energy equations from this site:

http://www.real-world-physics-problems.com/impulse-and-momentum.html

impulse_momentum_pr_7.png


The only tick on my neck is that, all the examples I've found are of one pivot with some moment of inertia of one wheel. In my case, you have TWO pivots:
1) at the center of the wheel, whereabout the center of mass (CM) of the cart is rotating.
2) at the step/wheel contact point.

The wheel will need enough "vertical velocity" to make it over the step, but doesn't that all depend on the force at which the momentum of the CM "pulls" the wheel over the step? My CM is relatively high above the ground, so in my motion analyses I have been seeing the cart tip forward (rear wheels lifted off the floor), and then the wheel rolling over the step, and then the cart come back down. There are two things going on. Any help would be appreciated!

-Mike
 
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I don't see anything in the sketch which could tip over, nor do I see a cart. Is there something missing?
 
The FBD I posted isn't of the cart, its just an example taken from the website. I was hoping my explanation would clear things up. But I here's a drawing (attached) without forces.
 

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Hmm.. if the rear wheel loses contact to the surface, torques on the front wheel (if it is powered) can become important. Otherwise, you just have more unknown parameters to determine. And the system will need a simulation, I think.
 
Yes, the rear wheel will lose contact due to the collision. And the cart is not powered, so I am trying to figure out speeds at which it will tip/go over the threshold. I guess simulation may be the best bet or an actual test.
 

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