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Cart tipping problem

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I am to solve a tipping problem of a 4-wheeled cart, weighing 36 kg, and being pushed to move in a range of between 1 and 6 m/sec. When the cart is moving at constant velocity within this range, the front two wheels suddenly encounter a permanent barrier and are stopped instantaneuosly. The cart is to be redesigned for no or minimal tipping-up of the back wheels over this operting range, see drawing.

How do you decribe the dynamics of the cart? I realize I can sum the moments about the front axle of the cart, with position vectors times the cart's weight from the center of mass, and the normal forces acting on the cart wheels. What I don't understand is how to express the cart's momentum / kinetic energy as a force. The cart is moving at constant velocity, and the stop is instantaneous. I want to design the cart so that it does not tip within this speed range, any thoughts on how to approach?

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UPDATE:
Student Comment:
I was grateful that the response came in well before the deadline, so that I had time to review it fully. While he did solve the problem, here were a few areas where I still have questions and would have liked a capability to ask them. For example, how do you define the magnitude of force F? Why is the tipping point at point A, rather than the point where the wheel center makes contact with the obstruction? If I could get a response to these thoughts, it would aid my understanding. There was also learning I gained from viewing his solution that he did not state- for example, the easiest way to changethe cart is to make the wheels bigger, so that (h-c) is ...

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