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I dont own the first 3 pictures

Imagine a car with a high center of gravity and front and back wheels close together.
car high cg][Imgur Similar to this.
car stopped][Imgur

This is the car before moving. Ignore the force arrows.
It gets some speed and then brakes, and the front goes down.
car braking][Imgur

This is the car after its braked, when its just come to a stop. The center of gravity is somewhere on the blue line. You can see how it moved closer to the front wheels.

When the load tranfer is done, theres no force from braking pushing the front down, only weight transfer from the center of gravity moving, specifically a line from the center of gravity straight down to the ground moving closer to the front wheels because of the rotation of the body, putting more of the cars weight on the front two wheels.

car stuck forward][Imgur

Is there ever a situation where it will stay in this position? It has springs and dampers on all 4 wheels and theres no damage. Also dont include fluids shifting due to inertia in weight transfer. What equations talk about this? Why do cars generally right themselves and return to level and not some other angle based on the center of gravity and the 4 spring forces?

I see 3 main things that would effect whether or not the car will do this, spring force or spring constant, center of gravity location, and distance between the front and back wheels. Basically, what equations talk about weight transfer overcoming the spring force? Can you possibly find the spring force or spring constant that is the threshold where this will start to happen? Or some other way? Please use equations. I think this has to do with spring systems. How would you go about solving this? What physics ideas would you use?

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Once it has stopped the car will settle in the lowest energy state - where the weight on each wheel balances the spring force from the suspension at that wheel.

Assuming the weight distribution remains the same (cargo doesn't shift) and the springs aren't permanently deformed by the stopping - it will be the same as before

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Basically, what equations talk about weight transfer overcoming the spring force?

"overcoming" seems the wrong word here.

During the deceleration, the wheels have to create a force on the car, and this force becomes a torque that tries to roll the car forward.

The car pitches forward a bit and (by Hooke's law) causes the front springs to compress more. The forces from this action create a counter torque that stops the car from pitching farther forward.

But this only happens during the deceleration. Once the car stops (and the deceleration stops), the torque is removed. The harder pushing front springs untip the car until the front and rear springs are in balance.

As long as the springs are in the linear zone (obey Hooke's law), then the car will always return to the original position. Of course real materials aren't perfect. It's possible to overstress a spring to the point that it doesn't return to the original location. In that case, you could "bend" a spring and the new equilibrium would be tilted with respect to the old position.

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It will until there is no force exerted by one set of wheels, and then it will topple. Think of a Unicycle, or a Segway. For a very high COG this could be controlled by the load bearing wheels in the same way. The higher the COG the greater the moment of inertia....

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