Math/Physics Question: Stability of an abruptly stopped object
March 5, 2013 9:16 PM Subscribe
If you have an object with a given base length and a given CG height, how fast can it travel before you have to worry about it running over an obstacle and falling over?
posted by Popular Ethics to science & nature (16 answers total)
This is for a work problem. I have a cart of given length and CG height. I'm trying to specify a "safe speed" which will guarantee that, if the cart were to run over an obstacle, it would not topple.
My first pass at this problem went as follows: The potential energy required to rotate the CG over the front wheels is:
delta_height = sqrt(cg_height^2 + (base_length/2)^2) - cg_height)
that is, the radius from the front wheels to the CG, minus the original Cg height
Ep = delta_height * mass * g
The kinetic energy at a given speed is:
Ek = 1/2 * mass * speed^2
Assuming all of the kinetic energy is transferred into potential energy when the front wheels hit an obstacle I equate the two E values and solve for speed:
speed_max = sqrt( 2 * delta_height * g)
This gives me a very pretty low value for speed_max (slower than a slow walk, for a base_length/cg_height ratio of about 1.5) which seems unreasonable. Have I made a mistake? Are my assumptions too stringent?