Is there a way to calculate the acceleration (in g's) applied to a truck as it is stopped in a runaway escape ramp? Do I need to know how long it takes or how far it goes in the ramp to calculate the acceleration?
If you knew the elapsed time until the truck stops (T), you could calculate the average acceleration by dividing the truck's initial velocity (V0) into T. It's important to realize this quotient gives only the average acceleration; if you want the actual motion you'd need extra data about the escape track (slope, surface, wind and many more things)
I think all you need is the angle of the incline. If the angle formed by the ramp and the horizontal is [tex]\theta[/tex], then the deceleration component alone the truck's trajectory would then just be [tex]g \sin \theta[/tex], where g is the familiar 9.8 m/sec^2 gravitational acceleration of the Earth.
But if the truck's brakes work, then the deceleration would be greater, but at least you could get a reasonable upper bound.
We must decide whether we're speaking of an idealized truck (and road) or a real one. Escape tracks are inclined but they're also covered with a layer of small rocks. These rocks play an important role; the tyres virtually "sink" in the bed of small rocks, thus expending a great amount of energy. This accounts for most of the braking action.
Thanks Gordianus. Ultimately, I am trying to figure out if there is a way to calculate the maximum acceleration that an escape ramp will apply to any truck that enters it - real world truck and ramp. My physics/math knowledge is a little limited - I understand the formulae, it's picking the right ones to apply that is hampering me.
My gut feeling is that it is not possible to calculate a maximum acceleration that a ramp will impart without knowing EVERYTHING about both the ramp and the truck that is using it.
It also seems that the acceleration on two different trucks using the same ramp will be dependent on their speeds and weights. Wouldn't a 50k lb truck be stopped much quicker than an 80k lb one at the same speed, in the same ramp?
I am beginning to believe that the only way to solve the question is to instrument a bunch of trucks with different weights and drive them into several different escape ramps at various speeds.
Thanks again for all your help, Everyone.
"Not everything that can be counted counts, and not everything that counts can be counted." ------Albert Einstein