- #1
thepopasmurf
- 76
- 0
Homework Statement
The problem is what are the odds of an incident object of radius r1 colliding with any of a collection of target objects of radius r2, where the r2 objects have a number density N / m^3 = n and the incident object travels a distance L. Incident object is moving much faster than the other objects so they can be considered still.
Homework Equations
Collision cross-section for collision between incident object and a single target is:
σ = [itex]\pi[/itex] (r1 + r2)^2
Probability of collision for a single target object is
P1 = σ/A
were A is the total area of the domain in question.
Probability no collision for a single target object is 1-P1
Maybe relevant, the mean free path is
λ = 1 / nσ
The Attempt at a Solution
My thinking is, if probability of no collision for a single target is (1-p1), then if the incident object travels a distance L, the number of targets to consider is Ln. So the total probability for no collision is
(1-p1)^(Ln)
And probability of colliding with a single one of these is 1 minus this answer.
Is this correct?
I was also trying to use the mean free path but I wasn't sure how.
Thanks