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Homework Statement
Imagine we are observing the motion of frictionless, elastically colliding billiard balls.
Using sensible assumptions about the size of things, show that, if someone enters the
room, small deflections of the balls due this visitor's gravitational pull will completely
alter their trajectories after just about 10 collisions.
Hint: For simplicity, consider all balls but one fixed in place and then analyse the
motion of one ball.
Homework Equations
The Attempt at a Solution
Not entirely sure how to approach this problem. I chose to consider a one ball rebouinding between a wall and another fixed ball, such that the distance between the wall and th3 fised ball is 2m, and the the bal was moving at 0.1 m/s. Then i assumed the person is 2 m away perpendicular to the direction of motion. the person is 70kg and the ball is 1kg.
For image
http://img802.imageshack.us/img802/1383/smallperturbationsprobl.png
[tex] F = \frac{Gm_pm_b}{r^2} [/tex]
[tex] F=\frac{6.6726*10^-11*70*1}{2^2} [/tex]
[tex] F=1.1*10^-9 [/tex]
Then if we assume tyen collsions, the ball will travle 20m horizontally and hence will travel for 200s.
If we consider only the vertical force and assume that it is constant.
since [itex] F=ma [/itex]
[tex] a=1.16*10^-9 [/tex]
[tex] s=ut+\frac{at^2}{2} [/tex]
therefore s = 2.3366*10^-5 m, whcih is clearly not enough to be considered to have completely altered the trajectory of the ball.
I don't think this approach is right, so please could you advise how it would be best to tackle this problem. Thanks for the help!
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