# Would Air Resistance Alone Completely Stop an Object?

Imagine there is a small ball of mass m which is set loose with an initial speed v into a chamber filled with oxygen gas. For simplicity's sake, say gravity is inconsequential. As I understand it, the ball would continue moving with that same initial velocity v until one of two things happens:

a) It hits an O2, likely imparting a higher speed to the particle and changing the ball's direction, but definitely changing the ball's speed (and thus kinetic energy)

b) It hits the wall and (assuming an elastic collision) continues according to Snell's Law with the same speed and energy

At some point, the ball will have lost enough energy that it is moving very, very slowly. Now, I understand that O2 particles will statistically continue to counter the ball's motion, but given a ball 10 or 50 times the mass of an O2 molecule, what are the chances that the ball will ever actually stop? Is it even possible? Better still, is there a formula which relates the mass, surface area, gas MW to determine the speed at which a certain object in a certain gas would stabilize?

• classically speaking, as the velocity of the ball reduces, so does the force acting on it , because of lower relative velocity now during collisions. the force on it changes with each collision by a multiplicative factor (like e --- coefficient of restitution). Hence it should never be zero statistically. – Lelouch Sep 6 '16 at 5:50