Question

2. In addition, we will derive an expression for the pressure that a gas exerts on the walls of a container. The remainder of this pre-lab asks you to take the first steps in that process: Imagine that the gas inside a cube of side length L has such low density that its particles almost never collide with each other; they collide only with the walls of the container. Assume a model of the gas as tiny moving billiard balls obeying Newton's laws. We wish to derive an expression for the pressure that the gas exerts on the walls of the container. Uo a. Start with one of the "balls" of mass mo traveling at speed v parallel to the x-axis at speed v The ball bounces back and forth between two surfaces that are separated by distance L and that are perpendicular to the x-axis. Use your knowledge of the impulse-momentum principle to show that the impulse of the ball, as a result of one collision against one surface, has magnitude 2mvo 2L b. Show that the time interval between hits for the one ball against that same wall is

Answer 1

(a) Impulse = change of momentum = momentum after collision - momentum before collision m times V_0 - (- mV_0) = 2m V_0 (b) After collision with a wall, ball returns back and hat the opposite wall and return back to first wall Total length Covered = 2L with speed v_0 therefore time interval = 2L/V_0