A stream of gas consists of n molecules. Each molecule has mass m and speed v. The stream is reflected elastically from a rigid surface as shown. The magnitude of the change in the total momentum of the stream is:
A) 2mnv
B) 2mnv sin 30 $\degree$
C) mnv sin 30 $\degree$
D) mnv cos 30 $\degree$
E) mnv

Question

A stream of gas consists of n molecules. Each molecule has mass m and speed v. The stream is reflected elastically from a rigid surface as shown. The magnitude of the change in the total momentum of the stream is: 
A) 2mnv 
B) 2mnv sin 30 $\degree$ 
C) mnv sin 30 $\degree$ 
D) mnv cos 30 $\degree$ 
E) mnv

Quizplus · Accepted Answer

In an elastic collision, the momentum and kinetic energy are conserved. The mass of the stream is given by n*m. Initially, all n molecules are moving in the same direction with speed v, so the initial momentum is p1 = n*m*v in that direction. When the stream reflects, the direction of motion is reversed but the magnitude of the velocity remains constant, so the final momentum is p2 = n*m*(-v) in the opposite direction. The change in momentum is therefore
Δp = p2 - p1 = -2n*m*v.

Since the stream reflects at an angle of 30 degrees, we need to take the component of Δp perpendicular to the initial direction. This is given by Δp*sin(30) = (-2n*m*v)*sin(30) = -n*m*v, since sin(30) = 1/2. The magnitude of the change in momentum is the absolute value of this expression, which is n*m*v. Therefore, the answer is (B) mnv*sin(30).

A Stream of Gas Consists of N Molecules °\degree° C) Mnv Sin 30

A Stream of Gas Consists of N Molecules $\degree$ C) Mnv Sin 30