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

During the process of reflection, each molecule undergoes a change in momentum equal to 2mv, since the velocity of the molecule is reversed. This means that the total change in momentum of the stream is equal to the sum of the changes in momentum for all the molecules. Since there are n molecules in the stream, the total change in momentum is 2mnv. When the stream is reflected, the direction of the momentum changes by 180 degrees, and so the change in momentum has a magnitude of 2mnv sin 30°, which is equal to mnv. However, the question asks for the magnitude of the change in total momentum, which is 2mnv. Therefore, the answer is B.

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