Physics 241
Assignment # 3
Date Due: November 3, 2017

1. Use equation C12.4 to calculate the average speed of an "air molecule" in air at normal pressure and room temperature of 300K. Next, show that you get a similar speed by thinking of the air pressure as a result of elastic collisions between the walls of a box and the air enclosed by the box. To help answer this consider the following:
   1. At any given time, what fraction of the air molecules strike a specific face of the enclosing box (for example - A in the image below)?
      
      
      
      
   2. If the molecules move with speed 'v' what is the total change in momentum experienced by a molecule? How does this momentum change occur - be specific in your answer and avoid stating the obvious like "by hitting the wall".
   3. If the density of air is given by ρ, explain why the mass of air colliding with the wall in time Δt can be given by the expression (1/6)vΔtA ρ where v is the average speed and A is the area of the wall
   4. Recall that Force (F) and Pressure (P) are related by the simple expression F = PA and that force and momentum are also related! Using P = 100 kPa and ρ = 1.2 kg/m³ develop an expression for the average speed of air molecules.
   5. Use your expression to make an estimate for the value of Boltzmann's Constant used in equation C12.4.
      
      

2. You are a gifted lawyer who studied physics before law school and are investigating an accident that occurred in the Rockies on the Canadian National Railroad. On a fall evening in 2017 a railroad car was parked at the top of a steep incline. At the bottom of the incline a car of same mass was parked. The brakeman is adamant that he securely locked the brakes of the car at the top of the incline before leaving at the end of the night shift. In the morning both cars were found coupled together in a lake at the end of the train yard. The foreman dismissed the brakeman charging that he did not lock the brakes, the car rolled down the hill during the night and hence the brakeman was negligent. Your client, the brakeman, swears to you that he had locked the car and that someone must have tampered with the car, released the brake and given it a push. Show that indeed your client's story is plausible and that the police should explore a possible crime. See the diagram below for relevant details.
   
   

(this problem has an unfortunate similarity to the events surrounding the Lac Megantic rail disaster that occurred on July 6, 2013)

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