Hyperloop: Air can be unpleasant

Classical Mechanics Level 3

The Hyperloop is a hypothetical new fast transport system between cities, which works by launching pods that carry people through a very low air pressure tunnel. The normal pressure in the tunnel is \(99~\mbox{Pa}\), which is very low compared to the usual atmospheric pressure of \(101,325~\mbox{Pa}\). Since the pressure is so low the Hyperloop tunnel must be well sealed to prevent outside air from rushing in. A sudden increase in air pressure in a section of the tunnel can be rather unpleasant for the passengers in the pod.

Consider for example a hole being created in the Hyperloop tunnel, which leads to a sudden increase in the local air pressure from \(99~\mbox{Pa}\) to \(101,325~\mbox{Pa}\) while maintaining constant temperature and volume. If the normal drag force on the Hyperloop is \(320~\mbox{N}\), how much acceleration in g's would the passengers in the Hyperloop experience if the pod hit the region of high pressure?

Details and assumptions

  • The mass of the pod is approximately \(15000~\mbox{kg}\).
  • \(g=9.8~\mbox{m/s}^2\)

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