Final answer:
Defiance Drake cannot open the hatch because the pressure differential created by a vacuum on one side and 1 atmosphere on the other generates a force that exceeds the 6000N she can exert. To open the door, pressure balance or a greater force is necessary.
Step-by-step explanation:
The question at hand requires an understanding of pressure differentials and the forces they create. Defiance Drake is faced with the challenge of opening a hatch into a vacuum from a pressurized environment. The force required to open the hatch will depend on the pressure differential and the surface area of the hatch door.
To calculate the required force to open the hatch, we use the formula F = p × A, where F is the force, p is the pressure differential, and A is the surface area of the hatch. The pressure in her environment is at 1 atmosphere, equivalent to ≈ 101,325 pascals, while the bridge is at vacuum, which we treat as 0 pascal pressure.
Assuming the door has a similar circular dimensions to the one provided in the reference (0.450 m in diameter), the area A = π(d/2)^2. However, since the pressure in the bridge is a vacuum, there's no counteracting pressure to the 1 atmosphere she's experiencing. Therefore, the full atmospheric pressure difference applies across the hatch area. If the door area is similar to the example provided, the force due to atmospheric pressure would be far greater than the 6000N Defiance can exert. Consequently, she wouldn't be able to open the door unless she can balance the pressure between the two areas or exert more force.