2.25 Problem Sets - Section 5


Problem 5.2: Answer C.

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The force in equation (1) originates from the fact that the hydrostatic pressure inside the pipe is higher than outside, since water has a much higher density than the ambient air. The integral of the x-component of the pressure force on the inside and the outside surfaces of the walls of the system to the right of the bellows gives the negative of (1) under static conditions. [Equation (1) is the counterforce to the pressure force.].

If the system to the right of the bellows is mounted on frictionless wheels, and you hold onto it and fill it with water and then let go, the net hydrostatic force on the walls will tend to push the system rightward, making the bellows extend. In our idealized model the bellows exerts no counterforce when it stretches and would keep extending indefinitely, which is absurd. A real bellows, of course, acts like a spring and will stop the system's motion after some displacement (and damped oscillation).