A piston, mp=5 kg, is fitted in a cylinder, A= 15 cm^2, that contains a gas. The setup is in a

step 1 So in this problem, we're solving for the pressure of the gas that's inside a cylinder where we

A piston, mp=5 kg, is fitted in a cylinder, A= 15 cm^2,...

A piston, $m_{p}=5 \mathrm{~kg},$ is fitted in a cylinder, $A=$ $15 \mathrm{~cm}^{2},$ that contains a gas. The setup is in a centrifuge that creates an acceleration of $25 \mathrm{~m} / \mathrm{s}^{2}$ in the direction of piston motion toward the gas. Assuming standard atmospheric pressure outside the cylinder, find the gas pressure.

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Key Concepts

Inertial Force

Inertial force is the apparent force experienced by objects in a non-inertial (accelerating) frame of reference. This force is proportional to the mass of the object and the acceleration of the frame, and it modifies the effective force balance needed to maintain equilibrium in the system.

Accelerated Reference Frames

When a system is in an accelerated reference frame, such as in a centrifuge, additional inertial forces appear. These pseudo forces must be taken into account because they effectively alter the net force experienced by the system, thereby affecting the conditions for equilibrium.

Pressure

Pressure is defined as the force exerted per unit area. It is a fundamental concept in fluid mechanics and thermodynamics, used to describe how much force is distributed over a given area, and is measured in pascals (Pa) in the SI system.

Force Equilibrium

Force equilibrium involves balancing the forces acting on a system such that the net force is zero. In the context of a piston, the internal gas pressure must provide an upward force that balances both the external atmospheric pressure and any additional forces due to acceleration acting on the piston.

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