The Pneumatic Piston Launcher · AI Generator #GEN-42E0FE9A

Physics · thermodynamics

Problem

A pneumatic launcher consists of a horizontal cylinder with a movable piston of mass m=0.50  kgm = 0.50\;\text{kg} and cross-sectional area A=25  cm2A = 25\;\text{cm}^2. Initially, the piston is held at rest against a compressed ideal gas at pressure P0=8.0  atmP_0 = 8.0\;\text{atm} and temperature T0=300  KT_0 = 300\;\text{K} occupying volume V0=150  cm3V_0 = 150\;\text{cm}^3. The piston is suddenly released and accelerates down the cylinder. During the expansion, the gas undergoes an adiabatic process, and the piston experiences a constant friction force f=12  Nf = 12\;\text{N}. The cylinder is long enough that the gas pressure drops to exactly atmospheric pressure Pf=1.0  atmP_f = 1.0\;\text{atm} when the piston reaches its maximum speed. Find the maximum speed of the piston. Use γ=1.4\gamma = 1.4 for air and atmospheric pressure Patm=1.01×105  PaP_{\text{atm}} = 1.01 \times 10^5\;\text{Pa}.

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