Question $3$

A piston$/$cylinder assembly with a spring contains air. The spring is exerting a force on the

piston equal to $F_3=k_{3}x$ where $k_3=50k\frac{N}{m}$ is the spring constant and $x=5cm$ is the

amount the spring is compressed. The mass and diameter of the piston are $m_D=250kg$ and

$D_0=0\mathrm{.}4m.$ Assume the atmospheric pressure is $P_0=100$kPa and the gravitational

acceleration is $g=9\mathrm{.}81\frac{m}{s^2}.$

a$)$ Draw a free body diagram of the piston showing all the forces acting on it$.$

b$)$ Determine the pressure of the air, $P_a.$