Problem 6: A gas gun is used to accelerate the small block of mass m to higlh velocities. The block is held in place while gas is pumped into the tube to a high pressure po on the left and the tube is evacuated on the right. The block is then released and is accelerated by the expanding gas. Assume that the pressure p of the gas is related po Xo to the volume V it occupies by the relation pyr-constant, where is a constant. Assume the cross-sectional area of the block is A. Neglect friction a) Write the equations of motion of the particle. b) Solve the equations of motion numerically using MATLAB and ode45 under the conditions m 0.1 kg, Xo-1 m, po-5000 Pa, A-0.1 m2, and -: 1.4 (air). Choose a time interval t E [0,0.21s with a time step of 0.0001 s. i) Plot the velocity of the block as a function of time and compare it to the closed-form solution given below. What is notable about the velocity? m(y - 10 i) On a different figure, plot the pressure in the cavity as a function of time. Note that the force on the block is equal to the pressure times the cross-sectional area of the block Problem 6: A gas gun is used to accelerate the small block of mass m to higlh velocities. The block is held in place while gas is pumped into the tube to a high pressure po on the left and the tube is evacuated on the right. The block is then released and is accelerated by the expanding gas. Assume that the pressure p of the gas is related po Xo to the volume V it occupies by the relation pyr-constant, where is a constant. Assume the cross-sectional area of the block is A. Neglect friction a) Write the equations of motion of the particle. b) Solve the equations of motion numerically using MATLAB and ode45 under the conditions m 0.1 kg, Xo-1 m, po-5000 Pa, A-0.1 m2, and -: 1.4 (air). Choose a time interval t E [0,0.21s with a time step of 0.0001 s. i) Plot the velocity of the block as a function of time and compare it to the closed-form solution given below. What is notable about the velocity? m(y - 10 i) On a different figure, plot the pressure in the cavity as a function of time. Note that the force on the block is equal to the pressure times the cross-sectional area of the block