Chapter 12, Problem 4P

A 40.0-g projectile is launched by the expansion of hot gas in an arrangement shown in Figure P12.4a. The cross sectional area of the launch tube is 1.0 cm², and the length that the projectile travels down the tube after starting from rest is 52 cm. As the gas expands, the pressure varies as shown in Figure P12.4b. The values for the initial pressure and volume are P₁ = 11 × 10⁵ Pa and V_i = 8.0 cm³ while the final values are P_f = 1.0 × 10⁵ Pa and V_f = 8.0 cm³. Friction between the projectile and the launch tube is negligible, (a) If the projectile is launched into a vacuum, what is the speed of the projectile as it leaves the launch tube? (b) If instead the projectile is launched into air at a pressure of 1.0 × 10⁵ Pa. what fraction of the work done by the expanding gas in the tube is spent by the projectile pushing air out of the way as it proceeds down tile tube?