Question

You and your younger brother are designing an air rifle that will shoot a lead pellet with mass m 1.00 g and cross-sectional area A = 0.0250 cm2. The rifle works by allowing high-pressure air to expand, propelling the pellet down the rifle barrel. Because this process happens very quickly, no appreciable thermal conduction occurs and the expansion is essentially adiabatic. Your design is such that, once the pressure begins pushing on the pellet, it moves a distance of L = 45.0 cm before leaving the open end of the rifle at your desired speed of v 110 m/s Your design also includes a chamber of volume V = 13.0 cm3 in which the high-pressure air is stored until it is released. Your brother reminds you that you need to purchase a pump to pressurize the chamber. To determine what kind of pump to buy, you need to find what the pressure of the air must be in the chamber (in Pa) to achieve your desired muzzle speed. Ignore the effects of the air in front of the bullet and friction with the inside walls of the barrel. (Assume that air is diatomic.)

Answer 1

No-(a Answer Giuen that a lead petlet with mass m-1.00 01 Cross-Sectional Arca = 00250 cm distance L- 45 0 um speed chamber volume V, desived по ml tinitial 3.0 cm value) We know that Volume d barrel AxL O. O 250m x 45.0 m 125 cm3. final volume air 13.0 cm 14. 125 cm. V. for Adiabatic Expansion Pr VI PL V

NO(2 For Adiabatrc process, The uatue Y - 1.4 1.4 13 14 125 PL O 8 903 the Work dont by XA W I Y1 CP-PL2) PC13)-4125)(o 8903 4-1 12.54bf 13P O.4 oAJ 0 4346 3.0615 P We tnowthat, mv2 C1) (10 x102) 10615A

시0:-3 (ij C1ox102) P= 2 x 1.0615 5.6994 X1o dyne Ol X Q1Xbb9:9 Pa = 56994x 106