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The compressed gas canon illustrated in Figure 2.1 is used to launch a projectile at a fixed target on a wall. It can be assumed that the expansion is adiabatic, that there is no pressure drop between reservoir and barrel, and that there is no leakage of gas around the projectile. y Barrel Reservoir Vo Figure 2.1 a) By considering conservation of energy, and clearly explaining all steps, derive the following equation for the exit velocity of the projectile as a function of projectile area (A), barrel length (L), projectile mass (m) reservoir volume (Vo) and initial gas pressure (Po). 2 PoVo E (1-GAv)")- L(APatm + mg sin e) Vo AL + Vo Uexit = my -

The compressed gas canon illustrated in Figure 2.1 is used to launch a projectile at a fixed target on a wall. It can be assumed that the expansion is adiabatic, that there is no pressure drop between reservoir and barrel, and that there is no leakage of gas around the projectile. y Barrel Reservoir Vo Figure 2.1 a) By considering conservation of energy, and clearly explaining all steps, derive the following equation for the exit velocity of the projectile as a function of projectile area (A), barrel length (L), projectile mass (m) reservoir volume (Vo) and initial gas pressure (Po). 2 PoVo E (1-GAv)")- L(APatm + mg sin e) Vo AL + Vo Uexit = my -

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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b) For the pressure system, V, = 0.05 litres, po = 1.5bar and L = 0.8m. The projectiles used have the same cross-sectional area A = 20cm?, and a mass of m = 90g with a variation of +10%. What is the maximum and minimum exit velocity that is possible during operation when the angle of the barrel to the horizontal is 0 = 0°? c) The angle of the barrel to the horizontal is 0 = 45°. The location at which the projectile leaves the barrel is defined as x = 0 & y = 0, as shown in Figure 2.1. Find the values of y when the projectile hits a vertical wall at x = 0.8m with the minimum and maximum exit velocities obtained in part b. Drag can be neglected. d) Suggest ways in which a machine could be designed and controlled in order to improve accuracy in hitting a target, taking into consideration possible variations in the mass and diameter of the projectiles.
Transcribed Image Text:b) For the pressure system, V, = 0.05 litres, po = 1.5bar and L = 0.8m. The projectiles used have the same cross-sectional area A = 20cm?, and a mass of m = 90g with a variation of +10%. What is the maximum and minimum exit velocity that is possible during operation when the angle of the barrel to the horizontal is 0 = 0°? c) The angle of the barrel to the horizontal is 0 = 45°. The location at which the projectile leaves the barrel is defined as x = 0 & y = 0, as shown in Figure 2.1. Find the values of y when the projectile hits a vertical wall at x = 0.8m with the minimum and maximum exit velocities obtained in part b. Drag can be neglected. d) Suggest ways in which a machine could be designed and controlled in order to improve accuracy in hitting a target, taking into consideration possible variations in the mass and diameter of the projectiles.
Question 2 The compressed gas canon illustrated in Figure 2.1 is used to launch a projectile at a fixed target on a wall. It can be assumed that the expansion is adiabatic, that there is no pressure drop between reservoir and barrel, and that there is no leakage of gas around the projectile. Barrel Reservoir - Vo Figure 2.1 a) By considering conservation of energy, and clearly explaining all steps, derive the following equation for the exit velocity of the projectile as a function of projectile area (A), barrel length (L), projectile mass (m) reservoir volume (Vo) and initial gas pressure (po). 2 PoVo Uexit = Vo 1 - AL + Vo L(Apatm + mg sin 0) my -1
Transcribed Image Text:Question 2 The compressed gas canon illustrated in Figure 2.1 is used to launch a projectile at a fixed target on a wall. It can be assumed that the expansion is adiabatic, that there is no pressure drop between reservoir and barrel, and that there is no leakage of gas around the projectile. Barrel Reservoir - Vo Figure 2.1 a) By considering conservation of energy, and clearly explaining all steps, derive the following equation for the exit velocity of the projectile as a function of projectile area (A), barrel length (L), projectile mass (m) reservoir volume (Vo) and initial gas pressure (po). 2 PoVo Uexit = Vo 1 - AL + Vo L(Apatm + mg sin 0) my -1
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