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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.

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.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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part C 

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
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.
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