ENGR1412 F11 Project#1

ENGR1412 F11 Project#1 - ENGR 1412 - INTRODUCTION TO...

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ENGR 1412 - INTRODUCTION TO COMPUTER PROGRAMMING D R. AJ JOHANNES, FALL 2011 1 of 5 Project #1 - Due during the Week of September 5 – September 9, 2011 (Beginning of Labs) One of the techniques to determine the momentum of a gun-bullet combination is by firing the gun into a tank filled with a dense liquid (Figure below). As the bullet pierces the liquid surface and enters into the liquid, it experiences additional friction (form drag) due to the higher viscosity of the liquid medium. This results in the bullet slowing down very fast before coming to a halt. The distance travelled by the bullet in the tank can then be used to back calculate the bullet firing velocity and therefore its momentum. Such a system can be modeled using the basic kinematic equations of motion. However, the effect of the extra friction due to liquid media resistance needs to be considered when performing the calculations. The velocity of the bullet in the liquid is a function of time and is given as: u x t  u x 0 1 ku x 0 t (1) The inverse proportionality with time indicates that as time increases, the velocity of the bullet in the x-direction decreases proportionally. Based on this velocity, the total distance travelled by the bullet in time “t” can be calculated as:  00 1 1 x Dt x ln ku t k  (2) 2 1 28 FD Bullet Bullet CA Cd k mm   Where, “x 0 ” is the initial distance of the gun from the origin, “k” represents the friction resistance (form drag) on the bullet cross section, “C D ” stands for the drag coefficient (0.42 for
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ENGR 1412 - INTRODUCTION TO COMPUTER PROGRAMMING D R. AJ JOHANNES, FALL 2011 2 of 5 spheres, 0.04 for short cylinders), “ ρ F ” is the density of atmosphere (density of air in case of earth) and “d” is the diameter of the bullet cross section. Bullet Ricochet When a bullet is fired at a very shallow angle and high velocity, there is a possibility that the bullet might bounce/skip off the surface of the target, including liquids (Figure below). An example of a similar occurrence is the skipping of rocks thrown on the surface of a pond or lake. Equations (1) and (2) given above are only applicable for the case when the bullet penetrates the liquid surface. Therefore it is necessary to determine the conditions under which these equations apply. The two parameters governing this phenomenon are the bullet velocity and the angle at which the bullet is fired. Since, the type of gun used sets the firing velocity, the only adjustable variable is the angle of firing. The angle of firing which will result in the bullet to
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This note was uploaded on 10/12/2011 for the course ENGR 1412 taught by Professor Staff during the Spring '08 term at Oklahoma State.

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ENGR1412 F11 Project#1 - ENGR 1412 - INTRODUCTION TO...

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