Interweaving the Numerical Kinematic Symmetry Principles in School and Introductory University Physics Courses

Symmetry

Yuval Ben-Abu¹  Haim Eshach²  Hezi Yizhaq³  Ira Wolfson⁴ 

[1] Department of Physics and Project Unit, Sapir Academic College, Sderot, Hof Ashkelon 79165, Israel;Department of Science and Technology Education, Ben-Gurion University of Negev, P.O.B. 653, Beer-Sheva 8410501, Israel;Department of Solar Energy and Environmental Physics, Jacob Blaustein Institute for Desert Research, Ben-Gurion University of Negev, P.O.B. 653, Beer-Sheva 8410501, Israel;Department of physics, Ben Gurion University of the Negev, 84990, Israel;

关键词: numerical analysis;    super gun;    Paris gun;    equations of motion;    ballistic movement;    muzzle velocity;    ground temperature;    air density;    45-degree angle;   

DOI  :  10.3390/sym11020148

来源: DOAJ

【 摘 要 】

The “super-gun„ class of weaponry has been around for a long time. However, its unusual physics is largely ignored to this day in mainstream physics. We study an example of such a “super gun„, the “Paris gun„. We first look into the historic accounts of the firing distance of such a gun and try to reconcile it with our physical understanding of ballistics. We do this by looking into the drag component in the equations of motion for ballistic movement, which is usually neglected. The drag component of the equations of motion is the main reason for symmetry breaking in ballistics. We study ballistics for several air density profiles and discuss the results. We then proceed to look into the effects of muzzle velocity as well as mass and ground temperature on the optimal firing angle and firing range. We find that, even in the simplest case of fixed air density, the effects of including drag are far reaching. We also determine that in the “sensible„ range of projectile mass, the muzzle velocity is the most important factor in determining the maximal firing range. We have found that even the simplest of complications that include air density, shifts the optimal angle from the schoolbook’s 45-degree angle, ground temperature plays a major role. While the optimal angle changes by a mere two degrees in response to a huge change in ground temperature, the maximal distance is largely affected. Muzzle velocity is perhaps the most influential variable when working within a sensible projectile mass range. In the current essay, this principle is described and examples are provided where students can apply them. For each problem, we provide both the force consideration solution approach and the energy consideration solution approach.

【 授权许可】

Unknown