Abstract
Projectile motion in classical physics can be defined as a two-dimensional motion with constant acceleration in one direction and uniform motion in another direction. In classical mechanics this motion can be achieved if a force is applied in one direction and with some initial velocity in another direction. In relativistic dynamics, the equations of motion in both directions are coupled to each other and surprisingly the object experiences varying accelerations in both directions. We can say the non-relativistic projectile motion is not a projectile motion at all in relativistic physics. In this paper the conditions for the projectile motion in the relativistic regime are discussed. We discuss the two cases of constant force and constant acceleration. Another goal of this paper is that to show a computational example can be discussed in class for students to learn a topic in physics and improve their computational skills.
Highlights
The motion of an object subject to a constant force in one direction, for example, and some initial velocity in another direction, is known as projectile motion in Newtonian mechanics
Projectile motion in classical physics can be defined as a two-dimensional motion with constant acceleration in one direction and uniform motion in another direction
In the context of relativistic mechanics this problem is as simple as the force mentioned cases but what makes it interesting is the coupling nature of the two-dimensional problem in relativistic physics
Summary
The motion of an object subject to a constant force in one direction, for example , and some initial velocity in another direction, , is known as projectile motion in Newtonian mechanics. The component of the velocity remains constant and the component increases as result of the force applied in that direction This is a classical example of two-dimensional motion that is discussed in introductory physics. In the context of relativistic mechanics this problem is as simple as the force mentioned cases but what makes it interesting is the coupling nature of the two-dimensional problem in relativistic physics The simplicity of this problem helps us to educate students about the nature of the relativistic physics and especially the coupling between and components of the equation of motion. Case one (applying constant force) has been discussed elsewhere (Landaus & Lifshitz, 1975; Lapidus, 1972; Naddy, Dudley, & Haaland, 2002; Shahin, 2006; Price, 2005). The question of “How can non-relativistic projectile motion remain so in the relativistic limit?” can be addressed in the modern physics classes to understand a fundamental transition from the classical to relativistic physics
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