Projectile Motion Model

Contents

• BODY OF ARTICLE
• REFERENCES
• About the Author
• FIGURES

Textbooks almost always have a stroboscopic photograph of a ball falling alongside of one with an initial horizontal speed. These photos are great for showing how the two objects experience the same vertical acceleration; however, the photos don't usually illustrate what happens if a projectile is launched at some angle. There are a number of ways to illustrate the effects of the launch angle: shooting a ball or stream of water through hoops, for example.¹ Those demonstrations, though, do not allow for side-by-side comparison of the effects of various launch angles. Thus, a few years ago I constructed this three-dimensional projectile model to do just that. The model is composed of two three-dimensional "stroboscopic sculptures" representing the trajectory of two projectiles.

Each half of the model is built with a telescoping antenna (available at any electronics store), lengths of string, lead fishing-line weights (the clamp-on style), and double-sided sticky tape. Each section of antenna has a lead weight hanging from it via a length of string. (The double-sided sticky tape prevents the string from slipping along the antenna.) Each section of the antenna with its weight represents a moment of time after the projectile is launched; when taken all together, it is as if one viewed the projectile with a flashing strobe light.

The lengths of string represent the displacement of the projectile due to the acceleration of gravity, so they increase parabolically, e.g., 1 cm, 4 cm, 9 cm, 16 cm, etc. Distance along the antenna represents displacement along the original velocity vector; changing the lengths of the antenna sections then adjusts the "initial speed" of the projectile. (An alternative construction of the model would be to substitute suspended bungee cords for the antennae.)

The two halves are mounted on a support rod so that the inclination of the projectiles can be adjusted. With each projectile set at a different "speed," the class can explore questions regarding which projectile will hit the ground first. Figures 1, 2, and 3 show how the model can illustrate the three primary cases: horizontal, an inclination above horizontal, and an inclination below horizontal. Figure 4 shows a projectile shot over a "wall." If one is careful with a choice of string lengths, the model can even show how a projectile fired vertically upward will return to its starting point.

Figure 1.

Figure 2.

Figure 3.

Figure 4.

The model can be built for less than $15 in hardly any time at all.

Reference

1. "M-90. Water-Stream Parabola," in Demonstration Experiments if Physics, edited by Richard M. Sutton (McGraw Hill, New York, 1938), p.43. first citation in article
   

Sean Cordry did his Ph.D. in the area of sonoluminescence and has been teaching physics for eight years now. Although he still has interests in nonlinear dynamics and acoustics, his primary focus is pedagogical development and Science and Theology dialogue.Department of Physics, Northwestern College of Iowa, Orange City, IA 51041; scordry@nwciowa.edu

Full figure

Fig. 1. The model shows that two projectiles fired simultaneously and horizontally, but at different speeds, will hit the ground at the same time. (The string lengths represent vertical displacements due to gravitational acceleration.) First citation in article

Full figure

Fig. 2. When two projectiles are fired at an upward angle, the one with the slower initial speed will hit the ground first. First citation in article

Full figure

Fig. 3. If the projectiles are fired downward, say from a cliff into a canyon, the model shows that the one with the faster initial speed will hit the ground first. First citation in article

Full figure

Fig. 4. The model showing the projectiles going over a "wall." Notice that the one with the slower initial speed barely clears the obstacle. First citation in article

Up: Issue Table of Contents
Go to: Previous Article | Next Article
Other formats: HTML (smaller files) | PDF (85 kB)