In this extended essay, I will be investigating projectile motion via studying the movement of a metal ball bounced off by an unloaded spring. Experimental methods and theoretical models will be used to investigate how the projection height and compressed length of spring affect the projection range of the metal ball. A spring gun was constructed using a spring and 5 wooden boards. The metal ball served as ammunition for the spring gun.
While the simple spring gun was used to launch the metal ball , a zigzag ruler was used to measure the range of horizontal distance travelled by the metal ball at varying ranges of projection height and compressed spring length. The conclusion of this investigation will be drawn by comparing theoretical models and experimental data, considering whether experimental values were less than theoretical values. This may be attributed to air resistance in a vacuum-less environment, therefore it can be seen that gravity isn’t the only factor causing this uncertainty.
At the same time, it is should be noted that the elastic potential energy of the spring is converted into work done against friction, work done against air resistance and rotational kinetic energy of metal ball after spring release. Experimental results of the horizontal projection range of the metal ball followed an expected trend, in which the range increases with separate or synchronized increases of projection height and compressed spring length. It is discovered that by quadrupling the projection height and doubling the compressed spring length, it results in twice the previous horizontal projection range of the metal ball.
A further study of this investigation is exploring the effects of air resistance on the horizontal projection range of the metal balls varying in size, mass and shapes (e. g cylinder or cubes). Contents 1. Introduction 2. Theoretical Hypothesizing 3. Experimental Setup Description 4. Experimental Methods – Procedure – Determining range of metal ball by varying projection height – Procedure – Determining range of metal ball by varying compressed length of the spring 5. Graphing the experimental data and the theoretical data 6. Interpretation of the graphs 7. Comparing experimental results to theoretical hypothesis 8.
Evaluation and Conclusion 9. Appendix 1 10. Works and program cited Introduction Projectile motion is a form of parabolic motion when an object is subjected to a constant acceleration, where the initial horizontal velocity perpendicular to the vertical acceleration of gravity is not zero, forming a parabolic trajectory. An example of this projectile motion trajectory is shown in the diagram below. . Diagram 1: The trajectory of projectile motion www. quintic. com/education/case_studies/Projectile_Motion. html The Monkey and the Hunter is a thought experiment illustrating the effects of gravity on projectile motion.
A hunter aims a blowgun at a monkey hanging from a tree and fires. The instant the hunter fires the blowgun, the monkey releases itself from the tree and falls downward. However, this instinctive reflex does not spare the monkey, who instinctively believed that it was possible to fall below the trajectory of the bullet, because both the monkey and the bullet have the same constant acceleration, gravity, which acts vertically to both of them. When both the monkey and the bullet come into contact, their vertical mid-air displacement are the same. Therefore, the dart will inevitably hit the monkey.
Hence, we can conclude that the vertical acceleration of gravity does not affect the horizontal motion of the dart- vertical motion is independent of horizontal motion. In this extended essay, a spring connected to a container and a metal ball will be used to investigate projectile motion. The research question is “How does the projection height and the compressed spring length affect the horizontal projection range of the metal ball? ” This investigation will begin firstly through theoretical hypotheses and finally collecting data via experiments.
Moreover, I will investigate whether the projection height or the compressed spring length is proportional to the range of projectile motion, if so, determine how they are proportional to the projectile motion, directly or inversely. Theoretical Hypotheses To begin, let’s assume a metal ball is launched horizontally with a height above ground level by a released spring. However, since the projectile trajectory of the metal ball is extremely close to the Earth’s surface, the change in gravitational force acting on the metal ball is statistically minute and can be ignored.
Therefore, the vertical acceleration of the metal ball will be considered as constant throughout the entire trajectory and the vertical motion of metal ball is considerded to be under free fall after projection. Note that the vertical component of projection velocity of metal ball is zero as the metal ball is ejected parallel to the horizontal (surface of table), thus, the horizontal component of projection velocity of metal ball is equal to the projection velocity.
Since there is no acceleration to the horizontal motion of the metal ball, the horizontal component of velocity of metal ball, which is equal to the projection velocity of metal ball in this case, remains unchanged throughout the projectile motion. Also, the linear kinetic energy of metal ball just after the time it is ejected is given by the elastic potential energy which was stored in the spring before. First, use the equations for elastic potential energy (Eepe) and linear kinetic energy (Eke) based on the principle of conservation of energy to find the projection velocity.