Introduction
The ballistic pendulum is an equipment that scientists use to measure the momentum of a bullet. From the momentum, one can determine both the kinetic energy and velocity of the bullet. This is possible with the aid of a few formulae. However, this technique of measuring a bullet’s technology has been replaced by other techniques such as the use of modern chronographs that allow one to directly measure the velocity of a projectile. Despite the device being obsolete, it has steel remained in use for quite some time, opening doors to advancements in other areas of science related to ballistics. The reason the ballistic pendulum is still being found in laboratories today is due to its convenience. This is because, while determining the velocity of a projectile using this device, one does not require to measure time at any instant. All that is required are the masses and distances. This makes it easy to use and makes it easier for learners to grasp the basic principles governing momentum.
Objective
The main objective of this experiment is to set up and use the ballistic pendulum for its intended purposes. By undertaking this experiment, the basic principles of momentum and how this relates to velocity will have been learnt and implemented practically. The idea of how a projectile navigates when placed and launched at an angle to the horizontal will also have been investigated. All these will be achieved by the four simple main procedures outlined in the experiment and with the help of two main formulas. The formula relating momentum and velocity is given as:
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The other formula which is used to calculate the range of a projectile is given as:
Al these equations are discussed in detail in the theory section.
Theoretical Background
The ballistic pendulum functions under the principle of conservation of momentum. The principle of conservation of momentum dictates that the total initial momentum of a system is always equal to the final momentum provided no external force is introduced to the system. During the collision, energy is conserved. The equations of motion that govern this principle are:
M 1 = The projectile’s mass
M 2 = The pendulum’s mass
V 10 = Pendulum’s velocity before collision
V 2f = Pendulum’s velocity immediately after collision
h = Rise in centre of gravity of the system after collision
Once V 2f for the system is solved since all the other parameters can be obtained easily, the projectile’s speed is determined using the formula:
The range of a projectile can be determined using Newton’s laws of motion. For a projectile that is launched at some angle, the range is dependent on not only the initial velocity but also the angle at which it was launched. The equation that governs this phenomenon is given as:
R = the range being determined
V o = The projectile’s initial velocity
= The angle at which the projectile was launched
Conclusion
All procedures outlined were followed and the experiment performed successfully. The ballistic pendulum was used to measure the range of the projectile. The first step, which was to set up and operate the ballistic pendulum was achieved. The pendulum was then used to measure the velocity of the projectile using the equations provided. The range method was again employed to measure the velocity of the projectile. Finally, the projectile was launched at 45 degrees angle and its range measured. Slight errors must have been introduced in the experiment. However, these errors are negligible and do not affect the results obtained significantly. All objectives of the experiment were therefore achieved.
