The elastic ballistic pendulum

The famous theory of the parabolic motion of projectiles was at an early period found to give results not in accordance with practice. Manifestly, then, the air must offer a very sensible resistance to a body which is moving through it with a high velocity. This resistance will depend upon the form of the moving body, and upon the velocity with which it is moving. Hence, before the path of a projectile can be calculated, it will be necessary to determine experimentally the resistance opposed by the air to the motion of the projectile, corresponding to various velocities. According to Newton’s law, the resistance of the air varies as the square of the velocity. But the velocities were low in the experiments made under his direction. In 1719 John Bernoulli gave equations for finding by the method of Quadratures the path &c. of a projectile, when the resistance of the air was supposed to vary according to any power of the velocity. But in spite of grave doubts respecting the accuracy of Newton’s law, it has been adopted by most of the eminent mathematicians who have written on the subject, such as Euler (1753), Lambert (1765), Borda (1769), Bezout (1789), Tempelhof (1788-9), d’Ehrenmalm (1788), Lombard (1796), and Poisson. The first good experiments made with a view to determine the resistance of the air to the motion of projectiles were those of Robins in 1742. The projectiles used were leaden bullets of small size. When we consider the great density of the material used, its liability to change its form in the barrel of the gun, and the smallness of the solid projectiles, it is truly wonderful that Robins was able to accomplish so much with his ballistic pendulum. Afterwards Hutton carried on Robins’ system of experimenting both with the whirling machine and ballistic pendulum, introducing additional precautions, and using iron projectiles of greater size. In recent times MM. Didion, Morin, and Piobert have carried on experiments in France with heavier spherical projectiles, by the help of an improved ballistic pendulum; but they have done little more than confirm the results of Robins and Hutton, and extend them to spherical projectiles of larger diameter.

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On the calculation of the trajectories of shot

Proceedings of the Royal Society of London ◽

10.1098/rspl.1877.0040 ◽

1878 ◽

Vol 26 (179-184) ◽

pp. 268-287

Keyword(s):

Present State ◽

Equations Of Motion ◽

Exact Formula ◽

Limited Range ◽

Ballistic Pendulum ◽

Extensive Information ◽

The Law

In the present state of our knowledge of the resistance of the air to shot, the problem of integrating the equations of motion of the shot and of plotting-out a representation of the curve described by it is peculiar, because, according to the best experiments we possess, the law of the retardation cannot be expressed by a single exact formula which is available for the solution. We are therefore compelled to give a solution adapted to Tables, the magnitudes of the retardation being set down in those Tables for velocities which are common in practice. The formulæ given by Hutton and by Didion, even if they were true, apply only to spherical shot; and though they are very simple formulæ, the solutions obtained by means of them are not satisfactory—first, by reason of their complexity, and next on account of the rough approximations which characterize the proofs. Prof. Hélie, who gives an account of Didion’s method in his ‘ Traité' de Balistique,’ says that it gives results which are not in accordance with fact. The fault may probably be laid in a great measure to the charge of the formula; for there can be no doubt that Mr. Bashforth’s method of experimenting with his chronograph and screens gives more trustworthy and more extensive information than the ballistic pendulum experiments of Hutton and Didion; and Hutton’s formula, as well as Didion’s, agrees with Mr. Bashforth’s Tables only for a limited range of velocities.

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The Response of Circular Plates to Repeated Uniform Blast Loads

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.535-536.44 ◽

2013 ◽

Vol 535-536 ◽

pp. 44-47 ◽

Cited By ~ 3

Author(s):

Steeve Chung Kim Yuen ◽

Gerald Nurick ◽

Nzudzanyo Ranwaha ◽

Travis Henchie

Keyword(s):

Experimental Investigation ◽

Vickers Hardness ◽

Steel Plates ◽

Circular Plates ◽

Blast Loads ◽

Test Plate ◽

Charge Mass ◽

Ballistic Pendulum ◽

Incremental Increase

This paper presents an experimental investigation into the response of circular Domex-700 MC steel plates to repeated uniform blast loads. The experiments are carried out on a ballistic pendulum for a 3mm thick test plate to witness up to five similar uniform blast loads. As expected, a trend of increasing permanent mid-point deflection is observed for an increase in charge mass and number of blast loads. In general, the results showed that the incremental increase in mid-point deflection decreases while the Vickers hardness of the plate increases with increasing number of blast loads.

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Slow collisions in the ballistic pendulum: A computational study

American Journal of Physics ◽

10.1119/1.1538572 ◽

2003 ◽

Vol 71 (6) ◽

pp. 535-540 ◽

Cited By ~ 1

Author(s):

Denis Donnelly ◽

Joshua B. Diamond

Keyword(s):

Computational Study ◽

Ballistic Pendulum

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Propulsion of a flat tin target with pulsed CO2laser radiation: measurements using a ballistic pendulum

Laser Physics Letters ◽

10.1088/1612-202x/aa94ea ◽

2017 ◽

Vol 15 (1) ◽

pp. 016003 ◽

Cited By ~ 6

Author(s):

B V Lakatosh ◽

D B Abramenko ◽

V V Ivanov ◽

V V Medvedev ◽

V M Krivtsun ◽

...

Keyword(s):

Ballistic Pendulum ◽

Radiation Measurements

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Quartz gauge and ballistic pendulum measurements of the mechanical impulse imparted to a target by a laser pulse

10.1117/12.25960 ◽

1991 ◽

Author(s):

Jean-Yves David ◽

J. C. Wettling ◽

Patrick Combis ◽

G. Nierat ◽

M. Rostaing

Keyword(s):

Laser Pulse ◽

Ballistic Pendulum ◽

Mechanical Impulse

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Experiments in the Principia

The Oxford Handbook of Newton ◽

10.1093/oxfordhb/9780199930418.013.36 ◽

2020 ◽

Author(s):

George E. Smith

Keyword(s):

Gravitational Force ◽

The Core ◽

Gravitational Forces ◽

Fluid Resistance ◽

Open Questions ◽

Wide Range ◽

Ballistic Pendulum ◽

Elastic Responses ◽

Resistance Forces ◽

Pendulum Experiment

Newton carried out four groundbreaking experiments in conjunction with the Principia and proposed a fifth. This chapter reviews his reasons for doing them, their design, and what they achieved. The four include a two-pendulum experiment early in 1685 to establish that the action of gravitational forces on a body is always proportional to its mass and hence that all bodies at any point respond to a gravitational force in the same way. In that same year he conducted a ballistic pendulum experiment to establish that this third law of motion holds for impact of spheres of a wide range of elastic responses, in the process identifying what became known as the coefficient of restitution. He carried out two sets of experiments measuring fluid resistance forces on spheres, the less than successful first relying on pendulum decay and then, for the second edition, vertical-fall. All five experiments were designed to “put the question to nature” in the sense that the three laws of motion enable their results to yield theory-mediated answers to theretofore open questions about forces—and thus parallel the answers to questions about celestial forces drawn from planetary motions that form the core of the Principia.

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