Newton’s Laws in Words

I’ve been teaching my first-year Mathematical Physics students about Newton’s Laws of Motion so decided to record this little video as an aside discussing the history terminology and use of language.

Unfortunately the only microphone I have is the one built into my laptop and it tends to suffer sometimes from a crackle caused (I think) by the fan inside the machine interfering with the mike. I guess the noise appears when the CPU is working hard causing the machine to heat up so the fan works harder. The sound on video recordings I make this low budget way do break up from time to time, which is rather irritating. Obviously I need to buy an external microphone and when I do I might record this again but in the meantime you’ll just have to put up with it breaking up a couple of times!

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Newton’s Laws in Translation

I’m about to do some lectures about Newton’s Laws of Motion to my first-year Mathematical Physics class so I thought I’d put up a quick post about how these laws have been expressed through the years. The original versions in the Principia (frontispiece above, first published in 1687) are of course in Latin. I did five years of Latin at school, but found most of the Principia impenetrable when I tried to read it in the original

 

The laws of motion are however fairly clear, perhaps because they are familiar in English:

Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus illud a viribus impressis cogitur statum suum mutare.

Lex II: Mutationem motus proportionalem esse vi motrici impressæ, & fieri secundum lineam rectam qua vis illa imprimitur.

Lex III: Actioni contrariam semper & æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æqualeset in partes contrarias dirigi.

As I am teaching in a room in the old college here in Maynooth (which was founded in 1795), I looked for a contemporary English translation. This is from 1792:

Law I: Every body perseveres in a state of being at rest or of moving uniformly straight forward except insofar as it is compelled to change its state by forces impressed.

Law II: The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.

Law III: To every action there is always opposed an equal reaction: or the mutual action of two bodies upon each other are always equal, and directed to contrary parts.

And finally here’s the modern version I was taught at School:

First Law: Every body continues in a state of rest or uniform motion in a straight line unless it is acted upon by an external (unbalanced) force.

Second Law: The rate of change of momentum of a body is proportional to the impressed force, and is in the direction in which this force acts.

Third Law: To every action there is always an equal and opposite reaction,

an alternative form of the Third Law being:

Third Law: If Body A exerts a force on Body B then Body B exerts a force on Body A which is equal in magnitude and opposite in direction.

Going back to the 1792 English translation, the exposition of the second law continues:

If a force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively. And this motion (being always directed the same way with the generating force), if the body moved before, is added to or subtracted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joined, when they are oblique, so as to produce a new motion compounded from the determination of both.

If only Newton had known vector notation!

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A Problem with Spitfires

This problem stems from an interesting exchange on Twitter last night, prompted by a tweet from the Reverend Richard Coles:

WWII fighter pilot people: would firing the canon on a Spitfire or Hurricane reduce your airspeed? A lot?

— Richard Coles (@RevRichardColes) July 24, 2017

I think his clerical vocation may be responsible for the spelling mistake. The answer to his question doesn’t require any physics beyond GCSE but it does require data that I didn’t have access to last night.

Here’s a version for you to try at home with all the necessary numbers (though not necessarily in the right units):

A model of a Mark VI Spitfire showing its two 20mm cannons.

A Supermarine  Mark VI (Type 350) Spitfire fighter aircraft weighing 6740 lb is initially travelling at its top speed of 354 mph. The aircraft is armed with two Hispano-Suiza HS.404 20mm cannons, one on each wing, each of which is fed by a drum magazine containing 60 rounds. Each projectile  fired from  the cannon weighs 130 grams, the rate fire of each cannon is 700 rounds per minute and the muzzle velocity of each shell is 860 m/s.

(a) Calculate the reduction in the aircraft’s speed if the pilot fires both cannon simultaneously until the magazines are empty, if the pilot does nothing to compensate for the recoil. Express your answer in kilometres per hour.

(b) Calculate the average deceleration of the aircraft while the cannons are being fired, and express your result as a fraction of g, the acceleration due to gravity at the Earth’s surface which you can take to be 9.8 ms^-2.

(c) A Mark 24 Spitfire – which is somewhat heavier than the Mark VI, at 9,900 lb (4,490 kg) – is armed with 4×20mm cannons, two on each wing. The inboard cannon on each wing has a magazine containing 175 rounds; the outboard one has 150 rounds to fire. Repeat the above  analysis for these new parameters and comment on your  answer.

Answers through the comments box please!

 

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