Which of Newtons laws of motion explains why the cannon and the cannonball move in opposite directions?

Newton's cannonball was a thought experiment Isaac Newton used to hypothesize that the force of gravity was universal, and it was the key force for planetary motion. It appeared in his posthumously published 1728 work De mundi systemate (also published in English as A Treatise of the System of the World).[1][2]

Source of the experiment

Newton's original plan for Philosophiæ Naturalis Principia Mathematica was that it should consist of two books, the first analyzing basic laws of motion, and the second applying them to the Solar System. In order to include more material on motion in resisting media, the first book was split into two; the succeeding (now third) book, originally written in a more popular style, was rewritten to be more mathematical.[3][4] However, manuscripts of an earlier draft of this last book survived, and a version of it was published in 1728 as De mundi systemate; an English translation was also published earlier in 1728 under the name A Treatise of the System of the World.[1][2][4] The thought experiment occurs near the start of this work.

Thought experiment

In this experiment from his book (pp. 5–8),[2] Newton visualizes a stone (you could also use a cannonball) being projected on top of a very high mountain. If there were no forces of gravitation or air resistance, the body should follow a straight line away from Earth, in the direction that it was projected. If a gravitational force acts on the projectile, it will follow a different path depending on its initial velocity. If the speed is low, it will simply fall back on Earth. (A and B) for example horizontal speed of 0 to 7,000 m/s for Earth.

If the speed is the orbital speed at that altitude, it will go on circling around the Earth along a fixed circular orbit, just like the Moon. (C) for example horizontal speed of at approximately 7,300 m/s for Earth.

If the speed is higher than the orbital velocity, but not high enough to leave Earth altogether (lower than the escape velocity), it will continue revolving around Earth along an elliptical orbit. (D) for example horizontal speed of 7,300 to approximately 10,000 m/s for Earth.

If the speed is very high, it will leave Earth in a parabolic (at exactly escape velocity) or hyperbolic trajectory. (E) for example horizontal speed of approximately greater than 10,000 m/s for Earth.

Other appearances

An image of the page from A Treatise of the System of the World showing Newton's diagram of this experiment was included on the Voyager Golden Record[5] (image #111).

See also

• 
  Physics portal
• 
  Spaceflight portal

• Space gun
• Physics

Notes

1. ^ a b De mundi systemate, Isaac Newton, London: J. Tonson, J. Osborn, & T. Longman, 1728.
2. ^ a b c A Treatise of the System of the World, Isaac Newton, London: printed for F. Fayram, 1728.
3. ^ Newton’s Philosophiae Naturalis Principia Mathematica, George Smith, 2007, Stanford Encyclopedia of Philosophy. Retrieved 14 September 2021.
4. ^ a b A Treatise of the System of the World, Isaac Newton, introd. I. Bernard Cohen, Dover Phoenix Editions, 2004, ISBN 0-486-43880-5.
5. ^ Sagan, Carl et al. (1978) Murmurs of Earth: The Voyager Interstellar Record. New York: Random House. ISBN 0-394-41047-5 (hardcover), ISBN 0-345-28396-1 (paperback)

External links

• Newton Thought Experiment Simulator
• Bucknell.edu – Astronomy 101 Specials: Newton's Cannonball and the Speed of Orbiting Objects
• Drawing in the 1731 (2nd) edition of 'A Treatise of the System of the World' @ Google books
• Newton's Cannon animation

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Example 1

For every action, there is an equal and opposite reaction.

Skater A pushes against skater B.

Skater B will accelerate to the right according to `F=ma`

Skater A will accelerate to the left because there is an equal and opposite force.

Example 2

A woman on a boat tries to step off the boat on to a pier.

For every action, there is an equal and opposite reaction. Pushing your body forward will have an equal reaction backwards on the boat.

NOTE: Forces always come in pairs: that is why Newton's third law is sometimes referred to as his law of pairs.

Example 3

NOTE: Before we go on with example 3 you need to know what a normal line is. It is an imaginary line perpendicular (90°) to a tangent line (in this case the surface). To remember this better see Mammoth Memory convex lenses and concave lenses.

Example 3 is a book being pushed across a table.

This book being pushed along shows how forces come in pairs.

The book being pushed (thrust) has an opposing reaction of friction.

The weight of the book exerts a force downward and the table needs to exert an equal force upward or the table will collapse.

NOTE: You will note from the above that force is a vector, i.e. both magnitude and direction. The arrows denote the direction of the force.

NOTE: You will sometimes see the forces displayed as:

Example 4

Releasing a balloon full of air has an equal and opposite reaction.

Air is pushed out of the neck of the balloon but the balloon reacts in the opposite direction by moving upwards.

Example 5

A cannon firing.

The cannon exerting a force on a cannonball exhibits Newton's third law. Whenever an object exerts a force on a second object the second object exerts an equal and opposite force on the first object.

There will be an equal force on the cannon, but its larger mass and the bracing of the cannon in the ground, means it will not be kicked back too far.

Example 6

A car travelling on a road. The tyres push forward on the road but the road pushes on the tyres. The two forces are equal and opposite.

Example 7

Firing a large gun on a skateboard.

If you fire a gun on a skateboard or even throw a medicine ball away from you on a skateboard, you will demonstrate Newton's third law. As you fire the bullet forward there is an equal and opposite reaction and the skateboard will move backwards.