Does a cannon feel the same magnitude of force as a cannonball if so why does it not move as far?

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

In retrospect Newton's third law asserts isotropy of space.

I noticed many authors of textbooks opting for that reinterpretation. What that does is that it moves the third law away from the realm of causality

Causality
Causality is about how things happen sequentally in time. Causality is is all about time.

On the other hand, asserting that space is symmetric is complementary to any assertion about time.

The cannonball being propelled out of the cannon and the recoil of the cannon happen simultaneously: neither is the cause of the other.

About assertions of isotropy of space:
Newton's first law can be reinterpreted as asserting that space is euclidean, for motion of objects that are not subject to any force. More precisely: we can reinterpret the first law as asserting that space has the same symmetries as the geometric concept of euclidean space. (Symmetry under translation, symmetry under orientation change.)

The third law also asserts the isotropy of space, for pairs of objects that are exerting a force upon each other.

It's tempting to speculate why Newton felt a need for the third law.
My hypothesis for that starts with the point that to make the celestial mechanics work Newton needed that gravitional mass is equal to inertial mass.

But that makes gravity a rather nebulous force. (Earth is in orbit around the Sun, but we don't feel the gravitational attraction from the Sun because gravitational mass is equal to inertial mass.)

In Newton's time the observatoinal data were sufficiently accurate to demonstrate that the Sun and Jupiter are both orbiting their common center of mass. That is, the motion of the Sun and Jupiter demonstrates that the Sun and Jupiter, exerting gravitational force upon each other, are behaving as a third law force pair.

If the Sun would be stationary, despite the burden of having to swing Jupiter around, that would be very bad news for newtonian theory of gravity.

But: the Sun isn't stationary! The Sun and Jupiter's motion is in accordance with the motion of a third law force pair. Thus it is justified to regard gravity aa a force.

That is my hypothesis as to why Newton felt a need for the third law.

Newton's third law states

Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object.

Simply stated
"To every action there is always an equal and opposite reaction"

One force we call the action force and the other we call the reaction force. It does not matter which force we call action and which we call reaction.

Page 2

For example, lets look at a boulder falling towards the earth. Step 1 Identify the two objects that are interacting. In this case it is the boulder and the earth.

Step 2 The action and reaction forces can be stated in this way.

Action is the force exerted by the boulder on earth
Reaction is the force exerted by the earth on the boulder

It does not matter which force you call the action or reaction.

Page 3

Hide solution

Step 1 Identify the two objects that are interacting. In this case it is the shell and the tank.
Step 2 The action and reaction forces can be stated in this way.

Action is the force exerted by the shell on the tank.
Reaction is the force exerted by the tank on the shell.

Both the action and reaction are equal in strength. The tank hardly moves because it is many times heavier that the shell.