1. Newton's third law of motion

Newton's third law states that whenever one body exerts a force on another body, the second body exerts an oppositely directed force of equal magnitude on the first object.

Newton's Third Law of Motion
"For every force (or action) between two bodies there is always an equal but oppositely directed force (or reaction)."

Thus, if someone pushes horizontally against a wall with a force of 100 N, then the wall will push horizontally against the person with a force of 100N.

Do not confuse this situation with equilibrium of forces in which several forces act on the SAME OBJECT, with a zero resultant force. Here the forces act on DIFFERENT OBJECTS, i.e., the person on the wall and the wall on the person!

It is important to realise that forces always act in ACTION/REACTION pairs. Objects that are involved in such action/reaction pairs do not have to be in contact (contact forces), but can be separated, sometimes by vast distances (forces at a distance), as in the case, for example, of the sun's force on the planets.

Do you know how a rocket works?

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2. The force of reaction

Consider an object at rest on a horizontal table. Since it is not moving, by Newton's first law, there is no NETT force acting upon it. Referring to the diagram on the right, we see that it exerts a force on the surface of the table, which in this case happens to be equal to its weight mg, where m is the mass of the object and g the acceleration due to gravity. Since the object is not crashing through the table, nor is it being jerked upwards, there must be an EQUAL BUT OPPOSITELY DIRECTED force acting on the object. This is the FORCE OF REACTION, R = -F = -mg.

But there is still another action/reaction pair, not shown in the above diagram. That is the force of gravity, mg, on the mass, and the force of gravity of the mass on the earth. -mg. By the way, it does not matter what force is called the "action" or "reaction", as long as we bear in mind that the pair of forces act on different bodies (in this case, the mass and the table). The force of gravity acting on the mass and the reaction from the table are not an action/reaction pair since these two forces both act on only one body, the mass m.

3. Additional questions

How does a rocket work?

A rocket works on the basis of Newton's third law, and not, as many believe, by "the exhaust gases pushing against the ground (at lift-off), or against the outside atmosphere" (during flight). A rocket works even better in the near vacuum of space, where there is no frictional drag due to the atmosphere.

Rather, a large mass of gases is expelled at a very high velocity from the combustion chamber of the rocket engine through specially designed nozzles. The velocity of the exhaust gases is very high, (about 10 000 km·hr-1, or 2700 m·s-1), and as the gases are expelled, a change in the momentum of these gases takes place in the time the propellant takes to burn. This is the force causing the gases to be ejected.

By Newton's third law, this force has a reaction, in the opposite direction, and this is the force, or THRUST, that accelerates the rocket.

The propellant for the rocket consists of a fuel and an oxidant. For launching the space shuttle, for example, the fuel is liquid hydrogen and the oxidant liquid oxygen. As these react together, very large volumes of extremely hot gases are produced in the combustion chamber. The total mass of fuel and oxidant will equal the total mass of exhaust gases (assuming complete combustion). Let this mass be m kg. If the average velocity of the exhaust gases is v m·s-1, and the burn takes place in time, Δt s, and the mass of the rocket and its fuel and payload is M kg, then

The rocket will therefore be subjected to an average acceleration, a, m·s-2 during the "burn". This will cause motion in an opposite direction to the motion of the gases. In practice, the acceleration increases as the mass, M of the rocket decreases, since the propellant (several hundreds of tons for large rockets) is used up in a few minutes. The mass of propellant can be as much as 20 times the mass of the rocket and payload!