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Newton's Third Law and Units of Force

Newton's Third Law

All forces result from the interaction of two bodies. One body exerts a force on another. Yet we haven't discussed what force, if any, is felt by the body giving the original force. Experience tells us that there is in fact a force. When we push a crate across the floor, our hands and arms certainly feel a force in the opposite direction. In fact, Newton's Third Law tells us that this force is exactly equal in magnitude and opposite in direction of the force we exert on the crate. If body A exerts a force on body B, let us denote this force by F AB . Newton's Third Law, then, states that:


F AB = - F BA    

Stated in words, Newton's third law proclaims: to every action there is an equal and opposite reaction. This law is quite simple and generally more intuitive than the other two. It also gives us a reason for many observed physical facts. If I am in a sailboat, I cannot move the boat simply by pushing on the front. Though I do exert a force on the boat, I also feel a force in the opposite direction. Thus the net force on the system (me and the boat) is zero, and the boat doesn't move. We need some external force, like wind, to move the boat. Though this law seems obvious and unnecessary, we will see its importance when we apply Newton's laws.

Newton's third law also gives us a more complete definition of a force. Instead of merely a push or a pull, we can now understand a force as the mutual interaction between two bodies. Whenever two bodies interact in the physical world, a force results. Whether it be two balls bouncing off each other or the electrical attraction between a proton and an electron, the interaction of two bodies results in two equal and opposite forces, one acting on each body involved in the interaction.

Amazingly enough, Newton's Three Laws provide all the necessary information to describe the motion involved in any given situation. We will soon study the applications of Newton's Laws, but we first need to take care of the units of force.

Units of Force

The unit of force is defined, quite appropriately, as a Newton. What is a Newton in terms of fundamental units? Given that acceleration (a) = m/s 2 and mass = 1 kg, we can find out from Newton's Second Law: F = ma implies that a Newton, N = kg (m/s 2 ) = (kg ƒ m)/s 2 . Therefore, one Newton causes a one kilogram body to accelerate at a rate of one meter per second per second. Our definition of units becomes important when we get into practical applications of Newton's Laws.

Summary of Newton's Laws

We can now give an equation summary of Newton's Three Laws:

First Law: If F = 0 then a = 0 and v = constant
Second Law: F = ma
Third Law: F AB = - F BA