Physics! #27: University Physics 4.5

4.5: Newton’s Third Law

This is the famous ‘every action has an equal and opposite reaction’ law. It’s a bit unfortunate that it was originally phrased that way, in that the language often confuses students. But hey, it could’ve been worse.

The reason it’s confusing is that you assume “reaction” implies that something moves. However, as you know, when you hit a ball with a bat, the ball goes flying and you more or less stay still. The thing to understand is that, just because something isn’t moving, doesn’t mean something isn’t happening. If two people pull a rope with the same force in opposite directions, the rope stays put. If one person pulls with a higher magnitude of force, the difference between those two is shown in the change in momentum of the rope.

The book has a more modern description:

“If body A exerts a force on body B (an ‘action’), then body B exerts a force on body A (a ‘reaction’). These two forces have the same magnitude but are opposite in direction. These two forces act on different bodies.”

Okay, so it’s not as pretty, but that’s often the price of precision. They then supply the mathematical formulation which is, in fact, rather pretty:

\vec{F}_{A on B} = -\vec{F}_{B on A}

Here’s how I like to think about it:

“When two things interact, momentum is coserved.”

This is not the same as Newton’s Third, but it’s the underlying principle. If you see two billiard balls flying through space, then you see them smack each other, then you see them zoom away, you know the total value of mass*velocity is unchanged. I like this because it feels very fundamental. Whenever two things interact (whether it’s two asteroids or my open hand with your mother’s eager buttocks), two qualities define the interaction – mass and speed. That is, how much stuff there is and how fast it’s going.

Of course, in real life, things get complicated. Billiard balls are convenient because they’re spherical and small. If, on the other hand, it was two surfboards smacking in space, you can see how the specifics are going to depend on things other than mass and speed, such as the angle at which they hit, or whether any parts get broken off. Or, if it’s my hand smacking your mom’s ass, the ass won’t zoom away – it’ll wobble back and forth till it’s dissipated all its momentum.

That said, in all of these cases, conservation of momentum is preserved. We’ll get an even better sense of this once we get a rigorous grip on energy and collisions.

We’ve talked about some of this stuff in the past, so I won’t linger too long. But, the book gives you a lot of nice examples on how a physicist will think about objects in space. The apple on the table example is very important. Here’s how I like to think about it:

We all recognize that the apple is pushing down on the table, but it seems strange to say the table is pushing back. BUT, imagine what would happen if the table WASN’T pushing back. What happens to an apple is in a downward-pointing gravity field with nothing is pushing it away from the direction of the gravity field? It falls. If the table were not pushing up at the apple, the apple would fall through the table.

Another great example is 4.11. If Newton’s Third applies, how come when you yank on a box with a rope, the box moves but you don’t? It’s confusing until you think about it as a system of momentum. Because you’re yanking on the box, it has a tendency to move forward. This is countered by the friction between the box and floor, which makes the box have a tendency not to move forward. However, you’re yanking hard enough that you overcome this tendency and the box moves forward.

On your end, per newton’s third, there’s a tendency for you to move toward the box. However, there’s also friction between you in the floor, which gives you a tendency not to move toward the box. The reason you stay put but the box moves is that you have shoes with good traction, so it takes more force to move you than the box.

In other words, the “left over” force that allows the box to move forward hasn’t disappeared from the equation. It’s present in the extra force of friction between your shoes and the ground. If you were wearing ice skates and so was the box, you couldn’t do this trick. It only works because your shoes grip the ground more effectively than the box. We’ll get into more specifics on that when we talk about friction.

You’ll note that in these mechanics examples, people are always pulling things with ropes. You may start to wonder why nobody every just picks up the freakin’ box.

As always, this is for simplicity’s sake. You know from real life that how easy it is to pull something may depend on how you grip it. In these examples, what’s happening is not perfectly realistic – it’s what would happen if the entity being pulled had its weight concentrated at a single point at its center of mass and you were pulling on that. If the book showed a guy dragging the box by hand, it might get confusing since there are two points where force acts – one point at each hand. Having him yank a rope makes things nice and abstract.

Finally, the book introduces a concept I hate – tension. Why do we have a separate term for this? As I recall, it led to confusion among many kids in physics 101. I had issues until a friend recommended I always write \vec{F}_{rope} instead. That is, tension is juuuuuust the force on a body in the direction of a rope that’s being yanked on. It’s not anything complicated or different. Why it has a special name is over my head.

Next stop: FBDs!

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One Response to Physics! #27: University Physics 4.5

  1. John Hasier says:

    Tension gets a special name because elegance of analogy of pulling stuff across physical systems. This mostly is useful in continuum mechanics and structural mechanics where we see all kinds of crazy forces acting on a blob of stuff, and it is nice to break out the uniform opposed pulling forces acting along a line so we can get a cleaner look at the rest of what is going on. Things like tensile testing of materials and the surface tension effects in liquids are much easier to analyze if we acknowledge the symmetries of tension.

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