Newton's Third Law?

Question

I really don't understand the 'equal and opposite' part of the law. When I push a book across a table, it accelerates. Isn't this because I'm applying a greater force on the book than the force that the book is applying on me? How would this scenario work using Newton's Third Law? I've looked everywhere and can't find an answer that makes sense to me. Please try to keep it easy to understand! Thanks.

Answer 1

Sorry, some of the other responders are way off the mark.



> "When I push a book across a table, it accelerates."



In some cases, yes.



> "Isn't this because I'm applying a greater force on the book than the force that the book is applying on me?"



NO! This is a common source of confusion. The force that book exerts on you is ALWAYS THE SAME amount as the force that you apply on the book. This is guaranteed by Newton's 3rd Law, and it is ALWAYS true whether the book is accelerating or not.



Here's the thing: The book's acceleration depends only on the forces that are acting ON THE BOOK. Any forces that the BOOK exerts on OTHER objects (like your hand) are IRRELEVANT in determining how much the book accelerates.



So, here's an example; say you push on the book, and say even that there's a little friction. Here are the forces involved:



1. You exert 2 Newtons on the book, toward the right;

2. Book exerts 2 Newtons on your hand toward the left;

3. Table exerts 1.5 Newtons on the book, toward the left (a friction force);

4. Book exerts 1.5 Newtons on the table, toward the right.



Now, #1 and #2 are an action/reaction pair, satsfying Newton's 3rd Law. Likewise, #3 and #4 are an action/reaction pair, satisfying Newton's 3rd Law. Note that #1 MUST ALWAYS match #2; and #3 MUST ALWAYS match #4, whether the book is accelerating or not.



To determine the acceleration of the book, you must consider only those forces that ace ON THE BOOK. That means #1 and #3. Forces #2 and #4 are IRRELEVANT to the book's acceleration, because those forces don't act ON THE BOOK.



In this scenario, the net force on the book is 0.5 Newton's toward the right, so the book accelerates.

Answer 2

The scenario you speak of describes Newton's Second Law force equals mass times acceleration (F = ma). In order for a mass to accelerate, there must be a force exerted on it.



Later you will learn that in order for a mass to accelerate, F = ma. If a mass is stationary (static equilibrium), then sum of the forces must equal zero (sum(Forces) = 0). That would be an example of the third law.



Newton's second law : You push a shopping cart. You don't really notice, but when you push a shopping cart, you have to exert a force greater than the sum of the force of rolling resistance of the wheels, force of air resistance and the force of friction between the wheel and the ground.



Newton's third law: You push a door that is already closed. The force is being held in place by hinges as well as other forces. So the force you exert onto the door are equal. Thus, the door does NOT move. In any case, if you were to kick the door enough to get it open, you have exceeded the forces keeping that door closed, thus, the door moves (accelerates) in the direction of the force.

Answer 3

Newt's Third says SUM(f) = 0...always. Which is a shorthand for saying for every force f there is an equal but opposite force -f. Even when the body, M, is accelerating. Here's how.



SUM(f) = 0 = P - F - MA; where P is all the pushing or pulling applied forces, F is all the opposing forces to those, and, ta da, f = MA is the accelerating force. Yep, that's a force as you learned in Newt's Second.



So when the wall doesn't accelerate when you push on it P, you have SUM(f) = P - F - MA = P - F = 0. So the reaction F = P. The wall pushes back with equal but opposite force.



But when the book accelerates as you push on it P, you have SUM(f) = P - F - MA = 0 or MA = P - F and A = (P - F)/M > 0 so the book accelerates.



Bottom line, just keep in mind that f = MA is a force too.

Answer 4

I get what you're saying; if the book is moving, then surely the forces are *not* equal.



I'm trying to remember how this works. Maybe we're pairing the wrong forces? If you push on the book and it doesn't move, then it is exerting an equal force on your hand. But when you increase the force, the book will accelerate (F=ma) and there's a net force acting on it. So why doesn't this violate Newtons third law?



Whatever that force is, that you're applying to the book, the ground you are standing on is also applying to you. I mean, if you were sitting on frictionless ice you may not be able to move the book at all - you would just push yourself away.



So I think the "equal and opposite" force is the frictional force acting on your feet giving you the traction to be able to move the book. That force will be equal and opposite to the force you're applying on the book. (I think)

So there's a net force acting on the book,.,,,



Hmmm.... I'm sorry, I haven't quite helped, have I! :)



Edit: Maybe it's like this: Because we have a net force (ie the book is moving), the forces have to add up to that net force. So we have, the frictional force of the book, the force of your hand pushing the book.

And we're assuming that they add up to zero (equal and opposite) but that's just not the case, they should add up to the net force. So the book is still applying an opposite force on your hand but the hand is applying a greater force.

Answer 5

Well imagine punching a punching bag. The amount of force you punch it will be the same amount of force when it comes swinging back at you. Newton's Cradles are another perfect example of the Newton's Third Law.



So therefore, the book does apply a force on you because of friction. That frictional force being pushed on you is going to be the same amount of force that you push on the book. How is this possible?



Imagine pushing that book on a smooth icy surface. It's not going to take a lot of force to push that book but there is still a very small amount of friction that you have to overcome to still push that book. Now let's bump up friction with pushing it on sand paper. It's going to be a lot harder to push that book now because friction is preventing you from pushing that book.



Lastly, take these ideas into consideration.



If the force of friction was greater than you pushing on it, the book will start pushing you backwards.



If the force of friction was less than you pushing on it, the book will go flying off more than you intended it to be.



If the force of friction was equal to you pushing on it, then the book will move at an easy pace.

Answer 6

See the link below, guaranteed to make sense.



http://www.physicsclassroom.com/class/newtlaws/Lesson-4/Newton-s-Third-Law

Answer 7

Hi Amy,



Confusing, isn’t it? Even before the C20 weirdness of relativity and the quantum atomic realm, Isaac Newton’s C17 genius was to overcome such confusion, with mathematical precision. In his honour, the SI unit of force is named the newton.

» http://en.wikipedia.org/wiki/Newton_(unit)



> Please try to keep it easy to understand!



You got it! May take a while, but I hope you’ll find that it’s time well spent – and there’s a Video Prize waiting at the end. :-)



THOUGHT EXPERIMENT A – EARTH

Let’s say you’re sitting on a chair, at a table, and about to push a tabletop book away from you. Typically, all this occurs in Earth’s gravity field, which pins the table, the chair, and your bare feet to the floor, pins you to the chair, and pins the book to the table.



Newton's Third Law eg#1 – the force of gravity acting downwards (doing the pinning just mentioned) is matched newton-for-newton by an equal-and-opposite force acting upwards, arising from the electromagnetic (EM) bonding forces in the solid objects and the floor. You experience this as pressure in your buttocks and the soles of your feet – as gravity tries to pull you downwards, the seat and the floor resist with an equal-and-opposite upward-directional opposing force (EM in origin): you sit still, and the competing forces compress and deform the soft tissue of your buttocks and foot soles, allowing you to FEEL Newton's Third Law at work and in action (despite your current ‘sitting still’ inaction).



Thanks to the Earth’s gravity field, for stuff to move horizontally, the force of friction between the stuff and the thing gravity is currently pinning it to must first be overcome. You push on the book, overcome the force of friction ’tween book and table, and give it some acceleration away from you.



Newton's Third Law eg#2 – not so easy to feel this time, but… as you push the book away with only the tip of one index finger, do you notice a feeling of pressure in your finger tip? It is Happening AGAIN! Your muscles use chemical potential energy (EM in origin again) from your last meal and convert it to kinetic potential energy, in pushing forcefully against the book. But friction initially holds the book in place, allowing the book to resists your push, and matching you newton-for-newton with an equal-and-opposite force acting towards you (see Fig 1 below) – the competing forces compressing and deforming the soft tissue of your fingertip, as you begin to FEEL Newton's Third Law at work and in action again.



Now since you are (usually) WAAAAY more massive than the book, the sum to the friction of (you+chair) on the floor is FAR greater than the friction ’tween book and table, giving you a sold stationary base from which to push the book away.



Newton's Third Law eg#3 – once your muscles have overcome the friction ’tween book and table, you accelerate the book away from you – and the pressure in your fingertip is STILL there… how come? To accelerate (a) the mass of the book (m) you have to continue to apply a force (F), where F = ma (ie: Newton's Second Law; plus you’ll be adding some more force to continue to overcome the on-going resistive-to-relative-motion frictional force ’tween book and table). The sum of (inertia of the book + book-table friction) meets your book-pushing-force at the finger-tip/book contact point, matching you newton-for-newton with an equal-and-opposite force acting towards you – and again, the competing forces continue to compress and deform the soft tissue of your fingertip, as you continue to FEEL Newton's Third Law at work and in action.



THOUGHT EXPERIMENT B – SPACE

OK, so now let’s get to imagine some book pushing WITHOUT an effective gravity field, and in an effectively FRICTIONLESS environment – say on a space walk outside the International Space Station with just your spacesuited body plus the book – and I hope you’ll come to agree that it’s Much Easier to Feel AND to SEE IT (in your mind’s eye, that is – like YOU get to be playing Sandra Bullock’s character in the movie ‘Gravity’). Initially, you’re stationary, relative to the ISS – then you shove the book away from you.



Newton's Third Law eg#4 – let’s say (you+spacesuit) have 100 times the mass of the book. You accelerate the book so your parting velocity sees it moving away at 1 m/s, or 1000 mm/s, relative to the ISS. You look towards the ISS, and now notice that YOU ARE MOVING TOO – in the opposite direction to the book, at 10 mm/s. The equal-and-opposite accelerative forces operating on (you+spacesuit) and the book, generated by your muscles in shoving it away, impart equal-and-opposite parting velocities on (you+spacesuit) and the book – and the ratio of your masses is matched by the ratio of your parting speeds, relative to the ISS.



Sorry it’s so long – but I hope you find it intuitively easy to feel, imagine, and understand now.



Your Prize: Listen to astronaut Gene Cernan explain how he lost 10.5 lbs in a 2 hr 05 min space walk – by failing (alongside the NASA mission planners) to take Newton's Third Law in to account! (as in my eg#4) http://youtu.be/PrJnWTcW55s • ‘Newton's Third Law of Motion: Astronauts in Outer Space’

– video, 4:50



Fig 1 – some of those equal-and-opposite forces, before the book begins to accelerate