Newton's ThirdLaw 'When

you push on the edge o{ etable or desk with your hand, your palm indents in a way that can only happen if something is pushing on your hand (as in Figure 1). If you use your fingers to push on something your fingers bend back in Lway th"t cen only happen if something is pushing on your fingers. So what's going on) SThenever you push on something thet something pushes back on you. It doesn't matter if the something is at rest or moving or eYen accelerating.

Eigure

1

The idea of things pushing back on you is a bit strange. SThy would somethin& especially a nonliving object, push back on you) This means that when you sit on a chair and exert a force on ig the chair is pushing back on you. Huh) Well, we really don'tknow why things push back on you when you push on them, but we can sort of understand it. The next time you're in your bedroom, push down on the mattress on your bed. For now, imagine you're doing that. Does the mattress push back) Sure. You can even feel it pushing back. If you have a spring mattress, it's easy to see why the mattress is pushing back. Springs do that. See Figure 2.

Figure

2

Now push on your desktop. You know that the desktop is pushing back on you because of what it does to your hand, but you can also think of your desktop as being a lot like a mattress. Your desktop contains little things called atoms that behave as if. the:/te connected by little springs. See Figure 3.

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Newton's Eigure

IhirdLaw

3

not connected by springs, but they act like they are- And all things So, it sort of makes sense that when you push on things,

Atoms

^re are made of atoms. they push back.

This "pushingback" thing happens even when the two things pushing on each other,r.,ottiuing. In ttte aciivity PushingBack,you made two coins collide' For the moment, just focus on the coin that was at rest. After the collision, this coin was moving which means it changed its velocity. A change in v-elocity is called an acceleration. !flhat causes things to accelerate) Unbalanced forces, of course. So what exerted an unbalanced force on this coin to make it 4' accelerate? Pretty easy. It was the coin that you pushed into it. See Figure

figure

4

\ \ Force that moving coin exerts on coin at rest

Next focus on the coin that you pushed toward the other one' It was moving before the collision. After the collision, it was either stopped or moving in a different direction. Both of those things ate changes in velocity, and a;re therefore accelerations. So what exerted the force on this coin that made it accelerate) The other coiry of course. See Figure 5 (p' 18a)'

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Nenton's Figure

Ihirdlaw

t

that coin at rest exerts on moving coin Force

So, the coin that was movin gbefore the collision exerted a force on the coin

that wasn't moving before the collision. Also, the coin that wasn't moving before the collision exerted a force on the coin that was moving before the collision. The "pushingback" thing happens between two things even when the things are nonliving. Not surprisingly, Newton has alaw thet deals with this. It's Newton's third law, ;rnd here's a complete statement:1

lf

obiect A exerfs o force on objecl B, ihen obiecl B exerls on equol ond opposife force bock on obiect A.

So far w{ye dealt with the fact that when A exerts a force on B, then B exerts a force back on A. We heven't talked ebout them being equal. We'7I get to that, but first think ebout how you walk.]ffien you walk across the floot, yau starting at rest and are then moving. In other words, you accelerate. "re Accelerations require forces, so what force is causing your acceleration when you start and rest and then begin walking) Is there an "invrsible walking force" that pushes you) Nope. To figure out what's pushing you, you have to focus on what you do in order to walk. Stand up and do tha;q payrng attention to exactly what it is you do in order to get moving. We'Llwait here for you

t

You will often see Newton's third low stoled os "For every oclion, there is on equol ond opposile reoclion." We're nol going lo use lhol stotement, becouse it's loo vogue ond leods people lo misunderslond the low. The next time you heor someone use "oc'fion-reociion," check wheiher or not lhot person is using the slolemenl correctly. Chonces ore they oren'i. For exomple, people might soy thol someone getting mod ond someone else getiing mod becouse of somelhing the first person did is on exomple of oction ond reoction. Not occording to Newtonl

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Newton's Third Law

Back already) What did you find out) Hopefully you noticed that in order to walk forward, you push backward on thi flooi. see Figure 6.

Elgure 6

The force you exert on the floor

Okay fine, but how does you exerting a force on the floor make you eccelerute? else has to exert an unbalanced force on you. Newton's third law tells us how this happens. When you push on the floor, the third law tells us that the floor pushei Lack on you. rt,s-th at force that causes you to accelerate. See Figure 7.

In order for you to accelerate, something

Figure

7

The force the floor exerts on you

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185

Nenton's

Ihird Law

Okay. Newton's third law says that the forces two obfects exert on each other are eqaal. You showed that this was uue when you and a partlner pulled on each other using spring scales. No matter how hard each of you pulled, the two scales read the same thing. That's because the forces you exert on each other are eqval, as Newton's third law says they should be. Sq, when you throw abal7, the force you exert on the ball is the same (but in the opposite direction) as the force the ball exerts on you. Really) Does that make sense? Maybe not, but it's true. To try and make sense of this, think about the demonstration done in your class. A large-mass person a;nd t smallmass person sat in chairs with wheels. One of the people pushed on the other person's chair. Both people tccelerated, no matter who did the pushing. But the small-mass person accelerated more than the large-mass person. Doesn't that mean that the force exerted on the small-mass person wes greater than the force exerted on the large-mass person) Check out Figure 8.

Figure

t small-mass person

small-mass person

large-mass person

large-mass person


.+> smaller acceleration

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Newton's Third Latw It might seem that the person who has a gteatcr acceleration experiences

a

greatff force, but that's not what's going on. To explain whtt's happening we'll need both r\ewton's third hw md Newton's second law. With the people in chairs, Newton's third law says tha.- no matter who pushes, the two people in chairs experience the same fotce, as shown in Figure 9.

Figure 9 These two forces have

the same magnitude

Force on smallmass person

Force on largemass person

small-mass person

If

Iarge-mass person

we write Newton's second law for these two people,

it looks like this:

For the small-mass person:

F=mQ For the large-mass persor:

F

= lflo

Notice that the size of F is the same for eacb, because they exert equal forces on each other. For the forces to be eqaal, the small-mass person must have a large accelerarion and the large-mass person must have a small acceleration. Figure 10 shows how it looks with teeter-tottersr

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Nenton's

Thirdltw small mass

maSs

Forces are the same I

\

I

v

So eyen though the forces on each are equal, the masses are different. That leeds to different accelerattons.

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