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Lecture Comments (13)

1 answer

Last reply by: Professor Selhorst-Jones
Mon Feb 17, 2014 11:19 PM

Post by Christopher Bunce on February 15, 2014

are you going to solve for the velocity and the displacement in to problem. I calculated a velocity of -20m/s
and a displacement of -100 m/.

2 answers

Last reply by: Sarawut Chaiyadech
Fri Jun 28, 2013 3:46 AM

Post by Tanveer Sehgal on November 19, 2012


I am a little confused with the last example. Since the force acting on the smaller block is 19.6 N why is it the force acting on the larger clock not 19.6 N and the acceleration = 1.96 m/s^2?

1 answer

Last reply by: Professor Selhorst-Jones
Tue Oct 23, 2012 2:04 PM

Post by Andrew Stewart on October 23, 2012

Yes, we didn't figure out the velocity in 5 seconds or the displacement after 5 seconds.

5 answers

Last reply by: Peter Ke
Sun Feb 28, 2016 1:00 PM

Post by james Oh on June 17, 2012

on the second to last example could you please answer the velocity and displacement questions

Newton's 2nd Law: Introduction

  • For a given mass, more force means more acceleration.
  • For a given acceleration, more mass means more force.
  • Forces can cancel each other out. If two equal magnitude forces are pushing in opposite directions, they result in no acceleration.
  • Fnet = m ·a  . The unit for force is the newton (N), which is equivalent to [(kg ·m/s)/s].
  • When working with forces, a diagram is extremely important for understanding what's going on.
  • Since we know the acceleration of gravity (g), we can figure out the force of gravity: Fg = m ·g.
  • When an object is resting on a surface, there must be a force canceling out gravity. We call this force the normal force (FN).
  • If you pull on a rope (or something else), you put a tension into the rope that is equal to the force. That tension pulls on the other end of the rope with the same force.

Newton's 2nd Law: Introduction

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Net Force 1:42
    • Consider a Block That is Pushed On Equally From Both Sides
    • What if One of the Forces was Greater Than the Other?
    • The Net Force is All the Forces Put Together
  • Newton's Second Law 3:14
    • Net Force = (Mass) x (Acceleration)
  • Units 3:48
    • The Units of Newton's Second Law
  • Free-Body Diagram 5:34
    • Free-Body Diagram
  • Special Forces: Gravity (Weight) 8:05
    • Force of Gravity
  • Special Forces: Normal Force 9:22
    • Normal Force
  • Special Forces: Tension 10:34
    • Tension
  • Example 1: Force and Acceleration 12:19
  • Example 2: A 5kg Block is Pushed by Five Forces 13:24
  • Example 3: A 10kg Block Resting On a Table is Tethered Over a Pulley to a Free-Hanging 2kg Block 16:30

Transcription: Newton's 2nd Law: Introduction

Hi, welcome back to, today we are going to be talking about Newton's second law, we are going to be getting our first look at how this works.0000

The next three lessons will all be involving Newton's second law, but this is our primary introduction.0006

Say we are pushing a wood block along some frictionless surface.0011

We push the wood block.0017

That would cause it to accelerate.0019

We would have some wood block, and e put some force into that block, it gets some acceleration out of it.0020

What if we are going to do it to a steel block?0032

Steel block is going to be denser, so it is going to have a higher mass.0034

If we put in the same force, we are going to get a small acceleration, which is no surprise at all.0043

If you push on a skateboard with the same force as you push on a car, the skateboard is going to accelerate a whole lot faster than that car is.0049

Alternatively, if we had the same (wood) blocks, and in one version we pushed with a big force, and in another version we pushed with a tiny force, which one do you think is going to accelerate faster?0055

Of course, the one we pushed hard is going to accelerate faster.0074

The one we pushed softly is going to accelerate slower.0077

So there is a connection between the amount of force we put in, and either the amount of mass that we are able to push around with a certain acceleration, or the amount of acceleration that we are able to get in at a certain mass.0081

Either mass is fixed and acceleration is allowed to change, or acceleration is fixed and mass is allowed to change.0091

We have got his relation that force is something to mass and acceleration.0096

With that in mind, consider this other idea, what if we had a block that we pushed on with the exact same force from the left and the right side?0100

Assuming that the block is able to maintain the amount of force and not crumble, (if I were pushing on an egg carton really hard, it would crush), would it move?0110

It would not!, if you take, for example, this pen, and I push on it from both sides, nothing happens, I am pushing reasonably hard on it, but nothing happens; we call it a static equilibrium.0126

So, the net force is what is going to really matter.0147

What if we were to consider, we pushed hard on one side, and just lightly on the other side, then we would get some acceleration, but less than we would have had for just the one force on one side.0150

We got to understand here that it is not just about the force that is acting on an object.0164

If we look into each force individually, it is all the forces put together, so it is the net force.0169

In this case, if we had 'F' here, and 'f' here, and consider going to the right as positive, then the net force would be these two forces put together.0174

So for this case up here, (f - F) is what we would get.0186

With all these ideas in mind, we are able to formulate the Newton's second law.0192

Net force on an object = mass × acceleration, which gives us that relationship of varying mass and same acceleration for varying force, or varying force, same mass and varying acceleration.0199

Or in symbolic form, Fnet = mass of the object × acceleration of the object = ma .0215

So, what you need to use for Newton's second law?0229

We use this.0233

How do we get to this?0235

In S.I. units, 'm' is in kg, 'a' is in m/s/s, so if, F = ma, then F = kg × (m/s/s) .0237

This is what the unit for force is, which makes sense.0256

If we have 1 N of force, then that is the force it takes to take 1 kg and speed it up by 1 m/s/s .0260

So, if you were to have 2 N, you could either move 2 kg at 1 m/s/s, or you could move 1 kg at 2 m/s/s, that is how we see that how all the pieces of the formula come in.0269

We are going to call this unit, newton.0281

This is on Isaac Newton, the person who created these three laws that we are talking about and also added many things to many scientific disciplines such as Math and Physics and variety of things.0287

We simply use a 'N', we call it a newton, so you might push something with 1 N of force, or 50 N of force or something might have a force of -50 units if it were going in the backwards direction in our frame of reference.0297

One thing to keep in mind is that 'newton' is the S.I. unit of force.0315

If you are using a different measurement system, say the American-English system, you will have to use a different unit for force.0321

But, if we are keeping everything in the metric system, we use 'N', so that is what we will be using in this Physics course.0328

The other thing to keep in mind while we are doing all these force problems, is that we are going to be using 'free-body diagrams'.0335

What is a free-body diagram?0343

It means that you are just looking at the object itself being acted upon by the forces.0345

It is little bit of a strange name, but that is what it is called.0349

Free-body diagram, is looking at the object, and putting all the forces.0352

Say we had three forces acting on an object, say we had forces of 3 N, 8 N and -7N (7 N backwards).0359

Let me point out that these arrows are all the same size.0374

These arrows are effectively the same size, even though this is 3 N, this is 8 N, I have made the arrow about the same thing.0380

It is because the arrow does not have to be connected to the length, we have marked how long it is with a number, so we know what that arrow represents, so the same arrow could be a one, the same arrow could be a thousand.0389

The important thing is we have marked next to it what we doing with it, so it is up to us to pay attention.0404

There are a lot of things in Physics where we are modeling things in your diagram, but it is up to you to pay attention to what you mean with it.0408

For this case, what we would want to find out is, what is the net force on the object?0414

Before we can figure out where it is going to move, we will have to get the net force.0419

Once again, to the right - positive, up - positive, down - negative, left - negative, traditionally.0422

Net force = 3 + 8 + (-7) = 11 - 7 = 4 N, and that is how free body diagram works.0435

You have the object, you have each of the forces acting upon the object, and then when you need to find out what the net force is, you can total it.0455

Also, we do not have anything moving in the vertical direction for this.0462

We are going to be talking about multi-dimensional force movement later, so I will avoid that right now, but if this object were on a flat plane, it would still be affected by the force of gravity.0467

What is the force of gravity?0480

That is a special force and we are just about to talk about that.0481

First special force that we are going to talk about is gravity.0483

Gravity means weight.0490

As we mentioned before, weight just means the force that gravity exerts on an object.0492

How much force does gravity exert on an object?0497

That is going to depend on where we are, but most of our work is going to be on Earth, so we know what 'g' is, we know what the acceleration due to gravity is.0499

We have got this wonderful formula: F = ma .0507

If we know what the mass of the object is, and if we know what the acceleration in a free-fall is, then we know what the force of gravity must be.0510

The force of gravity = mg, that is why all objects fall at the same rate, the amount of force on them correlates to the amount of mass they have.0519

If you have a 1 kg object, it is going to get 9.8 N, and if you got a 10 kg object, it is going to get 98 N .0533

We just put Fg = 1 kg × (9.8 m/s/s), and it will now be pulling directly towards the centre of the Earth.0542

So gravity is pulling us down to the centre of the Earth, but most of us are not accelerating or hurdling very quickly to the centre of the Earth.0562

What is going on?0573

There is got to be something else at hand here.0575

We do not care about the each force, we care about the total force.0577

There must be something opposing the force of gravity, and that is what we call the normal force.0583

You are being held up by something.0588

Right now, either you are standing up or sitting down, but something is under you keeping you from being pulled into the centre of the Earth, whether it is the ground, a chair; right now I am sitting on a chair and the chair is holding me up.0589

I am being pulled into the chair by the force of gravity.0601

But at the same time, the chair is giving me resistive force, which is called the normal force, and in this case, since I do not have any vertical acceleration, we know that the normal force has to be equal to the force of gravity.0605

They have to cancel each other out, otherwise you have to have a positive or negative acceleration.0619

So, the normal force is going to be how much gravity gets canceled out by the object you are currently sitting upon, what you are being resisted by.0624

Final special force we will talk about right now is tension.0633

If you have a rope or a tether or a string, and you pull on it, you are going to put in a tensile force, you have got tension in that object.0638

If you pull on that rope with 5 N, you will have tension of 5 N, that force is going to go in and it is going to pull along throughout.0649

So this 5 N will get translated into this block, and this is assuming that we are dealing with a mass-less rope.0661

If you had a rope that weighed 1 kg, part of the force that you are putting in would go into accelerating the rope as well as accelerate the object that it is attached to.0669

But, all the problems in this course, we will assume that it is a mass-less rope, some other problems might not.0680

It is all basically the idea that, what is the force that it takes to accelerate that object.0686

In our case, we are not going to worry about accelerating the connecting object (rope or tether).0699

But, you might have to consider it in other course, but it is then just looking at that as another object being accelerated.0705

In our case, we will just consider the easier case, because in most cases the rope is considerably lighter and something that is negligible when we are looking at the larger object.0711

So, if we were to pull at 5 N from this end, we would wind up translating that into the rope which will give it a tension of 5 N which would pull all the way through the rope, everything in the rope would be pulled at 5 N, whiich means that where it is getting connected to would also get pulled at 5 N .0720

So we would be able to pull that block along at 5 N if we pull the rope at 5 N.0735

Our first example: We have got a 12 kg block and it is sitting on a frictionless table.0740

We know that the mass = 12 kg .0752

If we have a force of 144 N acting on this, parallel to the table, what is the acceleration of the block?0756

We just use F = ma .0762

In this case, we know that Fnet = 144 N, because the only thing acting on it is that one force.0766

What is our mass, what is our acceleration?0772

Do not know the acceleration yet, but we know what everything else in this equation is.0774

144 N = 12 kg × a0779

We get, 12 m/s/s = a0787

Which direction is it going?0793

It is going the same direction as our force went, so there is our acceleration vector, it is going at 12 m/s/s, to the right, to the positive direction.0795

Example 2: Very similar to our last example, but this time we have got a bunch of forces acting on the block.0803

We have got 3 forces acting to the right, which are 5 N, 27 N and 9 N .0812

To the left, we have 2 forces, -14 N and -47 N .0826

Actually this is technically a misnomer, the fact that I have got the -14 N going with an arrow going this way, it should actually be positive, because the negative goes into the fact that we, if we do not have the direction given to us, remember, a vector is a magnitude and direction, so in this case we have got the direction by having the arrow, so we just have to put the magnitude.0837

But at the same time, when we are doing the actual Math, it is going to be up to us to put in the negative sign, otherwise the Math will get screwed up.0859

Sometimes it is OK to leave in that negative sign as a reminder of what you need to do when the Math gets in, but at the same time it is important to understand that if you were to have an arrow going like this, and if it is a -5 N, that could also mean what you are really saying is you have got an arrow going this way at 5 N .0865

So it depends on what you are trying to say.0882

In this case, I will leave it as the +14 N and +47 N over there, but it is up to us to remember that when we add it together to get the net force, we are going to have to pay attention to that.0885

Finally, the block's mass = 5 kg .0899

So, Fnet = 5+ 27 +9 + (-14) + (-47) = -20 N .0907

We put that into, Fnet = ma .0934

So we have got, -20 = 5 × a, which gives us, a = -4 m/s/s .0945

Remember, that is going to be going in the left direction.0957

So we have got here, a = 4 m/s/s (in the figure), which is the same thing as -4 m/s/s .0959

Remember it is just a matter of whether or not the direction has been shown in our graphics.0969

But this can get confusing sometimes, and it is up to you to pay attention to what you are writing and what you are meaning by what you are writing.0974

The important is that you understand what you are doing, and whoever you are going to show it to is also able to understand what you are doing.0984

Final example :There are two different ways to solve this.0990

One will be considering this a system of all together, and one is going to be looking at it independently.0993

I prefer the system way, but first we are going to be looking at it independently because it is a good way to understand what is going on, but the system, I think it is a little bit more intuitive, and slightly a more accurate representation.0998

But they are both useful, they are both important to understand, and both give us the same answer.1011

We have got a 10 kg block, and it is resting on a table, and we call the block 'A'.1015

Over here, we have got block 'B', with mass = 2 kg .1026

They are tethered together by a mass-less tether, and also a mass-less pulley, and the pulley and table are frictionless.1032

The only thing pulling them around is gravity, we do not have to worry about any friction, or any inertias getting in the way other than their own inertias.1042

What is the acceleration of the 2 kg and 10 kg blocks?1050

First we have to assign the units.1055

Here is an interesting thing to know.1058

Normally we consider down to be negative and right to be positive.1060

So we will make right to be positive, but notice that they are connected.1065

These two objects are actually connected over by the pulley.1068

So what is positive up here, suddenly flips when it gets over the pulley, and it stays positive.1071

So if we are not going to have these two different ways of looking go in conflict, because really this is a one dimensional problem that just has a flip in the middle, so we are actually going to look at down as positive, which is a strange thing to think about, but that is because we are thinking of going right as positive.1079

Whatever cause this block right here to move to the right is going to be the same thing as positive, so this moves down, then that is going to be another form of positive.1098

With that in mind, let us find out what forces are acting on these two objects.1108

Over here, we have got 2 forces, the force of gravity is pulling down on it (which we will find out in a while), and the rope that is attached to it is going to have some tension 'T', which we going to solve for.1114

Over here, we are going to have that same tension 'T' pulling on it, but what else is going to be operating on it?1130

Of course gravity is going to be operating on it (which we do not know), but what underneath it is a table.1136

The table is completely resisting it going down.1143

If we were to keep this system still, the force of gravity will always be completely canceled out.1146

So we have got a normal force that is equal to the force of gravity.1155

So we are going to just cancel the force of gravity and normal force out, we do not have to worry about them, so it keeps it as a one dimensional problem.1160

The only thing acting on block A is tension, the only thing acting on block B is a combination, we have a net force there, and that is the force of gravity and tension.1167

Which one of these is positive?1177

Not the one you would expect, tension is the negative one, force of gravity is the positive one; why?1179

Because going down is considered positive, going right is considered positive, and that pulley causes us to wrap our coordinate system.1185

What is the force of gravity?1193

Well, how much does it weigh?1195

Weight = 2 × 9.8 = 19.6 N .1197

What is the net force on B?1210

Fnet on B = 19.6 - (T) = massB × aB , (we let tension 'T' be a positive quantity, which is subtracted from 19.6 since it is in the other direction.)1215

That gives us 2 unknowns.1263

So far we have got, tension and acceleration of block B.1266

We cannot solve for that yet, we have got too many unknowns there.1269

We know mass, but we have 2 unknowns in that equation nonetheless.1272

Let us look at A.1275

What is the net force on A?1277

That is going to be equal to just tension.1281

So we have got T = mA × aA .1284

Once again we have got another problem here.1292

We have got 2 unknowns, we do not know what aA is, we do not know what the tension is.1294

But, here is where we have got a cool trick.1298

This rope is going to stay taut the entire time.1301

There is going to be a little bit of tension, so the entire time, if one moves, the other one is going to move, if this one moves down a little bit, this one is going to move over a little bit, if this one moves back a little bit, this one is going to move back a little bit.1308

So, we know that there is a direct connection.1320

Whatever acceleration one of them has, the other will have to have the exact same acceleration, which is the really important reason why we kept these coordinates having to be the same, it is because they are going to have the exact same acceleration, because the rope effectively connects them into being one system.1322

So we get, aA = aB .1338

Now, we can do this problem.1343

We will erase the subs A and B since accelerations are the same.1352

Now, mBa = mAa .1353

Now we have only got 2 unknowns in 2 equations, we are able to solve for it.1359

So, T = 10a and 19.6 - T = 2a .1363

Plug in T, we get, 19.6 - 10a = 2a, 19.6 = 12a, a = 1.63 m/s/s .1374

One important thing to keep in mind, this changes, this one has acceleration here, and this one has acceleration here.1395

So they are different.1404

What if we want to know what the tension in the rope was?1405

We could just solve for it over here.1408

We get, T = 10 kg × 1.63 m/s/s = 16.3 N .1412

Now, we have got everything solved, but the important thing is, the acceleration between the 2 blocks is going to have to be the same thing.1433

So this question is little bit of a red herring.1440

The acceleration has to be the same, otherwise we will not be able to solve the problem.1443

Now, what if there is another way to solve this problem?1446

What if that basic fundamental assumption of the fact that our system is connected together could be used to our advantage from the beginning?1449

We think of this as one whole system, (it is a rigid connection, if one moves, the other one has to move) that is we have that basic assumption that the two accelerations are going to be equal from the beginning.1458

We could think, what forces act on the system as a whole?1477

What forces are acting on this block up here?1484

The only thing acting on it is the tension T, and on B, we have got the tension T as well, and we have got the force of gravity.1488

So, those two tensions, if we look at them over the whole system, those two tensions are actually going to cancel each other out.1498

So, the whole system only has one force operating on it.1504

The force of gravity of block B.1507

The force of gravity of the little block, which is = 19.6 N .1514

Then, Fnet for the system = 19.6 N .1518

So, Fnet of the system = mass of the system × acceleration of the system , acceleration being the same for both.1527

There is only one thing that is acting on everything, we can treat it as one whole thing working together, because of the fact that they have got this rope rigidly connecting them one another, rigidly being something that can still bend around a corner, but one moving, the other one has got to move, and vice versa.1538

So, 19.6 = (10+2) × a = 12 × a, a=1.63 m/s/s , exact same as what we had before.1555

So, both work in different ways, one work it as a complete free body diagram where we consider each object on its own, and that works great, it is a good way to do things, but I think that it is a little bit more elegant if we can look at the system as a whole.1574

That is something we can generally do, when we do not want to look at all the complicated workings inside a thing, because what we are interested is, how does the whole thing move, we can just consider what operates on the whole thing.1586

The stuff inside gets canceled out as long as it is not able to get to outside.1598

As long as what is inside is not going to affect the external stuff, then you can look at just the external stuff.1602

In this case, the only external force acting on the system is the force of gravity acting on the little block.1608

But they both work, they are both great ways to do it.1613

Figure out which one you prefer and which one makes more sense to you, and that is the way you should approach it.1616

Hope you enjoyed this, hope you learned something, and we will see you at for the next lesson.1620