AP Physics C: Mechanics Newton's First Law & Free Body Diagrams

Hello, everyone, and welcome back to www.educator.com.0000

I am Dan Fullerton and today we are going to start our study of dynamics with a lesson on Newton’s first law and free body diagrams.0003

Our objectives are going to be to analyze situations in which a particle remains at rest0011

or it moves with the constant velocity under the influence of several forces.0016

To draw free body diagrams for objects under the influence of multiple forces.0021

As we talk about these let us start with Newton’s first law of motion and it is a very simple law.0028

Everybody thinks they know it but there as so many pieces to it and it is really tough to understand because it is tough to see here on Earth.0034

Let us take our time and walk through it slowly.0039

An object at rest will remain at rest.0044

An object in motion will remain in motion at a constant velocity, constant speed, and constant direction in a straight line0048

that is constant direction part unless acted upon by that net force or an unbalanced force.0059

And that is also known as the law of inertia.0067

What we are going to do is just dive into what that means in detail.0069

I suppose first we probably will talk about forces.0074

A force is a push or pull on an object.0077

The units of force are Newton's the symbol is N.0081

1N is 1 kg × m/s², it is a derived unit.0085

To give you an idea how much is in a Newton it is about the weight of a regular sized apple.0090

If you think of Isaac Newton sitting under a tree the apple comes down bops him on the head.0096

He needs all the help to remember that Newton was about the weight of 1 medium small sized apple somewhere in there.0100

Forces are pushes or pulls but we can divide forces into a couple different types.0108

We can talk about contact forces and we can talk about field forces.0112

Contact forces are things like that tension in a rope string pull and applied force is when you literally go push on something or pull on something.0126

Friction is a contact force.0139

All these forces that arise from the inter atomic attraction and repulsion of the electrons, the charges on atoms when we look at the very small scale.0141

Field forces on the other hand can act in the distance, things like gravity, the electrical force, and the magnetic force.0154

Electrical and magnetic are 2 different sides of the same point.0166

Contact forces and field forces.0170

What then is a net force?0174

Besides being a set of books by Tom Clancy and another author, a net force in physics is the vector sum of all the forces acting on an object.0177

Add up all the forces on an object and whenever you have left over after everything cancels out that is your net force.0189

It is the unbalanced force on an object.0196

If all the forces are balanced, if we have a 20 N force this way and 20 N force exactly opposing it our net force would be 0.0198

If all forces are balance there is no net force and that leads to a situation known as translational equilibrium.0208

Net force unbalanced force mean the same thing.0218

If we took an example we have some object here we have a 5 N force to the right.0222

We have of 5 N force to the left.0228

Our net force is 0.0231

On the other hand what happens if we have a 5 N force to the left a 3 N force to the right.0234

How we can find that out you can probably see just by looking at what the answer is but we can add this up in vector edition.0246

We would draw our 5 N force to add vectors we line them up to tail so we will move that 3 N force so it is lined up to tail there.0253

There is our 3 N force and our resultant goes from the starting point of the first to the ending point of the last would be 2 N to the left.0263

Our net force would be 2 N.0272

What does Newton’s first law really mean?0276

An object is going to continue in its current state of motion unless an unbalanced force acts on it.0279

Whatever it is doing it is going to keep going until there is an unbalanced force.0285

Objects at rest will remain at rest that is easy.0293

I see that all the time.0296

Put the cat on a couch it is going to stay there and until an unbalanced force acts upon it.0299

Sometimes that happens to be the dog.0303

Object at rest, they are still very easy to see in our world.0307

If we want to look at objects in motion though those will remain in motion at a constant velocity and was acted upon by a net force.0311

That is much harder to observe here on earth because we have so much friction.0320

Think about, you put a car on the highway it is going down 15 m/s and it does not just keep going 50 m/s,0325

unless you apply force because you have all that air resistance and the friction between the tires and the car is going to slowdown.0333

You just do not see this every day unless you have a very low friction apparatus you can demonstrate this with.0339

Instead, think of doing this in space.0345

Throw a baseball in space send it flying out it is going to keep going and going and going and going.0347

Eventually, there will be some gravitational forces on it too so we cannot get away from that unbalanced force situation but you get the idea.0353

Talking about equilibrium in a bit more detail.0363

A couple types of equilibrium.0366

Static equilibrium occurs when a net force on an object is 0 and the net torque on an object is 0 and it is at rest.0368

It is still and it does not have any net force and so it is not accelerating in any direction.0375

It does not have a net torque on it either.0380

Mechanical equilibrium occurs when a net force on an object to 0 and the net torque to 0.0385

That does not mean it has to be at rest that just means whatever it is doing it is going to keep doing.0394

Translation of equilibrium is just when a net force on an object is 0.0399

A couple different types of equilibrium.0405

Let us talk about inertia for a moment.0409

Inertia is the tendency of an object to resist the change in velocity.0411

We talked about very early mass has 2 aspects.0416

We have talked about inertial mass.0420

How hard it is to change an objects velocity?0422

At some measure of the objects ability to resist a change in velocity or to resist acceleration.0426

The other type of mass we have talked about is gravitational mass.0433

How strongly a gravitational field affects a mass?0436

We are going to get to that soon.0438

But every time we have measured these they have always been the same.0440

For the purposes of basic intro physics mass and inertia are synonymous.0444

Mass is a measure of an object's inertia so we can almost use those interchangeably here if you see them in a problem.0452

Let us take a look at an example that does just that.0460

Which this objects has the greatest inertia? A falling leaf, a softball in flight, a seated high school student, or a helium filled toy balloon?0463

And of course the object of the greatest inertia is the one that has the greatest mass.0472

Mass is a measure of inertia must be C our seated high school student.0478

Or a question like this, which of these has the greatest inertia?0484

A 5 kg mass moving at 10 m/s, a 10 kg mass at 1 m/s and so on and so on.0487

These speeds do not matter.0495

Inertia masses a measure of inertia.0496

We are just looking for the one with the greatest mass.0500

As we talk about translational equilibrium draw the velocity time graph for an object in translational equilibrium.0506

Let us start by drawing our axis.0512

We have a velocity on the y, time on the x, and if it is in translational equilibrium we know that the net force on the object must be 0.0524

Newton’s first law is going to have no acceleration, no change in velocity, no change in velocity, no acceleration means velocity must be constant.0535

All we have to do is draw a graph of a constant velocity, nice straight line.0546

Let us do a net force problem.0559

What is the net force of an object experiencing a pull of 5 N to the north, a push of 3 N to the south and the pull of 2 N to the east.0561

Let us see if we can draw that.0573

We got 5 N to the north, 3 N to the south, this up to the tail, 3 N to the south and 2 N to the east.0575

As I look at my diagram there.0594

If this whole thing was 5 then we came back 3 that mean this piece must be 2 N.0596

We got 2 N to the right and our result as we draw from the starting point of the first to the ending point of the last.0601

We got this 45° angle vector.0608

What is the magnitude of that net force?0613

Magnitude of our net force is just going to be if we can use the Pythagorean theorem to figure that out √ 2² + 2² is about 2.83 N.0616

Our angle is going to be 45° NE.0628

As we talk about forces of objects a very useful tool is known as the free body diagram.0634

It shows all the forces acting on a single object.0641

What we do is we draw the object itself as a dot or rectangle and then we draw all of the forces acting on that single object.0644

Let us take the example of the following elephant.0653

We have a circus elephant that falls off a tight rope, draw a free body diagram for the following elephant neglecting air resistance.0656

I’m going to draw an elephant as a dot quite the artist there.0664

Neglecting air resistance what forces act on that elephant?0670

The only force I can think of its following is the force of gravity which we are going to write as mg.0675

Draw a free body diagram for a falling elephant but this time including air resistance.0684

There is our elephant we still have the force of gravity on the elephant.0690

We also have some air resistance and air resistance is a form of friction that opposes motion.0696

Let us draw a force in the opposite direction.0702

There is our force of air resistance.0707

It is pretty straightforward.0713

Draw a free body diagram for glass of soda sitting on the table.0716

Let us start with a quick diagram of our situation.0720

We have got some table here and sitting on that we have our glass.0725

What are all the forces acting on our glass of soda?0741

Let us draw that as a dot and there is our object.0745

We have the force of gravity mg.0749

There must be another force on this.0754

What is that?0757

There is a force of table pushing back up on our glass otherwise that object will accelerate through the table and we know that does not happen.0758

That is what we are going to call the normal force.0766

The normal force is a force of perpendicular to a surface.0771

What is really happening is if you look very closely at the surface the atoms on that are bending down a little bit0775

as you have that weight on top of it and pushing back almost like a spring action.0781

The force when we talk about normal force, by normal we mean perpendicular.0785

Perpendicular force from some surface.0795

Those 2 we now must be exactly balance I suppose I should draw the N vector a little bit bigger because it is not accelerating at all.0798

It is just sitting there.0805

If one of those vectors were bigger than the other there would be an unbalanced force0806

and we would have a change in the glasses motion.0810

It is just sitting there it is being nice and boring and still.0813

How about a free body diagram for a box on a ramp?0817

We have a 5 kg box sitting on a ramp incline of 30° what forces act on our box?0821

Let us see if we can identify them first.0828

We can see that we are applying a force up the incline it is just sitting there it is not moving or accelerating.0831

We have the weight of the box, the force of gravity on it mg.0836

We have a normal force n and assuming it is coming up the ramp we can assume let us say0843

that is going up the ramp we can go in some force of friction opposing that motion right there.0852

Let us try out what those forces just for example problem here.0859

I'm going to draw my free body diagram off to the side and0863

the trick here when you draw your free body diagram just look at the angle of our ramp.0867

If it is on a ramp just use that angle of the ramp as your x axis.0871

Try and draw one of the axis in the direction of the object is going to move.0874

I could draw that is my x and my y is going to be perpendicular to my x.0878

Pretty close to it I suppose and you have the greatest drawing ever.0887

X y there is our dot for our object and that will identify the forces acting on it.0891

We have f up the ramp.0898

We have force of gravity straight down.0901

We got friction acting in that direction and our normal force perpendicular to the surface, perpendicular to the ramp.0905

There is our free body diagram but when we get into analysis of these free body diagrams forces0916

that do not line up with one of these axis can get a little bit troublesome mathematically.0922

Although this is our free body diagram what we are going to do is we are going to draw what is called a pseudo free body diagram.0927

Or we are going to take this vector, this force it does not line up with the axis and breaking up the components that do.0935

It is a little easier to deal with.0940

On the AP exam if you are asked for a free body diagram this is the one you have to draw.0942

Do not go right ahead and make a drawing that has a pseudo free body diagram even if you can do that in your head.0948

You will lose points.0954

You need to have the separate free body diagram then redraw to another pseudo free body diagram to help you with your problem solving.0955

Let us draw our axis again.0964

We will see if I can get this a little bit more perpendicular this time.0967

There we go we get our y and x.0972

We will draw our dot and we can already put the forces that lineup with the axis back on here nice and simply.0978

Normal force, force of friction, the only troublesome one is this force of gravity and I'm going to draw that in green0986

just so it stands out you make a little bigger so you can see it pretty easily.0993

The trick here is it does not lineup with the axis.0999

It would be nice if we can break it up into a component that is parallel with the x and parallel with the y.1002

We can do that using trigonometry.1011

This piece the one that is perpendicular to the ramp I will call mg perpendicular by trigonometry1014

we can see that that is going to be adjacent to this angle which is the same as the angle as the ramp and that is going to be mg cos θ.1021

This piece that is parallel with the ramp mg parallel is opposite r angle θ, the same as our angle 30° on the ramp.1031

That is going to be mg sin θ.1039

What I could do is when I redraw my pseudo free body diagram I can replace this green vector an angle1043

with these 2 components to make that equivalent.1050

I will do that here just to illustrate how we are looking were all done.1053

There is our y, here is our x, we will call that y x.1058

There is our dot.1070

Of course we still have f up the ramp.1072

We have our normal force fn or n whichever you prefer perpendicular to the ramp, the normal.1075

We have our force of friction.1082

Although we could draw it back right here from the starting point it starts to get a little tough to say.1086

I like to draw these n to n so I can see them a little bit better.1090

We have in this direction mg sin θ and over here we have mg cos θ.1094

That would be the useful pseudo free body diagram that I would use when I was doing a more detailed analysis of something like this.1105

Let us take a look at an example of how we can put all this together.1114

We have a 10 kg traffic light suspended from a beam as shown.1118

Find the tension in each of the 3 cables T1, T2, T3 supporting the traffic light.1122

What we will do is, let start off by looking at what we have here and I'm going to analyze our object as this one right here.1129

We have on that little ring, we have got T3 up as 1 force tension from the rope and we have mg down.1139

The net force in the y direction then let us call up the positive y is going to be all now is add up all my forces in the y.1150

I got T3 - mg and because it is just sitting there it is equilibrium no acceleration and net force is going to be = 0.1159

There is no net force, therefore, I can state that T3 = mg or T3 is going to be = m 10 kg × g round it off to 10 m/s² or 100 N.1169

Let us take a look at the ring itself since we have already done the right.1187

If we look at the ring itself, we will draw free body diagram for it and I am going to draw my axis here first.1193

X makes these pretty small because we have a little bit of math to do here.1200

Extend at the touch.1206

Looking here there is our object.1210

We have pulling on a T3 down, we have T2 to the right which we have an angle of 30° there is T2 and we have T1 up to the left then angle of 60°.1214

If we want to break that up for a pseudo free body diagram I am going to redraw that over here, a little bit further on the left but we do not have to do that.1236

Let us just keep going with our components and get through this.1244

The net force in the x direction if we look at this we are going to have T2 is x component which could be T2 cos 30°.1249

I think you can see that right from the diagram.1257

Going to the left we have the x component of T1 which will be - T1 cos 60° and all of that has to equal 0.1260

We can try the same thing for the y direction the net force in the y which just means add up all the forces in the y direction.1271

We are going to have T1 sin 60° + T2 sin 30° - T3 which is 100 N -100 N all has to equal 0.1277

Those are the equations I have to solve in order to find my tensions.1295

Let us take a look here and then go back to my green one my net force in x direction as it looks like that just a little bit of math I can find T1 in terms of T2.1300

T2 cos 30 - T1 cos 60 = 0 I could write that T2 cos 30° = T1 cos 60° or T1 is going to be equal to T2 cos 30° / cos 60° which is about 1.732 T2.1310

T1 is that factor × T2.1337

We can take that and plug that into our red equation the net force for the y direction by writing that T1 sin 60° + T2 sin 30° = 100 N,1340

which implies then since we know that T1 = 1.732.1358

T2 we can replace T1 with that so we have 1.732 T2 sin 60° + T2 sin 30° is going to be equal to r 100 N,1364

which implies then that when we do all that together I get 1.5 T2 + 0.5 T2 = 100 N.1383

Therefore, T2 must be equal to 15 N.1395

Once I have done that if I know T2 is 15 N I can plug that back in here for T2 to find that T1 is 1.732.1400

T2 which was 50 N or 86.6 N.1410

We found the tensions T1, T2, and T3 in our suspended traffic light.1416

All right hopefully that gets you a good start with Newton’s first law with free body diagram.1427

We are going to continue to work on these and evolve them as we go to the course.1431

Thank you so much for your time everyone and make it a great day.1435