Skip to main content
Loading Explore guides…
Force and Newton's Laws · Acedra
Home
Explore
Physics
Force and Newton's Laws
Sign in to save
Chat
If YouTube asks you to sign in, open the video on YouTube.
Watch on YouTube
Reload player
Transcript
70 segments
Copy
Hide video
0:00
In this video, we're going to have an overview of force and Newton's Laws of Motion. We'll begin with the definition of force. A force is just a push or a pull. And will the note the force with a capital F? The units of force are kilograms times meters per second squared, which will make more sense later when we get to equations rather than carrying all of these units around everywhere we call one kilogram meter per second squared.
0:24
A Newton, which we will write with a capital in a force is always an interaction between two different objects. One of the object is always exerting the force and the other object is feeling the force or having the force applied to them. sometimes the object that is exerting this force is called the agent. This is an important detail we need to always keep track of which object is actually feeling. The force we're interested in
0:50
Force is also a vector quantity, so the direction matters If we push or pull in a different direction, we are trying to move an object more in that new direction. We cannot push something to the left in order to move it upward. For example, the role of forces is to change the motion of objects or to accelerate them. This is why we push or pull on something when we want it to move. Now let's look at different types of forces and examples of each.
1:16
These are the forces you may see in a first or second semester in physics and some we will spend more time on than others. the first category of forces is contact forces. In the first example of a contact force. It's called the Normal force, which I'll write with a lowercase in. sometimes it is also written with an capital F and a subscript in. we try to avoid using capital N since the units of force is a Newton which is abbreviated with a capital in the normal force arises
1:44
when an object is against a surface and this force is always perpendicular to the surface. We can think of this as the force that keeps an object from going through the surface. So when we stand on the floor of a building, for example, our weight is pushing us down onto the surface, but we're not moving. This is because our weight is balanced by the normal force of the floor, pushing back up on us. The floor also never pushes us to the side,
2:09
only upward, perpendicular to the surface. Also, sometimes you might see the normal force called the support force. The next force is friction or frictional force which we write with a lowercase f. This is the force that slows us down when we're moving across the surface. The direction of friction is always parallel to the surface because if an object is moving or sliding across the surface, friction will oppose that motion. So friction
2:38
is always opposite of velocity in terms of direction. There are different kinds of friction that we'll look at. Static friction is the force that works to keep an object from moving initially. Then when the object is moving, the kinetic friction opposes the motion and tries to slow down and stop the object. And finally, there is rolling friction that we'll see later. But you can imagine there must be friction in order for an object to roll. without friction, the object couldn't
3:06
push off the ground and it would slip kind of like spinning tires on ice. The next common contact force is tension. And we'll write this with either a capital T or a capital F with a subscript T, Capital T will also stand for the period or time of oscillatory motion later. but there are many cases where we'll see tension before we ever need to even worry about the period. Tension is a pulling force from something like a rope, string chain, cable, etc.
3:37
And notice that when you pull on something with a rope, as soon as you stop pulling, the rope goes lax. This is because ropes never push on an object. They only pull because of this. We think of ropes and other things that exert tension as one dimensional objects. So the tension can only point along the rope. And since it is a pulling force, it will always point away from the object. We will also look at springs and the spring force will write
4:05
with an F and subscript esp R that is short for spring. This is an elastic force from stretching or compressing the spring. If you've played with springs, they have a configuration or length that they are. Naturally, when we stretch or compress them, they exert a force that resists this change and tries to move them back to their equilibrium configuration. This is called a restoring force, since it restores the spring to the way it was before. And this force
4:35
always opposes the direction that the spring was displaced. Sometimes in physics we wait to discuss springs because they are unique. Other forces like friction and tension we often treat as constant because they are not changing much. With time before a spring. The more it is stretched or compressed, the more difficult it is to stretch or compress it because the force is increasing with the displacement we need to handle non constant forces carefully.
5:02
So be aware of this difference from simpler forces like tension. The last few contact forces we may see but will not discuss much. The first is drag, which is a resistive force of a fluid such as air or water. It is similar to friction in that it acts against an object to slow it down or oppose its motion. It can also be complicated to model because it depends on velocity. when you stick your hand out of the car while you're driving, you feel the air push against your hand
5:31
in the opposite direction that you're moving. If your speed increases, you feel more force from the air. The last contact force is thrust. This is a force that propels an object one way by expelling exhaust in the opposite direction. A common example is a rocket. But we can also think of you and a friend. Ice skating say you're holding onto each other and you're not moving. If you want to propel your friend one way, you push on them. But that sends you the other way.
6:00
This is the same idea. And we may look at this later and we may talk about rockets. Now for the other type of forces, which are non-contact forces or forces that act at a distance. The first is the force of gravity or gravitational force. We'll write this with a subscript capital G. Gravity is a long range force between any two masses. It is also always attractive, meaning a mass will always be pulled toward another mass. In general, the force varies with distance,
6:31
so the further away you are, the weaker the force. But near the surface of the earth or another large body or planet, it is approximately constant. This is because as as long as you stay near the surface of a spherical object, you are the same distance from the object center or center of mass. The next force is a special case of the gravitational force, and it's called weight, which you've likely heard before. We denote weight with a lowercase w.
6:59
The weight of an object is what we call it, the force of gravity on that object when it is near the surface of the earth, we can define the weight of an object anywhere, but we need to be careful. So for now, we'll stay near the Earth's surface. The weight of an object is equal to its mass times gravitational acceleration, or little g from freefall and projectile motion. So the formula for weight is just img. I'll mention two long range forces
7:26
that we'll see in electricity and magnetism which are usually covered in a physics two class. The electric force has a subscript capital E and is a force between two electric charges. This is called the Coulomb force and looks similar and works similar to gravitational force. however mass is always positive, while charge can be positive or negative. So this is a difference that we'll look at when we get to physics. Two The final force is the magnetic force or Lorenz force
7:54
that we denote with a subscript capital. B This force acts on charges that are moving in a magnetic field. now that we've seen all the forces that we might encounter in the first couple of semesters, let's look at Newton's laws of motion that tell us how forces affect motion. Newton's first law states that an object at rest will remain at rest, or an object in motion will stay in motion. specifically an object. The motion will continue at a constant velocity,
8:23
meaning that it has a constant speed and moves in the same direction or a straight line. This is true as long as there is no net force acting on the object. This law is often called the law of inertia. inertia is the property of all objects to resist changes to their velocity. Since change in velocity is also acceleration We can also think of inertia as the tendency of an object to resist accelerations. We measure inertia using mass, meaning the more mass an object
8:56
has, the more it will resist acceleration or changes in its velocity. Newton's second law states that the net force on an object will cause an acceleration, and that acceleration is proportional to the net force and inversely proportional to the object's mass written in an equation. Newton's second law is written as F equals MRA, but it is important to remember that this is the net force. The net force is what we get by adding all forces together that are acting on that object.
9:29
Since force is a vector, sometimes forces may cancel out and whatever is left over will be the net force written. This way we can read it as the net force F will cause a mass M to accelerate with the acceleration. A But it's also useful to rearrange the formula for acceleration. Now we can see that if we increase the net force on an object, the acceleration also increases because the forces in the numerator, if we increase the mass of the object, the acceleration will decrease
10:00
as the mass is in the denominator. Newton's third law states that forces always occur in pairs, which are equal in magnitude and opposite in direction. These pairs of forces are called action reaction pairs. Here the words action and reaction are just ways of labeling the forces, this law is often called the law of action and reaction. we said that for there to be a force, there must be two objects, an agent exerting the force and an object that is feeling the force.
10:33
Each force in the action reaction pair will act on only one of these two objects. So if we have two objects and B that are interacting, the force that A exerts on B will have the same magnitude but opposite direction or sign as the force from object B on object A If we look closer and Newton's first law, an object that has no net force, is said to be in mechanical equilibrium. This is true for both an object at rest that is motionless,
11:05
but also for an object moving at constant velocity or a constant speed along a straight line. It's easy to get confused and think that the object must not be moving to be in equilibrium. But this isn't true. An object that is not moving at all and is in equilibrium we say is in static equilibrium. But we'll talk more about this later. There are many ways an object could be in equilibrium. If there are no forces, the object is guaranteed to be in equilibrium.
11:34
There can be a pair of forces that are equal and opposite or multiple pairs of equal and opposite forces. The forces also don't have to come in pairs. If there are two forces that are perpendicular, it is possible for a third force to have just the right magnitude and direction to have components that will cancel out both of these forces. Also, if there is only one force, this force is the net force. Since there is nothing to cancel it out.
12:03
And when we only have one force, we often immediately treat it as the net force. And sometimes we don't mention it and we just plug it right into F equals in May. This leads to students forgetting that the F in F equals Emma is the net force. So be sure to keep this in mind. And it always helps to write a net in the subscript to not forget to get the net force. We add up all the individual forces acting on an object. We can write this with this subscript net
12:32
or with a Greek sigma representing a song for an object in equilibrium. This some is zero, but this also means that we can sum the X and Y components of the forces and they should also be equal to zero. in two dimensions. Forces can become difficult to keep up with, especially when there are many forces to help organize the forces and simplify problems. We draw what are called free body diagrams. These are diagrams that show only the forces acting on the object,
13:02
which is all we really need to solve problems. So in this case, a free body diagram. We are freeing ourselves from all of the details we don't need. First, we draw a coordinate system because we want to keep up with the direction of forces and which forces have X and Y component. Then we place a dot representing the object as a particle at the origin. We'll discuss how to draw free body diagrams when we can't represent the object as a particle later on. Now from the DOT,
13:33
we draw all of our forces as arrows away from the dot. I label my force arrows as I draw them, but if not, you should be sure to label them as your final step. Here's an example of a free body diagram. Notice The tension force has both X and Y component. Some people like to draw two additional arrows representing these component vectors. If you would like to do this, I recommend doing this on a new diagram where you only have horizontal and vertical forces in this way,
14:04
you keep your diagram from getting cluttered. Also, a free body diagram only applies to one object. And this also works for Newton's second law. F equals. May we only look at the forces on one object at a time. And this means any forces that are acting on different objects should not be included. We also don't include forces that our object that we're looking at is exerting on other objects. We only include the forces that our object is feeling
14:35
for other objects and the forces acting on those other objects. We would have to draw separate free body diagrams. Once we have our free body diagram drawn with the forces identified and labeled, now we need to know what to do with them. Some forces have formulas that may be used to find them or may be useful to solving the broader problem. Other forces do not have formulas and will depend on the scenario and are found using Newton's laws.
15:01
will begin with forces that have formulas associated with them. Forces with formulas are weight, frictional forces, gravity and spring forces. There are others, such as drag and electric forces that we can write formulas for, but we won't focus on those here. We'll look at those later forces without a formula or tension and the normal force. Both of these depend on the scenario since they are usually reactions to other forces. For example,
15:29
a rope won't have tension unless you pull on it and a surface won't push on an object unless that object is pushing against the surface. We will also sometimes be given that there is some external or some applied force without being told the nature of what kind of force it is. We may be given its magnitude in Newton's or we might be solving for it for these generic forces. They will also depend on the scenario and we will just write them as a capital F
15:57
or maybe use a subscript such as AP for applied force or T for external force. Now let's take a look at mass weight and gravity to make sure we know the differences between them. mass as a measure of inertia or typically thought of as the amount of matter in an object. A mass has units of kilograms. Gravity is a type of force, specifically a force between two masses. Weight is what we call the force of gravity near Earth's surface. So they're the same thing.
16:28
Since both are a force, they both have units of Newtons. So don't confuse them with mass. If we look at their formulas, weight is equal to mass times acceleration, and the more general force of gravity is a little more complicated. The big in front is a constant of nature that has a value that is known, and it would either be given to you or you would look it up if you needed to know it. The two M's are the two masses exerting forces on each other,
16:57
and R is the distance between the centers of those two masses. Now we said these two forces are equal near the surface of the earth. So we will consider an object at Earth's surface, and then we'll set these forces equal to each other and see what happens for the force of gravity on the right. One mass will be just m for the mass of our object, and the other will be the mass of the earth. Since we are at the surface of the Earth,
17:21
the distance ar is very close to the radius of the earth. Notice that the mass of our object just m is on both sides so we can divide by it on both sides to remove it. This leaves an equation for little g, which is our gravitational acceleration that we've been using since Big G is just a number that we can look up in the mass and the radius of the earth are also numbers that we know We can just plug in. When we do, we get the gravitational
17:48
acceleration is equal to 9.8 meters per second squared. And this is where this value of acceleration comes from. So when we find the weight using mass times, a little G, We're actually using this larger, more general formula for gravity. It's just that little G has all of these other values wrapped up inside of it. since they are always true when we're near their surface, we can't use mass times a little g when we get too far above Earth's surface
18:17
because now the distance is larger than the radius of Earth. And this means little G should be smaller. If we want to define the value of G at some height above earth. We could do this, but we would need to adjust the value of R accordingly. In fact, we can find the value of gravitational acceleration for other planets in other bodies by replacing the mass and radius of earth with the mass and radius of that object. So we could find the gravitational acceleration
18:44
for the moon Or for Mars, for example. Now, let's talk about the normal force. I wanted to talk about mass and weight first because the normal force often depends on the weight and many scenarios. We said that the normal force depends on the situation. So we'll look at a few situations and find the normal force. This will also give us a little peek into how we use Newton's second law to solve problems. First, let's take a box sitting on a flat surface.
19:11
If we draw a free body diagram for the box, it has a mass and therefore it will have a weight pointing downwards. since the box is pushing down against the surface, the surface will push back up on the box. Normal to the surface. These are our only two forces. Now we can use Newton's second law or as equals. Emma. in this case, all of the forces are in the wider action. So we need to sum them up this gives a positive, normal force minus the weight
19:39
which is in the negative Y direction. Our second step is to set our forces equal to mass times acceleration, which in this case we will use the Y component of acceleration. The box will not be accelerating downward through the floor, nor will it accelerate upward off of the surface. And so it is just sitting there. So the acceleration is zero. Now we can solve for the normal force and find that it's just equal to the weight or equal to m times. G. This may seem obvious.
20:05
The normal force is pushing against the box to keep it from going through the surface. But that's it. The forces must cancel or be equal in size. If the box is to remain still. Now let's see what happens when we push down on the box with an added force. Our box will still have a weight and fill a normal force from the surface. But now we also need to add a pushing force downward in our free body diagram. Sometimes this is drawn with a separate downward arrow,
20:32
but here I'll just combine them. And now we can use Newton's second law again. The normal force and weight will be the same as before. But now we need to subtract the pushing force since it is also negative like the weight. Even though we're pushing down on the box, it still isn't accelerating through or for or off of the floor. So we set the acceleration equal to zero again. Now, if we solve for the normal force, we see it as larger.
20:57
It is equal to the weight, plus this pushing force. And this also makes sense because the normal force must counter the weight and the added force to keep the box from going through the surface. We could also use a pulling force upward instead, say we have a force pulling upward, but it's not enough to pick the box up off the surface. Well, there will be a normal force upward since the box is still on the surface and the weight is still going down.
21:22
This pulling force will be positive since it is upward like the normal force and again acceleration will be zero. And solving for the normal force, we find that it is smaller this time or less than the way the normal force does not need to counter as much force from the box because the pulling force is also supporting some of the boxes weight. Hopefully you can see the normal force in a way is whatever it needs to be to support the object from going through the surface.
21:49
this will entirely depend on the other forces that are present. We'll also look at objects on sloped surfaces which will affect things as well. Now let's look at tension, which is very similar to the normal force, because it also depends on the situation. So we have a block suspended by a rope. If we draw a free body diagram for the box, the box has mass, so it will have weight pointing downward. This will cause tension in the rope to pull the box upward.
22:15
Now we apply Newton's second law. The tension is upward and the weight is downward. If the box is remaining steel as it is suspended, the acceleration is zero. And we find the tension is equal to the weight. Or just M.G.. This makes sense because the tension is just supporting the weight of the box, much like our surface did using a normal force. Now let's add a second block, so we'll have blocks A and B will treat the block as a single system or one big block.
22:43
Both blocks have mass. So looking at both of them together will have both of their weights going downward. And the tension is still going to go upward. Plugging into Newton's second law, we get the tension minus each weight and solving for the tension. We find that it is equal to the sum of the weights, which makes sense. The tension now has to support both weights and b, I quickly want to mention that we usually draw free body diagrams
23:09
and use Newton's second law on only one object at a time. But here again, we were treating both masses as a single object and they would behave the exact same way as one big block that had the mass of both individual blocks. Now let's do something different. We'll suspend one large block from two identical ropes that will each have equal tension, drawing the free body diagram for the block. We have the weight pulling downward and two equal tension forces pulling upward,
23:39
plugging into Newton's second law. We have a positive two T minus the weight. Solving for the tension. We get the tension is half of the weight here. Each rope is supporting half of the weight. So that makes sense. Now let's move on to forces which have formulas. We'll start with the spring force. The spring force is sometimes written in different ways. The first way is K times delta L Here K is a proportionality constant and Delta L is the displacement of the spring
24:07
or how much it is stretched from equilibrium. This proportionality constant just means that the force is proportional to how much the spring is stretched or compressed. The spring constant represents stiffness of the spring and has units of Newtons per meter. A large value of K is said to be a stiff spring, so it takes a lot of force to stretch the spring. A small amount. A spring with a low value of K is called a soft spring
24:34
and it doesn't take much force to stretch it or compress it. fact that the spring force is directly proportional to the displacement means that stretching the spring twice as far will take twice the force or equivalently stretching the spring twice as much, or calls the spring to exert twice as much force. We also see the spring force written as minus K times X. Here.
24:57
The minus sign represents the fact that the Spring force will always oppose the direction the spring is displaced. could also write Delta X here instead of x, but we often take the equilibrium position to be x equals zero. So in that case x is the same as the displacement delta x. Using the equation on the left, you will probably need to put the direction in by hand. I recommend doing this in most cases anyway, If you have a good picture and you know which direction
25:25
the spring is displaced, you will know whether the spring force will be in the positive or negative direction. The equation for the spring force is often called Hooke's Law, and Hooke's Law applies to restoring forces. The Spring Force acts in such a way to restore the spring to its original size or original configuration. Typically, restoring forces are recognized by being proportional to the displacement, and they have a minus sign, like the formula on the right,
25:52
indicating that the force opposes the displacement. Now, let's look at a couple of examples. We have a block connected to a spring which will assume is massless. At first, the spring is neither stretched nor compressed and the block is sitting still. We'll write the original length of the spring or position of the end of the spring as just capital. If we stretch the spring by pulling the block to the right, the displacement is to the right.
26:18
So the force that the spring exerts back on the block will be to the left opposing this displacement. Notice that the displacement is positive in the spring. Constant K is always positive. So to get the force of friction that is to the left or in the negative x direction, we must put the sign in by hand using the formula on the right. The minus sign would take care of the direction. Now let's imagine we take the same block and spring, but now we compress the spring.
26:47
The displacement is negative or to the left, giving a spring force that is positive or to the right. Again, the formula on the left can be used to find the magnitude of the spring force, but we'll need to correct the sign or put it in my hand. the formula on the right will give us the correct direction. If the displacement is entered as negative. Since the two minus signs will cancel and leave a positive force to the right, now we can wrap up with frictional forces.
27:11
Frictional forces are proportional to the normal force. We can think of the normal force as how much contact an object is having with a surface. Imagine that you're standing on a scale that's giving you your weight. In reality, it's measuring the normal force being applied to support you. If someone comes and pushes down your shoulder, the reading will increase because the scale is now having to support your weight. Plus the force pushing down on you.
27:36
But that doesn't mean that your weight actually changed. Now imagine the forces pulling you upward. As the upward force increases, the scale reads a smaller and smaller number. The scale will read zero the moment just as you leave the surface of the scale and no longer make contact. So again, in terms of friction, we'll think of the normal force as a measure of how much contact an object is having with a surface. We have two types of friction. The first is kinetic friction.
28:06
Kinetic in general, we can associate with motion. So kinetic friction is present when an object is moving or sliding across a surface. We'll use a subscript K for kinetic, and since friction is proportional to the normal force, we get
28:22
a constant of proportionality that will represent with a Greek letter mu. The other type of friction is static friction. Static meaning not moving. here will use a subscript s for static. These constants of proportionality are called coefficients of friction. So we have a coefficient of kinetic friction and we have a coefficient of static friction like the spring constant. We can think of these as numbers that tell us how strong friction is between the two materials.
28:49
but unlike the spring constant, the coefficient of friction are just numbers. They don't have any unit friction always opposes motion or in this case of static friction impending motion. So an object moving across a surface to the right will fill a force of kinetic friction to the left, which is opposing this motion and trying to decelerate the object. In the case of static friction, there must be a force that is attempting to move the object. Then static friction
29:17
will fight this force to keep the object from moving. Notice that static friction has a less than or equal to sign. This means that static friction can vary. specifically, if there are no forces attempting to cause the an object to move across the surface, then there is no static friction because there are no forces. For static friction to oppose as a force is applied in an attempt to move an object, static friction will begin to increase and oppose this force.
29:46
If the force increases, static friction will continue to increase as well, and eventually static friction will reach its maximum value. This maximum value occurs when static friction is equal to the coefficient of static friction, which again is just a number times the normal force. If the applied force trying to move the object is larger than this, then it will overcome static friction and now the object will start to move.
30:13
In most cases, static friction acts like the normal force. It's exactly as strong as it needs to be to prevent motion across the surface, so it's easy to find the case we're more interested in tends to be right when an object is about to move. After this point, the object is moving, so the friction changes from static to kinetic. A couple more things about friction. The coefficient of friction are always given based on the two materials rubbing against each other,
30:40
not just one, unless you're trying to solve for these numbers specifically, they will either be given to you or you would look them up in a table. For example, if you have a wooden block sliding across a steel table, you would need to look up the coefficient of friction for dry wood and steel. We also distinguish between the coefficient of static friction and the coefficient of kinetic friction. Because they are different, they have different values.
31:05
The coefficient of static friction tends to be higher, so it usually requires more force to overcome static friction and accelerate an object from rest. And it requires less force to keep an object moving by overcoming kinetic friction. Ultimately, friction is the result of the surfaces of the object being rough. small imperfections in the surfaces, rub together and push against each other. So typically the smoother a material, the less friction it will have.
31:33
But it's difficult to remove friction entirely. So unlike other forces which can be thought of as acting at a single point of the object, friction happens all over the surface in contact using the coefficient of friction and the normal force, we're able to approximately account for all of these small interactions over the whole contacting surface, though it's not always perfect. friction is not as well understood as some may think. So we'll always want to be careful
31:59
when friction is involved in the next video, we'll get practice solving all sorts of problems using all of these forces, Newton's laws and free body diagrams. So that's it for this video. I'll see you in the next one.
Here to help you learn
Sign in to keep a private conversation with your course tutor.
Ask me anything about the material…
Sign in to chat