**Lesson 1: Introduction of Forces**

**Good Day! and welcome back to another lesson!**

**Today we are entering into a new chapter in our physics curriculum, which is Dynamics, also commonly known as Forces.**

So What is Force? A force is a push or pull upon an object, resulting from its interaction with another object.

There are two things we will cover in today’s lesson. The types of forces, and the effects of forces.

How many types of forces are there? For simplicity, we can classify forces into two types, contact forces, and non-contact forces.

Contact forces are just what they sound like, forces that result from the interaction of two objects in contact with each other. For example. What happens when you start kicking a ball which is laying on the ground? You apply the force on the ball by kicking it, and there was contact between the ball and your shoe. This applied force is one of the contact forces. Next, there is a force of friction, which brings the ball to stop. As the ball is in contact with the ground, the frictional force is also a contact force. Don’t you think there was some air resistance? Yes, air resistance too, is a contact force. The normal force which is applying force in the upward direction is a contact force as well. These are some of the contact forces we know of, but these are not the only ones

How about non-contact forces? Can you think of any non-contact force? What happens when the ball is in the air? It will fall down, right? Why was the ball falling down? Yes, it’s because of the gravitational force which is trying to pull the ball towards the center of the Earth. This pulling force happens even if the ball is not in physical contact with the earth, therefore, the gravitational force, is an example of a non contact force. Other examples of non contact forces are electrical and magnetic forces, which we will learn in the near future.

Now, I want you to think about the next question I’m going to ask you. What can all the forces do? And what can be its effects? Let me give an example, a force can send a stationary object in motion. That’s one of the things force can do. Can you think of other things that force can do? Assuming an object is moving at a uniform velocity of two meters per second. If it is pushed harder, its velocity will increase. So force can also change the velocity of an object. A force can also stop a moving object. Anything else you can think of. Yes, force can also change the direction of the moving object. If a ball is moving towards the north, a kick from the right can change its direction, to the north-west.

Is there anything else you can think of that force can do? Come on, I want you to think really hard. Don’t think only in terms of motion. A force can also change the shape of an object. If the force is applied from both sides to a spherical ball, its shape changes. The position does not change, but its shape does. So these are some of the things that force can do.

**Good Job! That’s everything for today’s lesson. Now, proceed to the practice section for today’s Quizzes! And I’ll see you next time.**

**Lesson 2: Vector Diagram(I) Theory**

**Good Day! And welcome back to another lesson!!**

**In this lesson, we are going to learn what is A vector diagram, and how to construct a vector diagram.**

A vector diagram shows all the forces acting on an object, and also the angle between the forces. Vector diagrams are most commonly used to calculate the resultant force acting on an object.

We draw vector diagrams, by using the following steps.

First step, give a scale to represent forces in terms of length.

Second step, draw the lines with arrows to represent all forces, make sure that the correct angle is applied between these forces.

Third step, draw additional lines to make a parallelogram.

And last step, measure the diagonal length of the parallelogram. This is the length that represents the resultant force.

Here’s an example, a runner is running with a force of 10 Newtons. However, the strong wind is pushing the runner, with a magnitude of eight Newtons. The angle between the runner and the wind, is 30 degrees, find the resultant force that is acting on the runner.

Step one. Decide on a sensible scale. In this case, we can use a scale of one centimeter to one newton.

Step two. Draw the force produced by the runner, which is a line with a length of 10 centimeters to represent 10 newtons.

Step three. Draw the force of the wind acting on the runner, which is another line with a length of 8 centimeters to represent 8 newtons. Take note, that the angle between these two forces must be 30 degrees as indicated.

Step four. Complete a parallelogram by drawing additional parallel lines. Do take note to draw them in dotted lines.

Step five. Draw a line from the start point to the opposite corner, measure the length of this line. Use the scale to work out the magnitude of the force. According to the scale we set, 17 centimeters equals a resultant force of 17 Newtons.

Lastly, we will mark a double arrow, on the line that represents the resultant force. This is to indicate that this the line that represents the resultant force.

Alright! That’s how we draw a vector diagram, and how to find the resultant force with vector diagram.

**Good Job! That’s everything for today’s lesson. Now, proceed to the practice section for today’s Quizzes! And I’ll see you next time.**

**Lesson 4: Newton’s First Law**

**Good Day! And welcome back to another lesson!**

**In this lesson, we are going to learn Newton’s First Law.**

Imagine you’re sitting on a recliner chair, and watching your favorite movie on a lazy Sunday. And your mom calls out your name and asks you to run some errands. You can imagine how difficult it would be, for you to get up out of the comfortable chair, and do the work.

Now, imagine you’re practicing for your 100 meters race on a track, and somebody asks you to stop immediately within a second. Will you be able to do so? What if suddenly, you are asked to turn towards the right. Will you be able to make the turn immediately?

The answer to both of the two questions would be a big, No.

You can stop, Yes, but, gradually. You can also turn, but not sharply. And guess what, it’s the same story with every object. Every object will continue to do what it’s doing. If it’s at rest, it will remain at rest, and if it’s in motion, it will stay in motion.

But can this be changed? Yes, only an unbalanced force can change this. if it’s at rest, when an unbalanced force acts on it, it will move. If it’s in constant motion, when an unbalanced force acts on it, it may accelerate or change direction, and this is the Newton’s first law of motion.

Here’s the correct definition, an object at rest will stay at rest, and an object in motion will stay in motion with the same speed in a straight line, unless acted upon by an unbalanced force.

In simple words, it means that the objects continue to do what they’re doing, unless the external unbalanced force acts on them.

We can also understand this, by using a simple diagram. If the forces are balanced, there can only be two scenarios. The object may be at rest, or the object will be motion at a non zero constant velocity in a straight line. These can be the only two cases when the forces are balanced. In the first case, the object will continue to remain at rest, and in the second, the object will continue to stay in motion at the same velocity, And in the same direction. Don’t forget these two cases will remain true only if the forces are balanced.

**Great work! That’s everything for today’s lesson. Now, proceed to the practice section for today’s Quizzes! And I’ll see you in the next lesson.**

**Lesson 5: Newton’s Second Law**(Not done)

**Good Day! And welcome back to another lesson!**

**In this lesson, we are going to learn Newton’s Second Law of motion.**

But before we start, let us have a recall on the Newton’s first law.

The first law says that an object will continue to do what it’s doing, unless acted upon by an unbalanced force, which will create a net force. Now the important question is, what happens when this net force is acting on the object? That’s precisely what Newton’s second law of motion will discuss.

By understanding the first law of motion, if the forces are balanced, the acceleration will be zero. In this first case, the object will continue to remain at rest, and in the second case, the object will continue to stay in motion at the same velocity, in this same direction.

Don’t forget these two cases will remain true, only if the forces are balanced, only if the net force is zero.

Now let’s try to create a similar diagram for the second case. If the forces are unbalanced, then there will be an acceleration.

Now, I want to test your brain a bit. Let me ask you a question, and I’m sure you can answer it. On which two factors do you think the acceleration will depend on?

Okay, let’s say there’s an object on a table, you apply a net force of 10 units on it, and then you apply a net force of 20 units on it. In which case, do you think the acceleration will be more.

Of course the one in which the applied force was more. So we can say that one of the things the acceleration depends on, is net force, or resultant force. If more net force, than more will be the acceleration. If less net force, than lesser will be the acceleration. Acceleration of an object depends directly on the net force on the object.

Now, I want you to think of the second quantity, which acceleration will depend on. Let’s say there are two objects on the table.

Surely it’s the three kilogram one, because it has less mass. Lesser the mass, more the acceleration, and more the mass, less of the acceleration.

If you understand this concept well, then, understanding the second law of motion could be very easy. Mathematically, it can be written like this. In simple terms, the acceleration is directly proportional to the net force applied, and inversely proportional to the mass of the object. Or, as more people understand it like this. The net force or the resultant force is the product of mass and acceleration. With this, can you tell me the units of force. That should be easy. The standard unit of mass is kilograms, and that of acceleration is meters per second squared.

So the unit of force is, kilograms times meters per second squared. And this is what we call as, Newton. Thus, one newton is equals to one kilograms times meters per second squared.

So if the mass of the object is 10 kilograms, and the acceleration is 10 meters per second squared, then the force will equal 100 Newtons. We can say, that one newton is defined as the amount of force required to give a one kilogram mass an acceleration of one meter per second squared.

**Great work! That’s everything for today’s lesson. Now, proceed to the practice section for today’s Quizzes! And I’ll see you in the next lesson.**

**Lesson 6: Newton’s Third Law** (Not done)

**Good Day! And welcome back to another lesson!**

**In this lesson, we are going to learn Newton’s Third Law of motion.**

In Newtons First and Second law, we are learning about the effect of forces action on one object. So, the only question you need to ask yourself why study the third law is, what happens when two objects interact with each other?

Now, an object is placed on the table. Let us examine that is happening here. The object exerts a force on the table, and at the same time, the table exerts an upward force on the object to keep it in place. There are two forces that result from this interaction.

A force on the table, and a force on the object, the magnitudes of the two forces are the same, but the directions are opposite. These forces are called the action and reaction forces, the force exerted by the object or the table was an action force, and the force exerted by the table on the object is the reaction force.

What we are seeing here is a classic example of a display of the Newton’s third law of motion, every action has an equal and opposite reaction. That’s how simple the third law is. Every action, has an equal, and, opposite, reaction.

It seems that when two objects interact, there is a force on each object, the magnitude of force on the first object equals the magnitude of force on the second one. And what about the direction? the direction of force on the first object is also opposite to the direction of force on the second one.

Here is another example. While the frog is swimming, it pushes the water back, and the water pushes its body forward.

Now let me ask you a question. Say a bird is flying upwards. Will the Newton’s third law apply here? Sometimes, the third law is not so obvious at first. You’d probably say, that the bird is the only object here, and there’s no second object. But that’s not correct. The wings of the bird push the air downwards, and the air pushes the bird upwards, this pair of action and reaction forces, make it possible for birds to fly.

We take a look at one last example to understand something very interesting about the third law. What happens when a gun is fired? You are right, it exerts a forward force on the bullet. And the bullet exerts an equal and opposite reaction force on the gun. And this causes the recoil of the gun. A perfect example of Newton’s third law. But hold on. If the force exerted by the gun on the bullet is the same as the force exerted by the bullet on the gun. Then, why doesn’t the gun recoil with the same acceleration as the bullet? The gun recall, yes, but it doesn’t recoil at the same acceleration as the bullet right? Same magnitude of forces, but different magnitude of accelerations.

Why do you think this happens? Okay, so if your concept of the second law of motion was clear, you wouldn’t really be surprised with this. The second law of motion says that, the force is the product of the object’s mass and acceleration, or the acceleration of the object is equal to the force over its mass. What does this tell us? It tells us that if the mass is more, than the acceleration will be less. In this example, the mass of the gun is much more than that of the mass of the bullet, hence the acceleration of the gun is lesser than that of the bullet.

If you’re in a boat and stepping out of it onto the land. There are two forces involved, you are pushing the boat behind, and the boat is pushing you forward. And that’s why you see the boat goes behind when you go forward. Now, let’s say a sailor jumps off a huge ship. The sailor also apply a force on the ship, and the ship also applies a force on the sailor. But do you think the ship will accelerate as much as the sailor. Not really. And I think you know why.

**Great work! That’s everything for today’s lesson. Now, proceed to the practice section for today’s Quizzes! And I’ll see you in the next lesson.**

**Lesson 7: Free-Body Diagram** (Not done)

**Good Day! And welcome back to another lesson!**

**In this lesson, we are going to learn how to draw free-body diagram.**

Let’s start with a simple one. A box is at rest on a table, draw a free-body diagram for this.

Let this horizontal line be the top of the table, and the box is placed here. The free-body diagram shows all the forces acting on it. First, there’s a force of gravity acting on the box, it will be downwards. And then there’s a normal force acting upwards as the forces comes in equal and opposite pairs. The box does not move at all. It continues to remain at rest. And also notice that the size of the arrows are the same, this shows that this pair of the forces are balanced, and the net force is zero.

Now, let us move on to the second situation. In this situation, a right-ward force is applied to the box in order to move it across the table with a right-ward acceleration. Ignore the air resistance in this situation.

First things first, the force of gravity still exists, and pull the box in the downward direction, as it’s placed on the table, there will be also be an equal and opposite normal force acting upwards. Now, the right-ward force. This right-ward force makes the box move across the table with right-ward acceleration, the word acceleration is very very important in this situation. It means that there is a net or resultant force, which implies that the left and right pair of forces on the box are unbalanced, unlike the upward and the downward forces, which net each other off.

Now as the question states that there’s a right ward, applied force, we show an arrow towards the right. Will there be any leftward force on the box. As we’ve been asked to ignore air resistance, it will only be the force of friction acting towards the left. And because the box is accelerating towards the right, it means that the force of friction is lesser in magnitude than the applied force towards the right. Hence the size of the arrow of the applied force is bigger than that of the frictional force.

Now let us move on to the third situation, which is extremely interesting. A box on the table is moving towards the right at constant velocity. Ignore the air resistance for this situation as well.

So, the box is moving at a constant velocity towards the right. In any case, there will be the same gravitational and normal forces acting on the box as usual. But this time. the applied force, and the frictional force will be of the same in magnitude. Hence the size of these two arrows will be the same, as the net force is zero, thus the body will continue to move at the constant velocity.

Now, let’s move on to the next situation. A skydiver is falling with constant velocity. Would you like to try drawing the free-body diagrams for this situations? Give it a try.

Did you get it right? In this case, let us first discuss the forces that are acting on the skydiver. There will still be the force of gravity as do all objects on earth experience. The force of gravity is pulling the skydiver down, and since there is no table of ground, the normal force will not exist. And there’s no apply force on the skydiver either. But, as the sky diver is falling at a constant velocity, it implies that the net force must be zero. So, what is the force that will net the force of gravity acting on the skydiver? Yes, it will be the air resistance! As the velocity is constant, it implies that the magnitudes of these two forces are equal. And this is the free-body diagram of this situation.

Here’s the last situation. An airplane is flying at a constant velocity, and at the constant altitude. Try to draw the free-body diagram for this situation.

Did you get it right? The weight of the airplane is acting downwards towards the Earth due to gravity. However, the wings of the airplane produce a lift force on the airplane due to its areo-dynamic design. The lift force acts upwards, and has an equal magnitude as the downward force. This lift force keeps the plane traveling at a constant altitude. So the magnitude of the lengths for both forces must be equal. In order for the airplane to move forward, the engines of the plane produces a trust that pushes the airplane forward. But the plane is traveling at a constant velocity, which tells us that the magnitude of the air resistance or drag force is the same as the thrust force.

**Good Job! That’s everything for today’s lesson. Now, proceed to the practice section for today’s Quizzes! And I’ll see you in the next lesson.**

**Lesson 8: Friction(I)** (Not done)

**Good Day! And welcome back to another lesson!**

**In this lesson, we are going to learn what is friction.**

We see objects moving around us every days, cars driving, people walking, birds flying. Have you ever wondered, how could things move in real life?

If a ball is kicked once, will the ball, eventually come to a stop? Yes it will. Have you ever wondered why.

Say you’re skating on an ice rink, and your friend is skating on the grass. Whose movement do you think will be smoother? Definitely your!

When you hold a bottle in your hand. Why doesn’t the bottle just slip through and fall?

Sometimes when you’re walking around the mall. Do you remember seeing a caution sign to warn you about the floor being wet?

What explains all this? The answer is friction! The reason why the ball, eventually comes to a stop, is because of the force of friction. The reason why skating on an ice rink is easier, because the force of friction on ice is lesser. Why the bottle doesn’t slip through your hand? Because the force of friction between your hand and the bottle doesn’t allow it to do so. If the floor is wet, the friction of the floor reduces, and there are chances that you might slip and fall.

So what is this friction we are talking about. It’s actually quite easy to understand it’s concept.

Friction is nothing but a force. It is the opposing force exerted by a surface on an object, as the object moves across it.

In the first case, when the ball is moving in this direction, the force of friction is acting in the opposite direction to the motion of the ball, thus stops the ball eventually. The force of friction offered by the ice rink floor is much less than the force of friction on the grass floor. Hence skating on the ice rink is easier and seems effortless. The bottle does not slip down because the surface of your hand, offers a friction in the upward direction. And in the case of the floor in the mall, the soapy water reduces the normal friction offered by the floor, thus makes the floor slippery.

In the coming lessons we will learn a lot more about friction, we will see the factors affecting friction, We will understand if friction helps us in our everyday life, or not. And we will also cover the different types of friction.

**Good Job! That’s everything for today’s lesson. Now, proceed to the practice section for today’s Quizzes! And I’ll see you in the next lesson.**

**Lesson 9: Friction(II)** (Not done)

**Good Day! And welcome back to another lesson!**

**In this lesson, we are going to continue to explore friction and to learn what are the factors affecting friction.**

Here’s a cube that’s placed on the table. We know that we are pushing the cube in this direction, and the force of friction will act in the opposite direction. If we apply a force along the left. The force of friction will act towards the right, and vice versa. The force of friction, will always opposed the applied force.

So, what are the factors that affect the friction. Let me give you three situations, and then you tell me what it depends on.

The first situation is, when an object with a smooth surface, is moving on a surface which is very smooth. Second, in which the object has a smooth surface, and the surface which it moves on, is rough. Or the object has a rough surface and the surface on which it moves, is smooth. And in the last case, the surface of the object, as well as the surface of the table are both rough. In which situation, do you think, will the force of friction be the highest?

Intuitively, You will tell me that in the third case, the force of friction will be higher than the first two cases. And in the first situation is when the force of friction be the lowest, as both the surfaces are very smooth. So there will be friction here, although it will be less than that, in the other two cases.

If we just look at these three situations, we can say that the force of friction increases as the surface as rougher. So can you tell me, what is the first factor on which the force of friction depends on? Yes, It depends on the nature of the surface on which the object moves, and the nature of the surface of the object itself. Yes, it depends on the smoothness or the roughness of the two surfaces which are in contact with each other. In other words, it was caused due to the irregularities on the two surfaces in contact. What does it mean by irregularities? Now, even though the table looks smooth. If we zoom into the surface, we will see the surface irregularities. Even the surface of the object has irregularities, though they are minor, they still exist. Now the irregularities on the surfaces, locks into one another. So whenever we have to move an object, we need to overcome the irregularities. But what is the friction higher on rough surfaces. It’s because rougher the surfaces, more will be the irregularities. And if the irregularities are more, then more force will be required to overcome them.

The first factor affecting the friction is the nature of surfaces.

Is there any other factor you can think of that affects friction? Let’s say there are two bricks on a table, one weighs two kilograms, and the other weighs five kilograms. Now, if an equal force is applied on each of them towards the right, which brick, do you think will go further? Remember that they’re both kept on the same surface and the surfaces of the bricks are also the same. On applying the same amount of force, you will notice that the lighter brick covers more distance than the heavier one.

What does this tell us? It tells us that the friction also depends on the force with which the two surfaces are pressed together. If the two surfaces are pressed harder, the friction will be more. Why is that so? Because of the second brick’s greater weight, it presses on the table with greater force. Since its surface at the table surface are pressed together harder, the interlocking between the irregularities is more. And this results in more friction.

So mainly, there are two things on which the force of friction depends. The nature of surfaces, and the force with which the two surfaces are pressed together.

**Good Job! That’s everything for today’s lesson. Now, proceed to the practice section for today’s Quizzes! And I’ll see you in the next lesson.**

**Lesson 10: Tension(I)** (Not done)

**Good Day! And welcome back to another lesson!**

**In this lesson, we are going to learn another variant of force, Tension force.**

Tension, it is a kind of force we see when we pull on a rope for example.

Alright, so let’s get started.

Here we’ve got a ball hanging from the ceiling by a rope, what is keeping the ball from falling to the floor and weights. After all, gravity is acting on the ball, right? Well, it’s the rope that’s keeping the ball up. So the rope must be applying a force on the ball to prevent it from falling. We call that force, the tension force, as the rope is being put under tension by the ball’s weight. So any force that appears as a result of pulling on a rope, a string or anything similar to that is called tension.

Actually, we can think of tension forces as the opposite of normal forces. If you don’t remember what a normal force is, very briefly, we can say that a normal force occurs when a surface like a table, resists of being compressed by the weight of an object. The surface of the table applies a force, which prevents the object from moving into the table, and we call that the normal force. Tension force does something quite similar, except that instead of resisting compression, tension force resist forces that cause things to stretch.

For example, when we hang a ball on a rope. The rope applies a force to counter the weight of the ball, which makes it resist being stretched out. This results a tension in the rope.

Looking back at normal forces, it seems obvious that when an object is not pushing against a surface, the normal force must be zero. Tension forces are similar to this, but in an opposite sense. If an object is not pulling on a rope, the tension force is zero.

All right, I think we’ve got enough knowledge to look at a very simple example. Let’s look at the ball on a rope again. If the ball has a mass of 10 kilograms. What is the tension force on the rope? Give it a try.

Did you get it right? Well, the answer would be 100 Newtons upward. How did we get that answer, First of all, we have to look at the forces that are acting on the ball. One of them is obviously gravity. What other forces are there. Well, there’s really only one other force. The force of tension. More specifically, it’s the tension force being applied by the rope onto the ball. And since the ball isn’t moving, the two forces must cancel out each other. So our next step will be to find the weight of the ball due to gravity. To do so, we will use Newton’s second law. We already know the mass of the ball, which is 10 kilograms. As for the acceleration, that’s constant near the Earth’s surface, which is 10 meters per second squared downward. And once we substitute those values into the equation, we get 100 Newtons downward, for the weight of the ball. And since the gravitational force must be canceled by the tension on the rope, we can conclude that the tension force being applied by the rope on the ball is also 100 Newtons, but in the opposite direction, upwards.

**Lesson 11: Tension(II)** (Not done)

**Good Day! And welcome back to another lesson!**

**In this lesson, we are going to continue our journey on Tension force.**

**Let us look at the following example.**

P, Q and R are three identical blocks resting on a smooth surface. A force of 30 newton is applied at one end as shown in the diagram below. What is the tension T 1 on the rope between blocks P and Q? And what is tension T 2 on the rope between blocks Q and R? Ignore friction on the floor

Since it is given that the three blocks are identical, we can safely assume that their masses are the same, and can we can also safely let the mass of each block to be 1 kilogram, this can help us solve this question quickly.

So, let the mass of mass for block P, Q and R, to be 1 kilogram each. With this in mind, let’s move on. The applied force of 30 newton will cause the three connected masses to accelerate at the same rate.

To calculate this acceleration, we will use newton’s second law equation, F equals to M, A. F is resultant force, which equals to Applied Force minus friction force, and since the question stated to ignore friction, therefore resultant force is equals to Applied Force, which is 30 newton.

The total mass for the 3 blocks is 3 kilograms in total. Thus, the acceleration is equals to 10 meters per second squared.

Now, if T 1 is the tension on the rope to pull block P to the acceleration of 10 meters per second squared. We can work out this tension force. By applying newton’s second law equation, F equals to M, A, again. F is equals to T 1, since there friction is ignored. Mass is 1 kilogram since T 1 is only applied to block P. Acceleration remains at 10 meters per second squared as all three blocks accelerate at the same rate. And we get F equals to 10 newtons. Thus T 1 is 10 newtons.

Now, if T 2 is the tension on the rope to pull both block P and block Q, to the acceleration of 10 meters per second squared. We can work out this tension force. By again, applying newton’s second law equation, F equals to M, A. F is equals to T 2, since there friction is ignored. Mass is 2 kilograms, since T 2 is the force to pull both block P and block Q. Acceleration remains at 10 meters per second squared as all three blocks accelerate at the same rate. And we get F equals to 20 newtons. Thus T 2 is 20 newtons.