How to Solve Physics Problems with Forces – Physics – Mechanics | Edouard RENY | Skillshare

How to Solve Physics Problems with Forces – Physics – Mechanics

Edouard RENY, Music Producer & Tutor in Physics

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19 Lessons (2h 9m)
    • 1. How to Solve Physics Problems with Forces (Trailer)

      2:42
    • 2. The 5-step technique in a nutshell (Episode 1)-

      4:35
    • 3. Solved example in 1 dimension (Episode 2)

      5:12
    • 4. Solved example in 2 dimensions (Episode 3)

      10:11
    • 5. Free Body Diagrams - Step 1 (Episode 4)

      18:48
    • 6. Defining the Axes - Step 2 (Episode 5)

      4:51
    • 7. Manipulating Vectors (Episode 6)

      17:33
    • 8. Expressing the Net Force - Step 3 (Episode 7)

      4:06
    • 9. Applying Newton’s Laws - Step 4 (Episode 8)

      6:21
    • 10. Solving the Problem - Step 5 (Episode 9)

      4:50
    • 11. Tensions & Ropes - Exercise 1 (Episode 10)

      5:10
    • 12. Connected Blocks - Exercise 2 (Episode 11)

      4:28
    • 13. A Block on a Slope - Exercise 3 (Episode 12)

      3:53
    • 14. Understanding Friction (Episode 13)

      6:14
    • 15. Friction on an inclined plane - Exercise 4 (Episode 13B))

      4:19
    • 16. The Elevator - Exercise 5 (Episode 14)

      3:21
    • 17. The Crate and The Pit - Exercise 6 (Episode 15)

      6:02
    • 18. The Flea Jump - Exercise 7 (Episode 16)

      11:37
    • 19. The Asymmetric Rope - Exercise 8 (Episode 17)

      5:13

About This Class

Have you ever been stuck when trying to answer a mechanics question involving forces?
Maybe you were clueless on how to begin, or you got stuck at a certain point?

Well, this course is there to solve that problem: if you take this class till the end, and carry out all the exercises diligently, you will gain more than just the ability to solve mechanics problems. Hopefully, you will realize that Physics is actually pretty easy to handle: the patterns of thinking presented in this course are commonly used in many areas of physics, and could be very useful to you in your studies.

Class Structure:

This class presents a 5-step technique that can guide you through any physics problem involving force. It is structured in 3 sections.

The first three episodes contain a summary of the 5 steps and 2 solved examples. The goal of this first section is to for you to get an overview of the technique before diving into the details.

The second section consists in 6 lesson videos. The process of applying each step is presented in detail and in various situations. The conceptual and mathematical tools required to carry out each single step is also presented (1 step = 1 video + 1 extra video about the manipulation of vectors). You will learn how to draw a free body diagram, how to express a resultant force mathematically, how to manipulate vectors, when and how to apply Newton’s Laws etc…

The third section is your play-ground! You will find 8 exercises for you to train your skills in applying the 5-step technique. After giving you a chance to solve each question yourself, the presenter carries out a detailed correction on the white board. This section also contains a video lesson about mechanical friction forces.

The level of this class corresponds to the last years of High School Physics Programs. This makes it an ideal tool as support for the lessons you get at school, and to prepare any High School Diplomas in Physics, like for example IB Physics, A-Level Physics, AP Physics etc.

Enjoy!

Edouard Reny, PhD, Tutor in Physics.

 

Content Details:

Section 1: The 5-step technique to solve physics problems with forces (Introduction)

  • Episode 1: The 5-step technique in a nutshell
  • Episode 2: Solved example in 1 dimension
  • Episode 3: Solved example in 2 dimensions


Section 2: The 5 steps in detail (Lesson Videos)

  • Episode 4: Free Body Diagrams (Step 1)
  • Episode 5: Defining the Axes (Step 2)
  • Episode 6: Manipulating Vectors
  • Episode 7: Expressing the Net Force (Step 3)
  • Episode 8: Applying Newton’s Laws (Step 4)
  • Episode 9: Solving the Problem

 

Section 3: Applying the 5-step technique (Exercise Videos)

  • Episode 10: Tensions & Ropes (Exercise 1)
  • Episode 11: Connected Blocks (Exercise 2)
  • Episode 12: A Block on a Slope (Exercise 3)
  • Episode 13: Understanding Friction (Lesson Video)
  • Episode 13B: Friction on an inclined plane (Exercise 4)
  • Episode 14: The Elevator (Exercise 5)
  • Episode 15: The Crate and the Pit (Exercise 6)
  • Episode 16: The Flea Jump (Exercise 7)
  • Episode 17: The Asymmetric Rope (Exercise 8)

Transcripts

1. How to Solve Physics Problems with Forces (Trailer): hello and welcome to this course. Do you sometimes struggle when you are trying to solve a physics problem, which contains forces? Well, you are the white place because this course is for you. There is a systematic process in five steps that allows you to find solutions to these physics problems. At first, it may take a little time in practice to get used to the technique. But once the five steps becomes second nature, you can solve these problems quite easily. The five step technique is like a guide that directs you progressively towards a solution and that whatever the problem is, so if you encounter difficulties solving these types of questions do stick around. This course begins with the summary of the technique and a couple solved examples that is just for you to get a feel of what you can expect throughout the course. The series of videos that follow our lessons, teaching you the tools and concepts that you need to apply in each step off. The five step technique, for example, how to be a free body diagram. How to add vectors to each other, how to apply Newton's laws etcetera after the lessons video, you will be presented with a large array off exercises. For each exercise, you would have an opportunity to give a try it, solving it. Then I solve it for you on a white boat by applying the five steps off the technique. That way, you can witness by yourself how to apply the techniques in various situations. It was only after years of teaching physics that I realized that I was systematically applying a pattern when solving problems. And I also realized that is why the problems were so easy to solve, said No. It's time for me to share this experience with you. Once the five step technique becomes second nature to you, physics in general will become so much easier on makes so much more sent to you. Actually, at this point, you will not perceive a physics question like a painful task anymore, but more like an enjoyable puzzle. So let's get started. Oh, 2. The 5-step technique in a nutshell (Episode 1)-: you are sitting in the classroom, you are taking the physics exam. You receive the paper and open it. You read the first question. It's about forces in McAllen. And after reading the full problem, you wonder How do I begin? Then you start to feel the cold sweats coming. What do I do to solve this question? Where do I start? This course is going to solve that problem for you. It would provide you a direction for each time you encountered such a situation. What I will do here is show you a simple technique that works for all questions or problems where forces are involved in one way or another. In a nutshell, the technique consists off five minutes. Steps stepping on the one the free body diagram list all the forces that are applied on the object you are interested in and do this under the form of a drawing we call settled, drawing a free body diagram. Step number two, The axis on your free body diagram. They find some access and they're positive directions. Be careful. It's an easy step to forget because it is a very short one. But it is also a very important one. Step three The Net Force determine a mathematical expression for the Net force. The Net force is a some of the forces that are acting on the object. You know the forces that you drew on your free body diagram. I remember forces are victors. So for that step, you will need to carry out some vector additions. If you are in two dimensions, you might need also a little bit off trigonometry. Step full. Beautiful laws. Once you have an expression of the Net force, you can apply the first with the second law of Newton on it. If the object is at west went costing velocity, the expression of your net force will be equal to zero. If the object is accelerating, the expression of your net force would be equal to the mass of the object, but applied by the acceleration off the object. After these four steps, you will have in front of use on equations on the left side, you would have expressions for the net force On the light side, you will have either zero m A. If your problem is in one dimension, you will have one equation in two dimensionally will have to. And if your problem is in three damn entrance will have three. Step five consists in looking carefully at the equations you obtained, because within them there is a solution to the question. Maybe it will be straightforward. Maybe we need to treat the equations a little. But you know, in most cases, whatever you are looking for, you probably just need to rearrange these equations a little bit by putting the valuable that you're interested in as subject. So Step five could be called soul. If you are stuck at the beginning of a question or even confused, just apply this technique, even if it might appear somehow irrelevant at first. In the context of a question, just apply the techniques it will allow you to analyze. The problem on the equations you will get can guide you towards a solution. In the two following videos, I will present two simple examples so that you can already get a feel on how to apply the signage. But then we will go back to lesson videos in which we look into the different steps one by one, including free body diagram, affect traditions on neutrals, rules and finally, videos that follow will be solved. Examples that will show you how to apply this technique in various situations. Oh! 3. Solved example in 1 dimension (Episode 2): through this first example, I have a block. It rest on the flat surface. It's masses 10 kilograms. Then a guy wives and pushes a block with the force of 25 new terms. The ground reacts by applying force on the block off. Five new terms, a friction force. The question is, after five seconds off the man pushing the block ways it, How much has it moved? Let's apply the steps and see what happens. Step number one free body diagram at what docked with a box of Arabic, then our list. All the forces which are applied on the block only on the block so I would have gravity because of gravity. The block is pushing on the ground, so the ground reacts with the normal force. The man is pushing the block to build a light on the ground. Reacts with fiction. Force off five new terms. Forces are vectors, so when I'm drawing them, I'm doing vectors with directions. Had magnitudes. It's a good idea to also draw the magnitude like the lengths off the arrow, because when you look back, you can see a general situation of what's happening to the block. Good September 2 access. I need to define some access in their positive direction. So the block is going to move that way off essentially so I will draw and always until access and choose a positive direction represented by the hour. You can choose the direction you want, but I advise you to choose the direction corresponding to the initial motion. It will easy calculations. You will have less negative signs. What about the Y axis, where when the blood pushes on ground gun reacts with the force, which is the only force but which is also off the same magnitude. Therefore, ngn n will cancel each other with balance so nothing will happen on the Y axis. Really? Yeah. The block is not going to start to fly on the block is not going to start to dig in the ground. It's Tuscan to go on the horizontal axis. So I wouldn't expect the y axis. Good step number three, find the net falls. Well, I will just cause it does it enforcing this access so f Nance would be the some of the forces. So 25 new terms in the positive direction and five new terms in the negative damage. That's 20. Mutants. Step number four. Apply Newton's laws. Well, F net is not zero. So it's going to be cool to and a That's it. Step number one. Number two Stepping on the three. Step number four. What do you do now? Step five five. I look at the data. I have have the time, have the initial velocity of the block and also have the exploration time. Initial velocity acceleration. That looks like a motion question. So I will just trigger what I need to do when I want to solve emotion. Problem. Servant s u V a T. The access is positive. That way s That's what I'm looking for. Use the initial velocity. Zero v. I don't really care, because have acceleration and time. Acceleration will be 20 divided by 10. So two meters percent from squid too anti would be five seconds. I just choose the equation that contains S u a N t. That is s equals ut plus 1/2 it is Quit, you zero. So that's your the 1/2 it is quit and I'm done. I just supplies members s equals 1/2 by two by five squared 25 meters. So during the five seconds where the man push the block, the block moved by 25 meters. Oh! 4. Solved example in 2 dimensions (Episode 3): in this example the car is trying to climb up a here. It still has 50 meters to go. At this point, it's speed is 20 meters per second. The mass of the car, 1000 kilograms on the motor of the car provides to the car attraction of 1000 new terms. The angle of the slope is 10 degrees. In this example, we can neglect friction and resistance. The question is where the cow reached the top of the hill. Okay, how do you do that? I'll just some tighter steps. And again I would see what happens. Step number one Free body diagram. I don't my block on a slope nine or 10 degrees and I look at the forces that reply to my block. I would have gravity. I would have the normal force, which is purple Nikola to the ground and attraction. No fiction, no every systems, Right, that's done. So now let's look at the access step Number two. I could choose access like this, but what will happen if I do that is that I would have to forces which are having angles with the axis. I'll have two angles to humble. I'd rather have my access at this one of them parallel to the motion. The other one naturally Republicana. And you see now I only have one force which is having an angle with the axis. So less calculations in the end, Easier system. If you want to confuse any type off direction of access write, it will always work. But the calculations will be harder. So physicists are lazy people on. If we can avoid extract calculations, we do. So what'd elections? Well, as in the first example, I will choose a direction for the X axis which is in the direction of the motion of the car on the Y. Axis upwards like this stepped on with me. They find an expression for the net Falls here are problem is clearly in two dimensions. So we will have to find the components of the Net force in these two dimensions. There's trouble with the X component. Oh yeah, exact. This is this one and this is the white. So what I do is I start here, say, and I go around and see what are the X components off the forces which are my free body diagram. The attraction is fully lined with the X axis So a sex component is its magnitude Concerning the normal force is perpendicular to the X axis So it does not have a next component So it doesn't be here. Then you go OMG I'm she does have a component. I have to see it here. It's gonna be negative. Oh, so we need to find the angle there it will be 10 degrees. Why? I need to remind you of a little mathematical theory. If you have aspecto and you draw the purple Nicholas to both sides of the sector, you get another sector on the two angles Here are the same so in our situation. But we do have a sector 10 degrees The white access is going to be perpendicular to this Detroit 40 on the MGI is going to be perpendicular to the X axis. So So you see, we are in the same situation. We have two sectors which have the same Thank So what is a component on the X axis of M G? Well, the angle is not in between the vector and the production side is going to be signed. 10 Let's do the same thing for the Net falls on why access eventually pulls a video and do it yourself. Same idea yourself. Here we go around T doesn't have a component on the Y Axis because it's perpendicular to it and it's fully aligned with y axis so it could be in. And he will have a component with wax. Is that in the negative direction on the Idol is in between, uh, the doctor on the accesses Could be MGI course time. Step three. Done. Step four. Apply Newton's laws. You see, the block here is not going to move along the y axis. So it's addressed along the Y axis. So he have zoo. What about the X axis? But it will move right? So this would be cool to make kid. We are now at step five. So what do we do? We think about the problem. Why? Why? Why do we have this question in the first place? Because the skin here is going to change. Will it increase? Who will decrease? That would depend on the acceleration. So if we know the sign of the exploration, we know if the car would slow down, accelerate. So let's calculate the acceleration. So is going to be a good plugging numbers directly. Thousands minus 1000 by 10 by sign off 10 divided by another style. So you make a good for that. The acceleration I find is minors you upon 74 meters per second squared minus. That means that the car is decelerating. It is slowing down, making this question still relevant. A good idea would be to try to find out how far the car could go if the stroke continue. That infinite, that means where would the call stop? If the value is bigger than 50 meters, it means that the call can reach the top. So for that, let's just do that S is what we're looking for. Use initial velocities. 20 V The final velocity zero a The excavation. We just calculated it. My 0.74 and time. I don't really care about it because I already have Free off the data Which equation has thes full perimeters. The's squared equals U squared plus two a s the zero I can cancel it. So I will be in just to find s as equals minus who squared of a to a plug in numbers. Man is 20 squared, divided by two times minus 0.74. Let me grab my calculator which is somewhere here a fine for s 270 meters way above 50 meters. That means that the car will be able to reach the top without any difficulty. And even if it's still had up to 270 meters to go, it was tear reached the top. You see how this five step system can allow you to solve problems even if you don't know how to start. Estimize step number one Free body diagram September 2 Defined the access step number three Find expressions for the Net Falls stepped on the full priced futons rules Step number five . So I hope that these two last videos allowed you to get a good feel off what this five step technique is all about. I encourage you to continue the course the next videos. We'll go deeper in each of the steps. So, for example, you will learn in detail how to be in a free body diagram. Oh, how to carry the calculations in step three with the Nets bulls. Then once these less and type of videos are done, I will give you a bunch of examples examples that we relate to. What? Your Dreamcast Oh, which will relate even to what you could encounter at an exam. So it's definitely worth checking these out. In the meantime, I see in the next video, Oh! 5. Free Body Diagrams - Step 1 (Episode 4): the first step in the fire step technique to solve problems with forces is to draw a free body diagram. What is a free body diver? A free body diagram is just a representation off the forces that are applied on a specific body. Let's start with a simple example an object in free fall. I represent the object like a little box in which I put a point. What are the forces on the subject? There will be gravity and there will be also a resistance. So I would present the force of gravity with a narrow Yeah, I will give me the direction of the force on the length which will present the magnitude on the fools resistance. Now the body is actually pushing on the air. Idea is underneath, it pushes on it. Therefore the air reacts and we push back so they'll be a force of a resistance upwards. You see here that the resistant to smaller than the gravity. Therefore, I know that the object will be accelerating downwards. As you can see, this is quite an obvious case in this video. Are we present to you various situations off increasing complexity? What I suggest you do? Is that just off to have presented situation? You pulls a video and try to draw the free body. Diagram yourself. Then you resume the video and check out if you were correct. Situation number one. An object drops on the moon. I draw my object. What are the forces that the environment will apply on the object? Well, there will be the force of gravity due to the moon. Are there the forces? Well? No, because there's no atmosphere on the moon. Therefore, there's no resistance. A footballer hits a ball. The bull lies. India. Draw a free body diagram off the ball while it is in the air. What are the forces that are applied on the ball again? You would have gravity. Are there other forces? Yes, it can be a resistance which will always be opposed to the motion of the ball. So if he suppose a ball is doing this, I was instantly be like that. Are there other forces? No, A warning though When I present this exercise to my students, many off them tend to put an extra force there in the mind. The boy is going that way. So there must be a force that way. Of course, there's no force there. The fourth was applied before when the ball was in contact with the boot. But as soon as a boot and the bull left will stop being contact, then there was no more force here. So why is that emotion? That's way all the forces are the other way because I forced accelerates a force changes motion. That means that you do not need to apply a force to keep the motion as it is. On the contrary, If you wanted to stop the motion, you will need to apply a force to change the speed or the velocity. So be very careful with this next situation. Pretty standard. Also, it's that's an object with this staying at last on the table. I wanted everybody diagram on the subject. What are the forces involved? Well, the object will be affected by gravity. I've got forced downwards and dream due to the fact that the objective tries to go down is pushing on the table. Therefore third off Newton Actually reaction. That would be a reaction of the table on the object, which is called the normal force. What is this normal force? Why is there normal force in the first place? Let's look a little bit of the structure of the table. I'm going to zoom a bit. Hey, I've got my object, right? This is now object and let's look at what the table is made off. Well, it's made of molecules. Yeah, the molecules which form the table. These molecules are bound to each other. If they were not bound, that wouldn't be instructor. That wouldn't be a table. So there's bones here between them. Well, in physics, we can model a chemical bowled by a little spring. So if I could, if I was loopy, if I just take a pair here and said opening in line, I can put it in the spring. Well, if the object is doing is pushing on this into spring is applying force under this spring, which therefore is compressing and intuitively, you know in your everyday life. If you push in the spring, it pushes back, so the spring pushes back. So I got the object here, pushes back the object. Now if Nana moving. If the system is study, it means that both forces are balanced. Therefore the magnitude would be the same. So back to our table we have tons of little strings here, which all our go to push back in reaction to the compression they're feeling, and they're going to be back on the object that is a normal force. In this situation. We have a ball, a customer's drink itself, that to ceiling in order to build a free body diagram off the boat. I need to list the forces that affect the bowl so we'll have gravity as usual on because of gravity. The ball will be pulling on the strings. Therefore the stream will try to pull back. That's third love new term. The ball is not going up or down, Therefore the forces will be balanced. Attention in the stream will be equal to the gravitational force. Now suppose that I wife and I push a bull so at the moment are pushed a ball. There'll be an extra force here. I push it a little bit buff and then the ball starts moving. It accelerates in this direction, but I lose contact with the ball. So now my boys here I'm leaving the ball oscillate. What are the forces on the board. Can you draw a free body diagram on the ball? Now you still have gravity pulling the ball down and you'll have the tension off the stream . But this time with the night notice that I'm always drawing the forces starting from the center because I'm considering the bull like a point like a point mass just to go it with further look at the situation intuitively, you know that if I push a bullet of it, then I released the ball starts going that way and starts to oscillate. But why does he do that? If I make the sum of the two forces here, you realize that I will have a force and that force which would go that way. Therefore, it means that the ball will accelerate that way. Even if it's moving this way, it will decelerate, meaning that the velocity of the boy is going to decrease until it reaches zero where it stops and then it starts accelerating the other way when it policy could be a point. So what is here? But we realize attention will be this direction now. Therefore, the net force will be directed to the light opposite to its velocity, which is now this way. So the world continues to do this intimate and reaches zero as the acceleration is still that way. Because attention is that way on, we start going back to the Caribbean Point and also like what's oscillating is the direction of the tension. Well, uh, close brackets feebly, diagrams are not always obvious. Take my situation. I'm leaning against the wall. Can you draw a few body diagram? We're presenting my situation. If you end up in trouble trying to draw few Buddy Diver, you think that you'll feel you're missing something? Think about 1/3 of Mutar. Third or Newton states that when an object a applies a force to be and the reaction of rugby will apply a force on object a off opposite direction and say magnitude. Let's make an example here, have a war. I have an object. Yeah, in contact with the ball. It is not pushing on this jet in contact, but if I push on the object, apply force on the object, then they would push on the wall on the wall with automatic react by pushing back. So I'm going to consider this like my hand, right? At this point, I'm pushing on a so they would be pushing back on me at this point. A is pushing on the wall so the war will be pushing back on a Now, let's use a free body diagram of a This is an interaction diagram. That's a So what other forces on a Well, there's a force off the hand on a and there is a force off the wall. Okay. Hey, doesn't move. Now, let's go back to my situation. When I was against the war, that's me. So I'm leaning, So I have a good drover. So what are the forces on me? So it's a good idea. May be to do an interaction diagram first. I'm pushing in the world. Right. So the wall is pushing back on me. There's gravity. The reaction force is actually that I'm attracting the earth. Uh, what else? Well, I'm actually pushing with my feet on the ground. If I didn't, if the ground was slippery, I would fall. So it's fiction. I'm pushing on my feet against the ground. They're full. The ground is pushing. Yes, me. It's fiction. So what else? Oh, yeah, forgetting the normal force. I'm pushing on the ground, right. Say my feet here downwards. So the realm furtive back on me Now if I do the free body diagram off me leaning a little What forces have I have the force of the war on me? My name is Ed Walks and put force off the wall on it. I've got the normal force of the ground on me, both of the ground on Ebola. I have the full so friction here that is going this way. Prevent me to full and I would have gravity. As you can see, all the forces have the similar magnitudes. I'm not moving in this situation. I have a Plan B which is held by strings attached to a ceiling. I was playing me. I place a block A What is a free body diagram on a That's pretty straightforward. There'll be for a that gravity Onda normal force off the plank. Yes, is pushing on the banks of the blank. Push it back. What about the plank? What is a free body diagram on the plank? Well, there's gravity and there is also the fact that a is pushing on the plant force off a on B . So strings the streams are putting the plank up. So there are two forces. You can put them there so we can just have them. All right, Scarlett, Attention. While intention to attention one class tension too Black is not moving. So the some off these two magnitude should be called to that. Ah, the slope one. Now you have an object which is on a slope. So what are the forces that acting on the object that still gravity downloads and the normal force. But careful, the normal force is always perpendicular to the ground itself. So it's not gonna be apple. This is going to be this way. If this is a very slippery slope and he realized I do block is going to go downwards. There wouldn't be any friction. Yeah, And if you make the some of the forces, you realize that that the net force would be that. But usually that's fiction. So I would need to add fiction going against the motion Fiction always goes against the direction of the motion. We can add a little thing on this free body diagram the angle. I thought because once we define some access, it's useful to have some references with the angles to I think we see everything in one go . So if I have the angle Alpha here, I know I would find it there. Let me explain why? If you have a sector here and you draw the purple Nikola to each side off the sector, the anger which is there, will you find there too? It's a mathematical theory. So here you can see the sector's this sector. And if you draw the puppet Nicolas So here and there this angle will be the same s. That's what In this situation, we have a small mass m on a slope which is pulled via pre buy bigger mass m. So the mass M is going that way. The slope is not fiction nous. So what are the forces that are applying on little mass M? Well, you would have of course, gravity. You would have the normal force, you would have the tension in the string and you will have the fiction if you want to solve such a problem. For example, if you wanted to know how long it took before, it reaches this point or whatever. Well, even if the mass began was enough to pull the massive um, stuff like this, you would also need to do if you got the diagram on mass. Bigger. So here you would have to forces big MGI on that the country. If the party here has been fiction, then you could find attention there and also there. So this tension would be the same as this one. So when you apply the steps to find the net falls here, you could have place attention here by this one connecting everything together. In this situation, we have two blocks on the table on the surface of the table is not frictionless. The two blokes are connected by a rope on this bigger block is also connected to another block off pass began. Yeah, I hope Ana pulling the question is what is a free body diagram on broke and too. So let's draw it here. I have, of course, and jeeps and too cheap and a normal full since the table. Then I will have the tension in the string here. I will also have the fiction on the table on. I would have the tension in the string there. Let's go. Attention, attention will intentionally attention. What? Oh, 6. Defining the Axes - Step 2 (Episode 5): in your free body diagram. You represented the forces acting on a body. Forces are vectors. They have a direction. Therefore you need to define a positive direction for access. Andi, therefore define also the axis. Let's go to do a simple case. A call on the middle way says his attraction force. That's fiction or resistance. Gravity, normal force. He should be quote so to access need to be perpendicular so x and why. Basically you need to choose them carefully in order to line than that maximum when the forces of your free body diagram. So here it would be straightforward X with beauty always into while we beat the vertical, Then you need to choose a positive direction. So for the y axis well, whatever Here it we actually know Count in this problem because you know that your car is not moving up or down, so and would be cool TMG anyway. But for the X axis, I recommend that you choose a positive access positive direction so it in the direction off initial motion. Trust me, it will decrease significantly Some possibilities of mistakes with signs. If you want, you can choose different access, say a nexus. Why like this on the nexus extract that as long as they are perpendicular. If you apply this if you use these access for this problem, yeah, you probably would find the right answer probably because you are increasing the complexity of the situation. By doing so, you would add some angles. Now you would have some. These are the would have this angle this angle all the forces would have an angle with the access, so you would need to use trigonometry all the time. So don't complicate your life. Just try to line the axis to have a maximum of forces in them. So let let's, for example, take the case off a slope. Here we have a car which is going up the slope. So let's roll. The people die, Gran. Traction, gravity always downwards normal force and the fiction which opposes emotion. So what access for the truth I could do simply taking the vertical on the horizontal. That's fine. There perpendicular can do that. The problem here is that I would have three off the four forces making angles with the access and dying that in the next step I would have not of trigonometry involved how to minimize this by choosing access, which are much more convenient. I, for example, these two on the X axis that recede positively directed that way, along with motion on upwards for the Y axis. Now, look, I only have one force, which is making an angle with the excess gravity and actually this angle, as we discussed earlier. But the alpha wolves, the slope. So in the end, when you treat you access tourism in the most convenient way, just make sure that they're perfectly clue to each other. Make sure that you choose a positive direction in the initial direction of the motion, and this was simplify your next, taking a few seconds to define carefully you access on their direction is a good investment because in the next step, we need to find expressions for the Net falls, and that is for its components along the access. So if you have too many forces that make angles, you will have a lot of trigonometry cool calculations to do now. In that situation where we chose the access wisely, we will only have one angle involved. Okay, next video, I will talk about Vector addition, a little reminder and how to add two vectors graphically and analytically, that is needed before we start Step for me. Oh! 7. Manipulating Vectors (Episode 6): Once you have your feebly diagram and have defined some access in the directions, you would go to Step three, which is finding the net falls. The Net force is a some awful the forces acting on the body forces of vectors. So you will need to do some vector addition on if you're in two dimensions that be angles involved, so you will also need some trigonometry. So this video is a kind of general reminder of how Victor's work seeing like a math reminder that me two sections in this deal, I will show you how to add vectors graphically first, and then I will show you how to add them analytically. So let's start with adding vectors graphically, that's going to do two vectors if one enough to I want to draw the vector F, which is some of the two. For that. I draw the 1st 1 and at the tip off the 1st 1 I would draw the 2nd 1 to draw the result on Vector. I just need to start from the beginning of the 1st 1 An end of the end off the last one on that victor would be F, which is F one plus f two. Pretty straightforward. Now let's imagine that if two is in the other dollars, I this same story I draw F one and at the end of F one, I drove the tale of two like this and my resulting vector f equals F one class F two. We start at the beginning off if one and end up at the end of F two. So that would be f one plus have to Let's see this in two dimensions now. So close. I have a vector f one like this an effective have to like this to find a result in vector. I just need to draw if one and at the tip off. If one started your f two, my leg f will start at the tail off if one and end up at the tip left to when you have the component of the vector, it works also. Let me explain. Suppose I have the two components of the vectors have got X y for the access I go the vector If X and Victor if, why the resultant off these two vectors will be my vector f If I apply this technique I just use effects. Started the end of effects where I draw the 10 over If why so I drove f y on my resultant will be from the beginning to the end. If F would be the resultant off a text. That's why and also effect in f. Why? Because they are the axis Are the components off F way know how to add vectors graphically now. So let's learn how to add them analytically What does analytically me? It means that if I have some vectors have their direction and I have the magnitudes. When someone unable to find the magnitude and the direction off the result of victim that start with a basic example my bones always there to force is applied If one states 50 new terms and if to that saves 10 you Dems. I don't find the resultant force either Some of these two forces Yes, the resultant force was the net force is a some of these two forces so I need to add them as vectors. Doctors have directions. I need an axis with the direction so positive two will delight. Now if I want to go to magnitude, i c f one is a positive value. So it's gonna be plus F one F two years off negative value because it's in the negative direction, so minus have to giving me a result in force off 40 new terms. Pretty straightforward, like That's complicated a little bit. That's cause he do the same box this time. F one is making an angle theta with you always until and here I would have to In order to find the Net force, I need to have these vectors as vectors. So f equals f one cars have to. But here I will need to define the components along a to D reference frame. So I need to define some access X on Isis. Why? I think it was positive directions to the light and upwards, for example. Now I need to find the components. So let's look at FX. F one has a component on the X axis, which is positive. All right, So has come to be if one course have to is also on the X axis on is something of the science of minus two after is totally on the X axis so I can put all the full magnitude in the X component of the Net falls. I use Costa here because theta is in between the vector on the access. I'm interested on protecting this fact. Let's look at why my face is on this. Now I see that if one would have a component on the Y axis, the Idaho is not in between Victor and the access say is going to be f one signed that I'm considering here the same situation as before. Any differences at the angle here is bigger than 90 degrees. So if I want to find the net force A still just need to have the victors on to find the Net force. I need to find components that let's find the component on the X axis. It will be f one cost it minus F two. God, wait a minute. F one is on the negative side. You see, the component of F one would be nearly yes, because Acosta, it's negative. So f one cause it that way we get they're with me. Now Let's consider the same situation as we had before the origin or situation. The simple system. Where have the two forces like that F one enough to failing to find FX. I can just right that it is f one cost. The angle between F one and the access which is here zero plus have to cost the angle between the force here and the access which is now 1 80 cost of 1 80 is minus one cost of zero is one. So you see, you end up with F one myself to So you had two choices. Either you can decide just visually. Oh, I see the force is going in this directions the negative one. So I'm going to put a negative Oi! You can consider the full angle course of 1 80 will be minus one. It's up to that. You choose one and stick with. Let's consider now something more general. Imagine I have a vector f one that say it has a magnitude of two new dogs on an angle with the horizontal off 45 degrees on a vector F two off my need to say one u turn on what makes an angle here off minus 30 degrees. Yes, negative side in front of the angle, because I'm considering a positive direction for the angle canticle glass So I want to add these two vectors together. I can't do that graphically. Right. So I start from the tape of this was the care of this one until I reached the tape off the other one. And that will be my force f of his own. To Vic, we found to determine f analytically. I want its magnitude and also the angle here. So for that, I'm going to define some axes x and Y and find the components of if actually can see them graphically because you see the component off the net force, maybe the some of the components off the individual forces that make it so Here, I've got the X component off F one on the X component of F two. And when I someday too Well, I get if x neck. So let's talk my effects. It would be to the magnitude of f one deployed by the co sign off the angle, which is between the vector on the axis on which I want to project it. So it's gonna be to or despite it, fully f one co sign off 45 and for have to same thing plus F two co sign off a minus 30. Tracking the numbers I get to co sign of 45 is square root of 22 And if one is one co sign of minus 30 is still gonna be positive. You see, actually is in the political action for their component or have to along the x axis. Because if I draw the circle, I have gotten angle theta here that the coastline would be this. And if I got the negative value of the angle, I realize that the coastline is still the same value. Still positive. So it's gonna be co signed. A 30 is skirt of three or two, giving me tooth current of two glass squared off three over to good. Let's define now the y component off the net force. If one sign of 45 you see, the angle is not between the vector and the access, and considering for protection, it's the other side. So sign F one sign 45 now because I chose 45 here also have 45. So, cause I know 45 inside of 45 I was something. And for the son of this one, where is going to be plus have to sign off the 30. If I draw a unit circle here and take sign off my 30. They see it's going to be negative on. Indeed, when I look at the projection on the Y axis, the component of F two on the Y axis is negative. So I end up with F one to San 45 is also skated to a to plus one with a guide by minus 1/2 . Excuse me twos, quote of to of the to buy his baby keys closed up to quote of two minus 1/2. Let me grab my calculator to determine the values effects will be equal to true 0.28 and they fly 0.91. So I've determined here the magnitudes off the components on the x and Y axis off F that the f y so effects is 2.28 new terms. And if why is you poor 91 you Dems failing to find the magnitude off result in force. Well, you can realize that if y is here also. So I triangle that on I can you speak to go giving me the magnitude off net force as being the square it off the sum of the square of the components, I think squared plus F y squid killing the squared off 2.28 was glad plus 2.19 while squared, which is with my complete up here, 2.45 new terms. I still need to find a direction, and I can still use the same triangle on the final night. Go here I look, let's quit so far. So in this triangle, the tangent off Alpha will be the opposite on the adjustment. So f why of effects. So Alfaro will be the terms of minus one off. That was Super 91 divided by 2.28 calculator again, 21 point eight degrees. Now I have all the information all the analytical information about by resulted force Oh, my result in vector. Oh, good. Now you have all the tools you need to make the most of the rest of the course. But if you are still experiencing some trouble, I recommend that you check my cools. Dedicated to this topic, it's called mathematics for physics. It is in three sections out of Buffel physics vectors for physics and trigonometry for physics. In the schools, I go much more in depth. And here remember, this course is about the five step technique to solve problems with forces. So I have covered mostly what we need. But if you want more than check out the course mathematics for physics. In the next video, we will be discussing Step three, Step three, consistent funding an expression for the Net force. Here we went a bit further. We actually calculated the Net force. You felt this magnitude in this direction, but most of the time, we would need to do that. We are interested in the expressions off the components of the Net Force. Yes, after planks. Therefore, which is due to his laws. We will get some relationships and equations that will put into relation the different quantities that are involved in the problem. And by examining these equations, we will be able to find a solution to the problem. So see you in the next video. Oh, 8. Expressing the Net Force - Step 3 (Episode 7): Step three consistent. Finally, a mathematical expression of the Net falls the net force when my body is a some off all the forces that acting on this body. So it's actually a vector some on what we've seen. Everything we need to know Dr Sums in the previous video. So this video will probably be quite short. So I thought I just read an example with a practical situation. I hope you enjoy my drawing magnificient, don't you think? I think I'm going to take a picture of this copyrighted and probably sell it full good old money. I'm so bad. At least I think you can figure out what's going on here. I got a sled with some stuff on it, which is sliding on a service. It is pulled by a horse. Yes, it's alls. It's pulling my holes. Yeah, I hope. Here. Let's imagine that look makes with the horizontal on Go. I put it in med on Go. So the first step would be to build a feeble diagram. Let's let's for forces in our free body diagram. Well, that would be gravity. I'm talking about this later. Gravity tell me the normal force. There be the force of attraction from the from the horse. But then I go to dot here and there'll be some facial just defined access. A step too always into access positive in the direction of motion on the Y axis. Positive. Say upwards. Step three. Now we want to find the Net force. Oh, no. We want to find an expression of the Net force. Often we don't need to calculate the net falls fully. We just are interested in the expression of its components. So let's look at the x component. I start here and I go around. So I stopped with fools. F Yang was between the access on the vector. So it's gonna be f course no more. Force has no X component because it's pumpernickel. The fiction force is on the negative side of minus F on. The weight has no X component because it's perpendicular to the X axis. This look at the Y axis f will have a component on the Y axis. So here the angle is not between the victor and the access is gonna be f scientist and will be fully on the Y axis if we know be on the Y Axis because there's no component on the Y direction on the way it will be fully underway. Access. But it's in the negative direction, so minus injury. So that's it we have how components now the point would be to go to step Full step full is where we will apply Newton's laws. I will put an equal sign here, and in the next video we will see what we will put their. The next video. We will talk about Newton's laws. We remind ourselves what I knew to laws and what they mean. And after that we would come back to this exercise. I will see what we can put in here. Oh. 9. Applying Newton’s Laws - Step 4 (Episode 8): first and second law mutant are built on a very simple concept, but also a very deep one. These guys are the root of physics. There's defined a mass little them on which I apply a single force. F. It's the only force on the mass and so it's also the Net falls. What would happen to the Mass and it will accelerate and the acceleration will be proportional to the force you play on. It's like if force and acceleration were two sides of the same coin. When you play a force on the body, it absolutely is. If I body accelerates, it implies that there was a force on it. There's a kind of symmetry between force and acceleration, and in between them this mess. If I apply a constant force on the body and the body has a big mass, the acceleration that is a change of motion off the body will be small. If I apply the same force and the body of smallness, the change of motion off such a body would be launch so we can kind off. Guess what masses with that mass. If the property of the body that defines how much of motion off that body changes when the force is applied on it. It's called inertial nous. It's a kind of resistance to acceleration. Let's look at the first and second law, First law. The first will states that when the Net force on my body is zero, the acceleration of that body is seen. Be careful. And that force of zero doesn't mean there is no force is applied on the body. It just means that all these forces compensate each other. We say that the forces are balanced. Be careful. Also, a equals zero doesn't mean the object is no in motion. Remember, the excavation is a change of motion, so an object could be addressed and say it west of equal zero. But it could also be moving with a constant velocity. That is a speed is the same. And the direction of the motion doesn't change. We say that the motion is uniforms on having a speed of zero meaning at West is just a special case off uniform motion. Second Lord. So here f net equals I'm a wait A is different to zero. That means that the motion is changing and F net equals they may allow us to find out by how much. If we know the Net falls, let's go back to the example we discussed in the previous video. You remember the one with the horse and the sled. As a first step, we studied the forces that were acting on the sled, and we build a few body diagram. As a second step, he defined the X and Y axis as well as their positive directions. Third step, we found expressions off the components of the Net force along the X and Y axis. Now it's time for step full to fill in these. So let's start with why access this land? We would be going up and down. Now It's fast with remain parallel to the X axis. So what will be the speed off the sled on the Y axis zero Where the speed limit in constant . Yeah. So will there be an exploration? No. Zero? Yeah, this is a filter of Newton. All the forces. I understand that bounce because there's no accelerating up or down. Therefore, you can like that. It's exploration is evil. I may equals you. Now let's look at the X axis. Well there's a horse on. The reason for that is to make the slip move. So, yes, there will be movement on the X axis with a speed change. I don't know I the nights the speed will change. I need more data. Need to have the values that I would need to calculate this actually So in delves I'm just going to put em a It's not long because they could be zero. What? And also something important is that I'm allowed to do that because the white component off f all the Acceleration Zoo So what I should do actually is book a X. This would be the X component of the acceleration because I know that the Y component is zero. I can just write down that it's also equal to May A equals X. That's it. Now we have our relationships, this one on this one. It's time now to step back in time to look at the problem. But first we need a question. So I suggest that we will do this in the next video. I stepped five how we try to figure the question here that I could ask you, and you will see how we can use these questions to find a solution. Oh, 10. Solving the Problem - Step 5 (Episode 9): Step five consistent. Stepping back a little, we will hear the problem. So first you look at the data in the text. Then you look at the relationships who were able to build by following the 4th 1st steps. So you recognize here the the beautiful horse them to sled. You recognize the situation that we've been discussing in the previous videos? We just step one if you bought the diagram. Step two, we defined him Access Step three. We defined the components off the force and finally step for we applied new to laws and now we have relationships. What was the question? Well, I haven't given it to you yet. Here it comes. The angle here between the weapons he always antle is 15 degrees. The magnitude of the force which is deployed by the horse on the sled, is 300 new terms. The math of the sled is 100 kilograms. Uh, what else? You can use G as 10 meters per second squared and finally, important information. The velocity of the sled is constant. The question is, find a coefficient of kinetic friction between the wood of the sled and the snow. Now, for those of you that are not family with kinetic friction. It occurs when you have an object which is moving on the surface of another one. There's fiction that forms, right, so they'll be a force of fiction, which is proportional to the normal force that is on the object. So here you would have f because move and because its kinetic friction we put us up. Assemble, hear me. Okay. The question is to find UK. We want to find the coefficient of kinetic fiction. F equals make a and so make a is f of end Oh, the velocity of the slightest constant. So the X component won't have any acceleration. If I could three ranches equations and let them in here, that could be very useful, right? Because F is actually equal to F course data. I can like this now. So just as coast city, a feeling I now need to remove these. You see, I don't even care about the components. What I care about is a relationship that give me so now. N if I put empty the other side and that's antithetical other side, I get MGI minus F sign. See, It looks complicated equations, but its face simple to realize. Now let's take it the numbers we needed them f is 200. No sign of 15 Divided by m g. Said 100 by tens of 1000 minus 300. Sign off 15. Let me grab my calculator somewhere. See your 0.31. We have started to enter into exercise territo me there. So I suggest that you continue the course now with a pen. A calculator answered off paper Because all the next videos I'm going to be exposing you to different situations you can encounter in class or doing a test on. I'm create you to try to follow the steps, even if you do not know how to start the exercise. That's what this course is about. To help you figure out a way to find solutions. See you in the next videos. Oh, 11. Tensions & Ropes - Exercise 1 (Episode 10): Hi. It's time for exercises now. The 1st 1 is relatively easy. I don't want to go too hard on you at the beginning, but it's still into them entrance and you need to understand. Well, the the text. So here is the text you have to walls and in between the two balls, there is a well in the middle of this vote. There's a second world that is attached on at the l of this world. There's a mass M off five kilograms on. The whole system is balanced. Well, the first world would be pulled downwards, right on good form, and then go tittle three degrees with the horizontal. The question is, find the value for the tensions in the hopes that that's mutable calculations to do. Give it a shot. Okay, What will be the tensions here? They'll be attention in this world on also here and there. Well, that stuff with looking at the free body diagram on the mass. That's this guy causing all the trouble, right? So let's start with it. So, first step, the body diagram. Well, that would be gravity pulling the mass downwards on because the masses pulled downwards by gravity. It will also pull on this world that will respond by reaction with attention that's defined now and access Step number two Considerate positive inputs. Number three. My down, an expression for the Net falls so we would have the net force would be t minus energy the full, If you remember, apply new tools rules. So here the mass M is addressed. It's not moving, and it's not having its motion change either. So we have. Do you step five so well? That's pretty simple. It's just t equals M g. So if I use 10 full for G, I get 50 new terms. Good. I have now the tension in this world. It's 15. Utah, it's here. It would also be there, starting from the not here, but not between the ropes. Well, if we want to find the tensions which will occur, there could be a good idea to deaf people. Desire them off the connection between the ropes. So I will have 50 Newtons downwards on making Enugu off three degrees. We see presento. I would have the tensions notice. The's tensions will be identical. That's called Auntie Prime, so we don't confuse him with this one. They'll be identical because the whole system is symmetric. Good set number to access. Well, that's true. Is positive the X axis to the right and upwards for the white, that step expressive net falls. Where? On the X axis. I don't see the point. Why? Because the 50 Newton Force does not have any component on the X axis, so I would not be able to introduce my data so we'll focus on the Y Axis F. Why here? So I should actually separate these two f y I will be three prime sign off three twice plus P Prime sign off on minus 50. If I plan in droves, I realize that it's not. He's actually no emotion, so it's just gonna be equal to zero. If it's not in motion. It means he's not accelerating how you arrange days for tea de plane. So to t prime 73 equals 15. So tea party equals 50. Divide by to sign free. Did you check my calculator? 478 new terms. Oh, 12. Connected Blocks - Exercise 2 (Episode 11): in this exercise. We have three blocks off Mass three m to M and M, which I connected. Yeah, Woops. They stand on a surface, which is fiction. This on the little mass. M here is a brother Force F, which is No. The question is, what is attention in the rope between the block off now Sweet em on the block off Mass to you know how to start this exercise? Give it a shot. Uh, so how did it go for though? That didn't know how to start. Remember the steps, right? The first step is a few body diver so But everybody diagram on what? Well, listing TV. You might think I should do it on this one because attention is here. But the problem with this is you will introduce a man. No, Look at this. You have tension here. You have two mg that way normal force and you will have also attention here. Let's quit t prime. So you introducing an unknown you complex defying the problem. So instead you should remember that tension transports along a stream. The tension you have here you find it here also. Ah, that simplifies things because you could do the free body I grab on the three and block. Right. So let's do this. I would have three g normal force on the tension in the fall. Good. Step two, Axis. Why? I put thanks politic to do it. Expression of the net falls. Well, I realized that my net falls on the way Access would be zero. So the net force on the X axis will be the net force. Right? So he's going to be t half man. It's just so I could apply the full step. Bit of laws free. Hey, T is three and a I was looking for tea, right? So I've gone expression for tea and therefore I'm making progress. But if I could find a so many a good idea would be to step back and look at what I know. I know. If you what if I considered the whole system here, the three blocks, like one single block off Mass six. And if you really dive, I'm on it. What would be the forces? Well, I would have rate six m g. I would have the normal force and I would have the force f which I know I'm in. The same situation is here, meaning that my net force is the X component of the net force. It's just And if I planets of loss, just gonna be six and a I know f second, find a they would be f six n and I can fly a in here. Yeah, of course. If the block off my six and the whole thing is moving in on exploration A So where all the individual blocks, apparently their full attention now would be three m by f of six and math cancels attention is just f over to oh. 13. A Block on a Slope - Exercise 3 (Episode 12): in this one way have a slope off angle titter with your present on the slope, there is a mass bigger. The mass PGM is connected via why I'm a truly mass little There's no friction of pretty. There's no friction on the slope. Both masses, I think Libya. The question is finally and greeted them. Uh, that supply the steps First step free body diagram. I see that I have to masses here, So let's do it on one of them. For this one, I would have MGI tablets that gravity on a tension in the string him to access positive prints that free by dominate Fels his T minus N g stepped forward planning to draws the Matthew toe M is on the Caribbean. They're fools. So have t equals empty. I know the tension here, its engine So I know it here. I know it there and I will certainly there there's no fishing in the pulling, remember? So this is actually MGI That's everybody like them on nasty in I would have mg this way I would have big MGI that way on the normal force like this, like this has come to the X axis positive and directed that way on the Y axis. That way I chose of this way to make them more convenient to have the less angles possible in my free body diagram. You see, let's actually enjoy here. I have mg like this big country here on my normal falls on. You see, I have I got picked up here. Okay? My access. We said positive. That way for X. I'm positive that way. For what Best? Ruthie. Let's find an expression for the net force now on the X axis. I would have little G minus big MGI. Actually, I could stop now if you think about it. Mass began is in the Caribbean. So this would be zero. I noted toe m I know began. I can find it. M g equals big Angie. Sign atop the G's council. They sank it up. Equals little them over. Begin. So data is signed Minus one off little and over bigger, So Oh, 14. Understanding Friction (Episode 13): in the exercises that follow, there will be some fiction involved, so this video would be about friction. Mechanical friction is a concept that is very common in physics. But what is it? This is an out speaker. It's actually quite a heavy one. It used to be my grandfather's actually built in the sixties or seventies, something like this. Anyway, it's standing on some carpet. I want to push it. Don't move it. So I blunt force. I'm applying force now. Nothing's happening applying its total one still nothing, increasing the strength now the street to and it's actually quite easy to move after that. So what is going on? The action is actually occurring at the interface between the box on the carpet. Here I am representing the bottom of the box, and here I am, representing the carpet. Let's zoom right. I'm going to zoom on this point. The surface of my box is not perfectly smooth, so it will shop a bit like this. Maybe if I zoom, neither will be the surface on my carpet, which like so I need to be like that when I move my box, say like that with the force So this thing we move a tiny bit, it will move until it which is in contact with that. So I would be in this situation. At this point, there'll be a force of the box on the ground on the ground would react by a gang of force, the bunks. So if I do the free body diagram on the box, there will be me pushing it on the imperfections off the interfaith pushing back. Therefore, my box will not move. However, if I increase the full sum, the books the fools here becomes bigger on this one would also become bigger unless it breaks. If it drinks, then suddenly is going to be easier for the boxes. That'd be my first fiction. It's like you find punishing the ground on the surface of the box. Let's try to represent this phenomenon graphically on the X axes are placed before supply and on the y axis of fiction that results when a guy it's more force. I would get a friction off same magnitude but opposite direction. That's why my books is are accelerating, is not moving so I can draw a line here This group of one but if I pass a certain Fed told I apply a force above a certain value. Then suddenly my box moves easily. The fiction decreases. I've got two zones clearly here, two behaviors. I've got a static zone on the dynamics on food, Better newness, kinetic. So if I'm in a static zone, the fiction would be equal to the force. Our plan in managing. If I'm the Kennedy's own, it would be kind of constant. Let's consider this point the point in between the two zones, we can actually calculate the friction. At this point, the fiction at this point will be equal to the product off the coefficient of static friction, which would meet us by the normal force. We can also find out the fiction in the dining zone. The fiction in the dynamic zone will be equal to the product of the coefficient off kinetic friction with the blind by the normal force. And it makes sense. Imagine if my books was much heavier. In order to get it start to move, I would need to apply a bigger force, right, so that would be extended higher. Make sense like, because if I have a bigger mass have a bigger, normal force. So remember this relationship between fiction and normal force. Remember that if you are at a point off slipping, meaning that you are about to start to move, then you can always write down that the fiction is equal to us by the normal force. And also, if you are moving, you also have this relationship. But this time you have to consider the coefficient of kinetic friction. These coefficients depend on the two to face. For example, if you have some would on some snow or some word on carpets or some metal on some leather, whatever this combination of two interfaces will have associated with them to coefficient off fiction aesthetic one under Kennedy Oh! 15. Friction on an inclined plane - Exercise 4 (Episode 13B)): in this one. We have a slope which isn't making an angle tiptop with the Rozental. And actually it's more like a plant because he I could imagine a liver. And if I turn the lever, I can rotate the plant. So would change the on the plank. There is ah, box. You can easily imagine that if get a small, the books will stay as it is. It would be addressed. But if I increase the angle theta, then there'll be a point with Star slipping. So I moved my liver and I increased it up. And when the box just start slipping, I stopped and I measured it out. So titter this angle will be the anguished wish the box is about to start to slip. The question is, calculate the coefficient of static friction. Step number one, A free body diagram. Well, I have I'm Gene, I have no Biffle's, and I would have friction that opposes an emotion. That box could have then step to defend some access convenient ones. So X axis, for example, that way positive a long slope and y axis positive puts three expressions off the net, pulls two dimensions, so I will express and components effects will be cooled to minus f. And he looked so there. So plus m v sign a fly. Normal fools minus MGI course. Did them stepped under four. Newton's laws. The box is about to sleep. It's not actually slipping right now, so it's still at rest. But for long, frankly, sit down. But now it's still dressed, so it's do okay. Step number five sold. So that's where you step back in the tools and you check out the problem what you're looking for. I'm looking for the coefficient of static friction. What did I know is that I am at the point of slipping. Therefore, I can write down that f The fiction is equal to the product of the coefficient of static friction by the normal force. If I rearrange, I find this is F Now the relationships I got from step three and four allow me to find expressions for effort. Look here. I realize that F is equal to every scientist. If I put at the other side, I just get this something for end. If I put empty costed ideas aside, I get any calls and requested I could substitute these expressions in here. Right? Let's do that, Miss Equals I m she signed up. I m g cause the entries Councils leaving me with sandal costs, which is turn the coefficient of static fiction is turned off where theta is the angle from which my box is just about to stop sleeping Oh! 16. The Elevator - Exercise 5 (Episode 14): in this situation. We have a man in an elevator. The elevator is being pulled by cable and attention in the cable is 18 killed. New talks. The mass of the elevator is 1430 kilograms on the mass of the man. Little end is 70. The question is what is a normal force off the man? Try it out for yourself. Uh, Step one free body diagram. We'll do it on the man because we're looking for the normal force downwards. Will have the weight upwards. Will have the normal Fels like this upwards Positive. That's that made fools f net is equal to end minus Henry and four step future of laws. Well, it might be accelerating, right? So I so the normal force would be and G plus a Now I have an expression of what I'm looking for. The normal Fels. I know the mass of the man. I know the gravitational fear strengths, G. I'm looking for a Well, what could I do to find a I could consider the whole elevator like a block Elevated plasma . What? So for that. So this was for the man. The elevator. I'll do a feebly diagram to but you're having. I got attention and then I have before mass g together wait and t plus minus and plus G would be cool to m plus and okay, so I can find a that's plaguing every numbers. Here, I've got 18,000 minus 1500 by 10. So that's 15,000 is equal to 1500 a. A is 3000 divided by 1500 two meters per second squared. So I have a now I just need to take in paying him and would be 70. The massive amount by 10 for G plus two. That's 840 noodles. Oh! 17. The Crate and The Pit - Exercise 6 (Episode 15): way have a man which is pushing a 10 kilogram great with the force of 19 u turns. And he does this for five seconds. The coefficient of friction between the crate on the ground is 0.5. After five seconds, he releases a great, so he stops pushing at this point, the greatest 20 meters away from a pit. The question is where the great fall in the pit. He lets start to analyze what is happening at the beginning. While the guy is pushing the great people, these Iran, I would have the force of the guy. I would have the weight of the great. So 10 by 10. So they came by G. I would have the normal force on. I would have some fiction access. Let's consider positive that way for X and positive that way for what expressions of the Net force effects will be cool to F minus. F and F Y would be pulled two and minus energy, but it is equal to zero because the object is not going up or down. So an equals and jean on the X axis to blow could be accelerating. So is big good. So what can I get that? I can get the acceleration. Why would I want the acceleration? Because I know how long the guys pushing it right. If I can find the acceleration and we know the speed of the block at the moment Guy stopped pushing. That could be very useful. Because once I'm there, Well, when the guys are pushing, there's to be friction. So I would be able to calculate how much block disintegrates. And then it's about this to me. So let's find out the acceleration. The excavation is big F minus f divided by the I know f B f a small f Well, I'm in kinetic moat, right? So I know that f is equal to UK and an end if ngc UK OMG so half my ass Week A and G did I The numbers This is 19 minus 15 by 10 by 10 divided by 10. So in the end, I get 90 minutes 50 Yeah, yeah, no, into my feet to drive by 10. That's for me to spur Seconds clip. We have our exploration now so we can calculate the speed off the books when the guy just stops. Appreciate said t equals five seconds. The speed of the books that cycle you would be a my tea. Yeah. Every second the speed increases by four meters per seconds. After five seconds off, pushing it will be full by five 20 meters per second. Now I know that the box at five seconds is moving with a speed of 20 meters per second. But the guys are pushing. So let's everybody that going to understand what's going on. I was still half figmd normal force on the fiction force. The net force on the X axis will be minus of Fiction force. Probably know that the fiction force is me and G so minus mean g which is also equal to be in a That's four steps. So now we can actually cancel the M here, get a equals minus which is minus me is point 5/10 of minus, huh? Five meters per second clip. Therefore, I know that my book is going 20 meters per second and is dis aerating at a rate of five meters per second squared with it reached the pit. Well, we should find out how much distance it can cover until its speed becomes Ooh, that is a motion problem. So let's do the Sudan system. S u v a T. Yes. That's what I'm looking for. You is 20 the zero when it stops a minus five and time. We didn't care. So we have three out of five we can solve. Which equation has these four kilometers in the's squared equals U squared Class two A s. I'm looking for s the council's. So if I were ranges I've got s equals minus He's quit over to a so minus you square It was 20 so it could be miles 420 squared, divided by two A which is most to buy 5 10 40 meters. So if the track is Contin remember this the block will actually continue to move for 40 meters. Therefore, after 20 meters where the pit appears, it will fall in the pit. So yes, the box will read the picked Oh, 18. The Flea Jump - Exercise 7 (Episode 16): These are very imitating insects, but the Elson quite amazing. They can jump it heights which are incredible compared to their size. They do this by pushing on the loud. In this example, the fee is pushing on the ground with a force of 1.5 by 10 to minus five Newton and the reaction of the ground makes him jump in here. The wind is applying. A force off is entirely or feet by 10 to minus six. Mutants on three. The mass of the free is one milligram. The first question. Calculate the acceleration off the feet. That means the magnitude and the direction of the the second question when it pushes on the ground, it does serve for 0.4 seconds before it takes off. How far does it learned from its starting point? Good luck. Uh, way are looking for the acceleration off. So in other words, we're looking for the net force off the fleet because once we got the net falls, we can divide it by the mass off the fleet, and we get the acceleration. So if we're looking for the net Force, we should let the forces that are acting on your feet. So basically, this is a free body that where Step one, there will be the weight off the fleet. Damn blitz! The fee is pushing on the ground and we re expecting a fool's off same magnitude and opposite direction before that makes the thief spring upwards. It's cool in and then they'll be the force of the wind. Let's to find some access. The X axis positive to the right on for the y axis Positive up puts that three way down the components of the net force. So the X component is just gonna be the force of the wind And for the y component is test came to be the force applied of the ground on the fi, minus the weight of the fleet on the for a planet of laws. So that's going to be and a X how this would be an a white so we can find the X component off. Hey, which is just force of the wind value by the mass. The force of the wind was three by 10 to the minus six on the mass in kilograms. One milligram rights include grams 10 minus six kilograms. That's three meters per second. Squared the tomato season. What about a way? Well, it will be F minus mg. Divide by M. F was 1.5 by tens of five enemies 10 minus six by G. We just tense as 10 minus five and m is 10 minutes six. So that gives me 0.5 10 miles. Five divided by look inside of 10 minutes six, which is 0.5 minutes five. Actually 56 days could be five meters per second squared. So I have the two components of the acceleration. It's easy to find the magnitude and direction I can just use. But ago that's gonna be three squared plus five squared square with it. And for the angle. Yeah, that'd be a no. It's going to be competitive. Presentable. Sedita is tangent minus one off. Why? Over the exit. 5/3. Let me grab my time for NATO. For the magnitude of the acceleration are found 5.8 meters per second squared on for the ago. Compared to the X axis I found 59 Deletes The flea has jumped. It landed somewhere. Question be asked us. How far is a turning point? We let it lead to the jumping point. We have extra information here. We know that the fee has been accelerating for 0.4 seconds before losing contact with the ground. And we have the X and Y component of this acceleration so we can find out the X and Y component off the velocity off the free. At the moment it was his contact with the ground. Now remember that an acceleration is the rate of change of velocity. So when I say that in the X direction have an acceleration of three meters per second squared, that means every second the velocity in the X direction increases by three meters per second. The time for wishes exploration is applied is your 0.4 seconds. Therefore, on the extra election, I know that my velocity will be three times. Do you put full the 1 22 meters per second Same thing for white 54 that these two meters per second good. So let's draw what's going on with the fleet. It's living with a velocity X 1.2 y two like this on it will learn somewhere. Let's think about what's going on with the fee. Well into India. Actually, let's draw a free body diagram. There will be the force of the wind. Hey, the window Still that on their be the weight off the feet. So we want to know this testifying from access positive the X axis to light and positive for the Y axis downwards. That's right. Down the net falls. The X component of the net force will just be the force of the wind. The Y component of the net falls would just be the weight off the feet. You have a planet those laws on defined therefore, the acceleration off fee when it is in the air, the devil is not the same thing is this one? This one was the acceleration of fee when they just pushing in the right and we can find value for it. So aux would be the force of the whaler, which is C by tended them and the six divided by the mass of the fleet. So still see me too specific and sweat. This hasn't changed, but for the y axis. Well, this is gonna be Jeep. We have the acceleration off e. We have the initial velocity of three and we want to know how far the fee will travel along the X axis. That seems like the motion problem in two D. Just do some servants starting with the X axis s u V A T place. Well, that's what This basement along the X axis. That's what we're looking for. You. The initial velocity along the X axis. Yes, we have it. It's 1.2 the No, we don't have this one. We don't have the final velocity along the X axis. Okay. What is the acceleration along? The extent we have that and a T know we don't have. We don't know how long it takes for the future. Go from that to that. So we only have two other five recall sold. Just with the exactly. We need to find extra data on. We probably confined it from the why access. So s u V Hey, the fee jumps on, falls back on the ground. So the initial position and the final position on the Y axis are the same. Says the displacement is even initial velocity. Well, the way I see it is two meters per second, but let's be careful. We chose C access positive downwards. So here's minus two V. I don't know it. Hey, it's treat just gonna be tech team. We don't know it, but we can find because we have s you in a So we have three out of five confined either Vot , I'm going to focus on t because the time it takes for the feet to go up and down is the same time it takes for the fee to cover the distance X So the time here is the same The time that this here, let's have the time here I can find this. So let's choose s equals beauty plus 1/2 a t squared. This is your I can fact wise t 80 two traditions t equals zero off course. When there's no time that passes through, the statesmen will be viva. So that's not relevant. What we want is this to be zero. So we do you agent T equals minus two. You a minus two. You is minus two a is 10 0.4 seconds. So this is 0.4 seconds. This would be point full seconds. We can calculate s again. We can use s equals u t plus 1/2 a T squared. Let's do that. So s for X is beauty plus 1/2 a T squared. You just need to plug in the numbers 1.2 by 0.4 1st 1/2 three by 0.4 It's quit that we got my calculator 0.72 meters landing spot off. The fee is 0.72 meters away from the jumping spot. Oh! 19. The Asymmetric Rope - Exercise 8 (Episode 17): In this exercise, we will work again on tensions which are going inside a rope. The difference here is that the pose on which the group is attached I know I have the same height. So when a massive 60 kilograms is placed on the rope, these make different angles with the always gentle on the left side, you have a table 15 degrees and on the right side and then go off. Tell agrees. So you've guessed it. The question is, find the tensions which I devote, uh, step number one as usual free body diagram. But here on what? We will carry out a free body diagram on the mass. I know we want cafe tensions and the night is on the boat. So we need to find an object which is subjected to these tensions. That will be the point on the globe. Justin Lisa Mass. So what would be the forces on that point? Well, the masses pushing on the lobe, pushing on that point therefore this point would fear the push off the mass. And this push will be the force of gravity that is acting on the mass. So n g then there'll be the two tensions. It's called intention while intention to the angles here with the X axis. So let's define the access. Also maybe 10 on 15. The way access we can come to do it. Vertical apples. Step number three An expression for the net falls that starts with the X component. This will be t one cost 10. Yeah, The I go is between the victor and the access. Of course, Anti to is negative, says B minus two cause 15 If why of why is positive in the upward direction says will be managed only and then the y component of the tensions. So last one sign 10. The angle is not between the victor in the excessive sign. Plus two two fine 15 Okay, for beautiful clothes. Well, the object is obviously in balance into Nick Abia says the two components of the net force equal to zero on here we have our relations. This is just a system of two simultaneous equations with two unknowns t one and t two. So we could do Yeah, we could your substitution expressing. For example, T one s t two t one is t to cause 15 on coast 10. I'm plugging it in here so I get minus and Jean plus T to cause 15 sign on course would be turned. So term turn and then plastique to sign. 15 am I right here? Yeah, And that's equal to zero. So I can just factor ice t to put into you Get aside. Giving t two equals m. G. Cost. 15. Turn 10 plus sign. 50 Chris, kiss me directly to please. I find 1398 year terms so I can just inject this in t one. Now he one is 1398 new terms by cost. 15 because 10 This gives me 1271 year terms. Let's round this a bit because being four significant figures well, we only have two. Look super. This will be around 1400 new terms and this one around 1270 new terms. Oh,