welcome back to the study of ap physics 1 uh quick review for your upcoming ap physics 1 exam this is brian brown coming to you from beautiful central new jersey so tonight we're going to talk about dynamics uh really ties in a lot to last night's session where we talked focused on acceleration dynamics is a study of why objects accelerate or don't accelerate some of the key concepts that we want to talk about are forces different types of forces that we typically use free body diagrams and newton's laws of motion okay in this session we're going to look at forces in really the same lenses that we looked at motion last night we'll define the terms we'll talk about the equations that you can use look at the important graphs that show different meaning and talk about when you can apply these concepts and when you can't apply them we'll take a look at a multiple choice question and some free response questions as well let's begin our review of forces so we're going to start with the definition of forces which really is any push or pull that acts on an object turns out that all forces are interactions between two objects and so we'll take a look at forces from both these perspectives depending on the problem everyday forces that we use in physics are the force of gravity the force of friction the normal force tension and the spring force it's easy to remember all these forces because they have little subscripts next to the f that talk about which type of forces they are this is not an extensive list of all the forces out there but these five are the typical forces that come up in most ap physics 1 problems so we're going to break down these forces one by one the first one people are familiar with is the force of gravity right of all the forces that we have the common forces this is the only field force which means there's no physical contact between the two objects the object doesn't need to be touching the earth if we're talking about the gravitational force that earth has on that object all the other forces are contact forces the equation that's on the ap physics 1 equation sheet is g equals fg over m more commonly we just say the force of gravity equals mg you probably recognize that g equals 9.8 meters per second squared sometimes you round it to 10. and that's perfect we use that any time the situation takes place near or on the surface of earth where the gravitational field strength or the acceleration of gravity is about 10 meters per second squared this equation still works for objects near the surface or away even far away from other planet surfaces but g is going to have a different value we'll talk about that more tomorrow night okay so now the other contact forces the first one i want to talk about are the first two i want to talk about are forces with surfaces so together they're the normal force and the frictional force the normal force is always directed away from a surface perpendicular to the surface the friction always acts parallel to the surface are these forces always present if an object is touching a surface well it depends sometimes you need to know a little bit more about the situation to decide whether these forces are present and we'll talk about that so the normal force this one is an easier one to see as long as a surface is in contact with an object then absolutely there's a normal force pushing the object it's the force between the surface and the object so two examples to help demonstrate this force or as if you're standing on a scale so there's a little stick to your view we'll put the scale in so which way is the scale pushing on the scales pushing you up right away from its surface a lot of people think that the scale measures weight the scale technically doesn't measure weight it measures the force that the scale is pushing you with sometimes that happens to be your weight we'll get into more examples about that later as well you could have a small box being pushed by a large box so there's our small box and i'm going to put the large box to its left so the small box is being pushed to the right see the normal force doesn't have to be directly upwards it could be in any direction if you think about the scale again if you put the scale between you and the wall and leaned on the scale the scale would be pushing you away from the wall and it wouldn't be telling you what your weight was as long as the normal force is greater than zero the surface is in contact with you one condition is when the normal force becomes zero technically it's no longer in contact you just kind of left the surface even if microscopically and you can't see it if there's no normal force then the surface is not pushing you okay friction how's friction work well sometimes we ignore friction right sometimes the problem says if there's negligible friction or it's a smooth surface then we can assume that there's no frictional force again an object needs to be in contact with the surface but the direction of the force of friction even though we know it's parallel sometimes can be tricky if an object is sliding on a rough surface then there's kinetic friction kinetic goes along with sliding if an object's not sliding there still might be friction but it's again it depends on the situation and we call that friction static friction it doesn't mean that the object's not moving it just means that it's not sliding with the surface sorry it's not sliding on the surface okay so the key equations are friction equals mu which is this greek letter right the coefficient of friction times the normal force um this equation technically is not on the equation sheet the equation sheet has the definition of static friction which is that the force of friction is less than or equal to the coefficient times the normal force it's kind of included in there because there's an equals sign in the first equation and it's less than or equals in the second but the big thing to notice is that static friction doesn't have to be a certain value it's anything less than the coefficient times the normal force and kinetic friction has to be that certain value of the coefficient times the normal force these two coefficients are typically different for each other they depend on the surface and they depend on whether you're talking about the kinetic or static friction but just be careful about this less than sign for static friction let's talk a little bit more about kinetic friction connect friction is again it's sliding on a rough surface the direction of this is a little tricky the force of kinetic friction is opposite the relative direction the object is sliding so i'm going to give you two examples i hope clear this up the first is the more common one if a box is sliding to the right across the floor so let's have our box sliding to the right which way is the force of friction well as it slides the force of friction opposes the relative slide so the box is sliding to the right the force of friction must act to the left this one's a little bit trickier if a box is accelerating to the right as the large box underneath it is being pulled to the right but still slides watch what happens both objects are moving to the right but if you were sitting on the green box and watching the blue box it would be sliding to the left right it's getting further to the back of the green box so the relative slide between the blue box and the green box is to the left which means that the kinetic friction is acting to the right this reminds me of the clay tablecloth trick right as you pull the tablecloth forwards you're hoping that the glass of water doesn't move along with it but it could move a little bit probably is going to slide it's going to slide in the direction that the tablecloth is moving so the relative slide is backwards but it kind of makes sense that the friction is pulling it forwards a little bit to give it that motion okay so the key thing to ask yourself is which way is the relative slide of the object which way is it sliding tension tension's a obvious force when it acts because there's going to be a string or a cable this is an easy one because the force of tension is always acting in the direction that the string is pulling strings can't push so we don't worry about strings pushing an object so let's take a look at a box that might be pulled by two strings attached in different directions so each string has its own tension the force of tension one would be going up to the right and the force of tension of string two is going to the left a spring springs are a little tricky too because they can either push or pull an object unlike a string the magnitude of how much the spring force is depends on the compressed or stretched length and the direction is always opposite the direction of stretch or compression so here's a little example if my spring was originally this length and then i insert my object push the spring back the displacement is to the left which means that the force that the spring exerts on the object is to the right on the other hand if i start with my original length and i put my object in and pull the spring to the right the spring is going to pull the object back with a spring force to the left so if a spring is shortened it's going to push an object if the spring is lengthened it's going to pull the object that's goes along with this equation well actually the magnitude of the force goes along with this equation right the spring force equals the spring constant times the stretch length and that equation is on the equation sheet okay you've probably heard about free body diagrams these are representations of all the forces that act on the object so thus far my pictures have just been identifying single forces at a time in a free body diagram you want to include all the comp all the forces that act on an object don't draw the components on your free body diagram we'll talk about that later for the ap physics exam draw force is extending away from the object even if it's a pushing force you still want to draw it as if it's a pulling force and make every attempt to indicate the relative amount of the force with the length of the force vector so i'll give you a couple quick free body diagrams in the first case maybe we have a spring pulling an object up and the earth with force of gravity pulling the object down two forces that's our free body diagram in the second case i'll throw a couple more forces in we could have forces at angles so the tension's pulling up to the right there's friction there's normal force and force of gravity again depends on the situation you want to try to capture all the forces you can tell the largest forces are the forces with the longest vectors so let's take a break from free body diagrams for just a moment and talk about the first and second laws in in a minute i think the key to understanding first and second laws is going back to the topics that we talked about yesterday does the object have acceleration if your answer is no there's actually two choices it doesn't have to be at rest it could either be at rest or it could be moving with a constant velocity both of those are zero acceleration cases and when we recognize that recognize that the forces must be balanced right the net force has to be zero if the object is accelerating then we say the forces are unbalanced and the direction of the net force is always in the direction of acceleration so that's why we want to really understand which way the object has acceleration that has to be the direction of the net force the famous equation probably the most famous the most famous equation in physics is f equals m a on the equation sheet it's in a slightly different form the acceleration is defined to be the net force divided by the mass again don't ask yourself if the object is moving that really doesn't help clarify the difference between the first and second law both of these laws go by different names we talk about the law of inertia right objects have inertia that really talks about the first law and that is the tendency for an object to keep its motion whether it's at rest or at a constant velocity you know newton's first law as objects at rest they arrest objects in motion stay in motion again it's only if the net force is equal to zero right that the forces are balanced so now if i go back to those two free body diagrams i could look at them in a little bit more detail in terms of the net force if you draw your free body diagrams accurately you'll know which way the net force is right in case one the spring force was more than gravitational force so the net force is upwards and the acceleration is upwards again this object could be moving down but as we talked about yesterday we could be moving downwards but getting slower and that means that the acceleration is upwards in case two i have a more complicated situation from a force perspective the number of forces and i have a force at an angle but if you look at the relative lengths of everything this situation is actually a balance situation so the object's not accelerating again perhaps it's moving with a constant velocity the fact that there's friction and maybe it's a sliding friction kinetic friction to the left means that the object has a relative slide to the right so the object could be sliding with a constant velocity to the right and still have this picture so let's put all of that information together into some practice okay you can read the situation blake is accelerating his little sister and the first thing we're going to do is take a look at different representations so the first one is a free body diagram with all these forces acting so can you pick out the uh the clear forces first which one would you put first i think most people take the force of gravity again focus on sister on the sled right the sister sled is our system here so we want to draw the forces on the object we actually don't care about the forces on blake unless that happened to be the free body diagram that we wanted to draw so the force of gravity i'd say stiff start with that one that's a nice one to begin with a lot of people put the normal force second and they draw that the normal force will be going upwards ground is pushing the sled up okay i'm satisfied that we have the direction right with that one any other forces that you've come up with well there's a string so the string is pulling the sled and we know the sled is moving it's sliding to the left so there's tension sorry there's yeah there's tension and there's friction so now i've put all my forces there after you draw a free body diagram take a look at it carefully and ask yourself if it makes sense in terms of what you know about acceleration i've made a common mistake here that i think a lot of people do i made the force of the force of gravity equal to normal force because again i think a lot of people just assume that it is in in these kinds of situations but this looks like there is more force upwards than there is downwards and the sister is not accelerating upwards so i can't draw my gravitational force and i know that that's going downwards at a certain amount so i know that the upwards forces have to balance that force of gravity so i had to shorten my normal force it's okay if you make a mistake erase your forces and draw them to the proper lengths but i think it's important that you go back and do that um and not steer yourself in the wrong direction with your free body diagram okay here's an argumentation type problem that we come across in free response questions sometimes there's multiple multiple effects that of something might have on a different situation so in this case the question talks about the angle of the tension being a little bit steeper than it was initially and how would that affect different forces otherwise at other places in the free body diagram so angela suggests that increasing this will decrease the acceleration of the sled is there a reason that increasing this angle might decrease the acceleration of the sled carlos suggests that the increased angle would increase the acceleration of the sled is that possible sure now both of these things are possible you can explain why each of those might be the answer obviously only one of them is going to be the answer but you don't have to figure the problem out to that extent you just need to explain why each of these people are justified with their comments so let's start with angela if we increase the angle why might the acceleration decrease well this one gets back into components if you increase the angle you've decreased the horizontal component of the normal force since the acceleration is to the left that would decrease the acceleration to the left so there's a good reason that angela has for for her answer to justify that it's a decreased acceleration does increasing the angle change any of the other forces well what does this do to the vertical force it increasing the angle increases the tension's vertical force which would decrease the normal force does the normal force influence the force of friction we know it does based on the friction equals the coefficient times the normal force so by increasing the angle and decreasing the normal force you've actually decreased the friction so you see there's two effects that we have to really try to solve if we want to know if the acceleration increased or decreased but carlos is right in thinking that the force of friction has gone down and maybe the acceleration will increase okay another part of this free response question could be the analysis so here's our derivation of the original situation what's the force that the ground exerts on the system right the normal force well we have to go back to something that we did yesterday right we need to define our reference frame i'm going to call to the left positive because that's the direction of our acceleration and i know that's the direction of our net force i'm going to take a look at tension and resolve that into its two components in a different picture i'm not going to do this on my free body diagram because often there's just too much going on in a free body diagram so i know that there's two components of tension the x component and the y component based on the angle that the string makes with the horizontal the x component is ft cosine theta the y component is ft sine theta since the forces are balanced in the vertical direction i know that the two upwards forces the normal force and ft cosine theta have to balance out the force of gravity so i'll just try to make my expression nice and simple at first without any substitutions right and do exactly what i what i said in the sentence right the normal force plus the vertical force of tension minus fg equals zero and since we want to solve for the normal force i'll just do some algebra move things around and then i'll substitute in the terms i know for the different forces so the force of gravity we know is mg and the tension is ft sine theta for the y component of tension so we have our normal force the second question says well what's the force of friction well we know that the force of friction is mu times the normal force so i guess it's good that they asked us part one to find the normal force this leads me to some test taking strategy you really can't get too correct without getting part one correct however if you got part one wrong and you identified well there's the relationship between the force of friction um and the normal force if you just substituted in your answer to part one and multiply that by the coefficient of friction you would get partial credit at least for answering part two even though maybe you got part one incorrect so again don't stop a problem at the beginning if you can't get the first answer keep going come up with the best answer you can and then try to make as many true statements as you can for parts two and three etc so that you can get partial credit for the the other responses okay so now we have our friction term we have our normal force term and the last question asks about the acceleration let me go back to my original picture we know the acceleration is to the left so i'm looking for the net force to the left there are two horizontal forces so as i look at newton's second law f equals m a in the x direction i know that the left force is the tension in the x direction but i know that friction opposes that acceleration it's going in the right so minus my force of friction and set that equal to m a now i have to do a little substitution based on the other terms that i've already solved for but i know that my x component f t cosine theta minus the force of friction which is that big term that we got in part two divided by the mass has to be the acceleration so that was a long quantitative analysis let's take a look at a multiple choice question oftentimes when we have multiple objects students get flustered about what to do and and how to treat the problem so i wanted to include a multiple choice question with three objects so if you notice there's a 36 newton force pushing it's an external force if we think about these three blocks as our system so this 36 newtons is is pushing block a and block a is pushing block c and block b is pushing block c you'll notice one of the choices is 36 newtons and a lot of people think well okay so if there's this 36 newton force everything is being pushed by a 36 newton force based on what's next to it and that's not true in order to do a problem that has multiple objects you might need to make three free body diagrams all of these objects are accelerating to the right they all have the same acceleration so they all have a net force to the right but they all have very different free body diagrams i think c is the easiest block c only has block b pushing it right again i could call that the normal force that block b pushes block c or here is where i want to go into that second definition of forces that forces our interactions between two objects so instead of calling this a normal force i'm going to call it the force that block b pushes c or fbc okay let's go back to block a so block a has the 36 newton force pushing it forwards but it's also being pushed back because b has a surface and b is pushing block a back and i'm going to call that the force of block b on a or fba here's where these interactions become a useful way of looking at these forces if i look at block b i know that block a is pushing b to the right and c is pushing b to the left but by looking at these as interactions i know that the force of a on b is the same as the force of b on a this is newton's third law every action has an equal and opposite reaction so i'm dropping newton's third law into the discussion right here a lot of these forces are equal and opposite to each other right the force that b has on c is an action reaction pair with the force that c has on b so even though it looks like there are four different forces between the blocks there's really only two so now that i've drawn my free body diagram and i know that my accelerations of each are to the right each of them has a statement from newton's second law object a has a net force to the right of 36 minus the force of b on a and that's got to equal a's mass times its acceleration so it equals 6a i'm going to make the same statement for b right the net force on b equals the mass b times its acceleration and since accelerating to the right it's the force of a on b minus the force of c on b equals 2a the mass of a times a and i'm going to make the same statement for it block c again c is the easiest it only has one force on it b on c and that equals 4a so i'm getting closer to my answer so now i have three equations for what one equation for each of the three blocks and i have to relate them to each other so then one nice thing that you can do with equations like this is just put them in a column and add them up a lot of these internal forces will actually cancel out because we know that the force of a on b equals the force of b on a and i have the opposite signs so as i add these three equations up with each other i'm going to get 36 as my only term on the left hand side equals the sum of the masses 6 and 2 and 4 equals 12a and it's a quick calculation to figure out that the acceleration is 3 meters per second squared i could have gotten that answer a little quicker by combining all of these masses as a system and said oh yeah the total mass in the system is 12 kilograms and the only external force is the 36 newtons so i could have gotten this last step by using a systems approach but sometimes the systems approach isn't always easy so i want to make sure that i have a method in terms of individual objects of finding the accelerations and net forces and another way of kind of relating these accelerations but if you like the systems approach feel free to do that another note just before i finish this up is i did not include the force of gravity and the normal force from the table in my free body diagrams because i was really just looking for the horizontal motion and there was no friction so there's no other reason to have these horizontal sorry the vertical forces drawn here again you only have a minute for the multiple choice questions so if there's simplifications you can make and still get the correct answer you probably want to do that okay going back to this problem where the acceleration is 3 now i can go back to plugging in some of these original expressions so i know that the force of b on c is 4 times 3 it's 12 newtons that helps me figure out when i look at object b from its equation that f a b minus 12 because that's the same as force of c b has to equal 2a and so we can figure out that our force of a on b is 18 newtons again you can do a quick check the 18 newtons forwards and the 12 newtons back on b gives you a net force of 6 and a net force of 6 for a 2 kilogram object is going to accelerate that object at 3 meters per second squared so as i mentioned let's break out newton's third law a little bit more it's it's a statement not about the motion but more about the nature of forces themselves they are interactions between two objects even the simple force of the force of gravity which we've only talked about as fg is the interaction between earth and the object or any other planet and an object they're always about the interaction between two objects make up the action reaction pair the easy way of identifying action reaction pairs is you can just switch the order of the objects right so if you use the phrase the force of object a pulls or pushes b then the reaction is the force with which b pulls or pushes a if you just change the objects you have your action reaction pair which really helps you identify when it's not an action reaction pair again i think the most common misconception is the normal force and gravity are action reaction pairs uh they can't be right the earth pulls the object down and the ground pushes the object up that doesn't sound like an action reaction pair it's not action reaction pairs are always equal and opposite normal force could be equal and opposite to the gravitational force but that doesn't make it an action reaction pair another way that you can identify when it is or not when it's not an action reaction pair is when you're drawing a free body diagram for an object you're never going to have an action reaction pair on that object only one of the forces in an action reaction pair can actually act on the object in your free body diagram so what are the key points to take away again go back to that key question ask yourself is the object accelerating if you have the direction of the acceleration then you're well on your way to solving these problems draw a free body diagram based on all the forces that you have in this situation that you're dealing with try to make your free body diagrams as accurate as possible when you finish now that's a good time to double check does it look like my free body diagram like my forces are balanced or unbalanced again that's something on a free response question that may may count as points for you if you recognize the relative lengths of these forces and finally you're going to relate your statement of newton's second law f equals m a to the net force and the acceleration of the object if you have components be careful to use the components in the appropriate directions as part of that newton's second law statement thank you and looking forward to seeing you tomorrow when we're going to talk more about net forces but for a different type of motion you