Newton's Laws of Motion

in this video we're going to talk about newton's law of motion and there's three laws that we're going to go over let's talk about the first law so what exactly does newton's first law of motion state well one part states this an object at rest will remain at rest unless acted on by a force particularly an imbalanced force so let's say if we have a surface and if there's a box on the surface if we don't apply a force this box will not move all the forces that are currently acting on this box cancel they're balanced forces for example you have the weight force of the box let's say the box has a mass of 10 kilograms to calculate the weight force it's equal to m times g m is the mass in kilograms g is the gravitational acceleration so m is 10 kilograms g is 9.8 meters per second squared that is the acceleration due to gravity so the weight force is simply 10 times 9.8 so it's equal to 98 newtons the gravity exerts a downward weight force on any object now the block is not accelerating downward it's at rest so there must be some other force that keeps it at rest the force that the ground exerts on the box is known as the normal force and it has to balance the weight force in order to keep the block where it is and so the normal force is also 98. so as you can see these are balanced forces the net force on this box is equal to zero and so it remains at rest unless we apply an unbalanced force then the block may begin to move we may have to overcome static friction but if we apply force then it can move so an object at rest will remain at rest unless acted on by net force so that's the first part of newton's first law of motion now what about the second part of it newton's second law also states that an object in motion will continue in motion unless acted on by a net force it's basically a statement of the law of inertia now let's think about this let's say if we have a surface with let's say it's a rough surface let's use a carpet for example if you try to roll a ball on a carpet for the most part the ball is going to quickly come to a stop it's not going to move very far and the reason why that happens even though this object is in motion there's a lot of friction between the surface of the ball and the carpet and friction opposes motion and so because there's a net force this object will not continue in motion it's going to come to rest and that's what we see in real life if you roll a ball eventually comes to a stop it doesn't continue forever but newton's first law of motion states that an object in motion will continue in motion unless acted on by force now if you think about it what will happen if we can get rid of friction will the object continue to move forever now imagine if you have a smooth surface let's say like ice now if we take a puck and slide it across the ice it's going to move for a very very large distance it's not going to come to a rest like the ball on the carpet the ball in the carpet is going to stop after a very short distance but this puck is going to slide across the ice for a long time now let's say if we use a ball and we roll it on ice let's say if you put it on a frozen lake and you roll it across the lake it's going to roll for a very very long time until it comes to rest it's going to take a long time for it to come to rest now why is that why is it that if we roll a ball on a rough surface it takes a very short time to come to rest it comes to stop it comes to a stop quickly but if you take a ball and put it on the icy surface it will roll for a longer time the reason for that is because there's more friction between a ball and a rough carpet but between the ball and the icy surface there's less friction and so because there's less friction this ball will continue to travel for a much longer time now what's going to happen if we can completely get rid of friction will the object continue to move forever think about it now keep this in mind even though there's very little friction between the icy surface and the ball you also have air resistance as the ball is moving forward the air molecules can slow it down so you have air resistance and if it's moving fast this can be air drag as well but where can we find a place where there's virtually no friction the best place where there's almost no friction is outer space in outer space there's virtually no air it's almost non-existing might have a few molecules here and there but for the most part the pressure is extremely extremely low if you think about it we know that the earth revolves around the sun and the earth is an object in motion and the earth has been revolving around the sun for a very very very long time millions perhaps billions of years and it continues to keep moving and it makes sense because in space there's virtually no friction it's not enough to slow the earth down and so it continues to move in its orbit and thus we can see newton's first law of motion in action here an object in motion will continue in motion unless acted on by a net unbalanced force now you might be wondering all this information is great but how can i apply this information in a problem how will i see a question on a test well there's some things that you need to know if an object remains at rest then that force acted on the object is equal to zero make sure you understand that concept the second thing is if an object is in motion let's say if it's moving with constant velocity then the net force acting on that object is equal to zero make sure you understand that if the net force is not zero then there is a net acceleration but when the net force is zero the acceleration in that direction is also equal to zero which means that the velocity is constant keep in mind acceleration is defined as the change in velocity that is the final velocity minus the initial velocity divided by the change in time so our constant velocity v f and v o will be the same if you take a number and subtract it by the same number you're going to get zero so in constant velocity v f minus v o is zero zero over t is zero now according to newton's second law the net force is equal to the product of the mass and the acceleration so if the acceleration is constant and if you increase the mass of the object the net force will increase so the net force is proportional to the mass of the object now let's say if you keep the mass constant and if you increase the magnitude of the acceleration the net force will increase as well so the net force is also directly proportional to the acceleration now what if we keep the net force constant what is the relationship between the mass and acceleration if you increase the mass the acceleration will decrease provided if the force remains the same if you decrease the mass the acceleration will increase under constant force conditions now let's put some numbers to it if you double the mass while keeping the acceleration constant what effect will it have on the force by what factor will the force increase by to answer these questions simply plug in the values if you double the mass replace it with two if the acceleration is held constant replace it with one so the force will increase by a factor of two if we triple the mass and keep the acceleration constant the force will increase by a factor of three now what if we double the acceleration and triple the mass what effect will it have on the force so if you triple the mass and double the acceleration three times to a six the force will increase by a factor of six if you quadruple the mass triple the acceleration the force will increase by a factor of 12. so newton's second law basically states that the net force is equal to the mass times the acceleration now you can also describe newton's second law of motion using something else so let's start with the equation f is equal to ma that is the net force is equal to the mass times the acceleration now we said that the acceleration is the change in velocity v final minus v initial which we can write as delta v the triangle represents change is the change in velocity divided by the change in time so delta v over delta t is the same as saying v final minus v initial over t where this t represents a change in time now what is mass times velocity mass multiplied by velocity is equal to momentum indicated by the symbol lowercase p momentum is mass in motion an object at rest has zero momentum an object that's moving has momentum so let's say if here's the question for you which object has more momentum a car moving at 30 miles per hour or a train moving at 30 miles per hour if both objects are moving with the same speed then the one that has more mass will have more momentum the train has a lot of momentum it's very difficult to stop a train it's much easier to stop a car than a train so momentum is the product of mass and velocity so an object with a lot of mass and with a lot of speed has a lot of momentum now if mv is equal to p then that means that m delta v has to be equal to delta p that is the change in momentum so let's replace this term with delta p so we could say that the net force is equal to the rate of change of the momentum respect to time so this is another variation of newton's second law the net force is the change in momentum divided by the change in time by the way if you start from this equation and if you multiply both sides by delta t you're going to get another important theorem the force multiplied by the change in time is equal to the mass times the change in velocity the product of the force and the time is known as impulse and mass times the change in velocity is known as the change in momentum so this is known as the impulse momentum theorem the impulse is equal to the change in momentum now what about newton's third law of motion what exactly does that state the third law states that for every action there is an equal and opposite reaction so f a is equal to negative fb so if you apply a force there's going to be a reaction force applied to you both forces will have the same magnitude but the direction of the two forces will be opposite to each other so let's go through some examples let's say if a person jumps in the air and throws a basketball as the basketball moves in that direction he applies a force on it but he also while in the air he's going to move back so there's like a recoil force applied to him now because the mass of the ball is less than the mass of the person the ball is going to travel a further distance away from the person because the ball will experience a greater acceleration remember for the same force if you decrease the mass the acceleration increases these two are inversely related but the force exerted on the ball and on the person is the same so let's put numbers to this so you can see how it works so let's say the ball has a mass of two kilograms and the person has a mass of 80 kilograms actually let's say 100 100 is a nice number now let's say that the person applies a force of 200 newtons on a ball the person is going to fill a reaction force of 200 newtons in the opposite direction now what is the acceleration of the person and the ball now we know that according to newton's second law f is equal to m a so the acceleration is the force divided by the mass so if we take 200 divided by 2 the acceleration will be equal to positive 100 meters per second squared now for the person 200 divided by 100 is only two so the acceleration is negative two meters per second squared acceleration is a vector and vectors have magnitude and direction because the person feels a force directed towards the left his force should be negative and therefore his acceleration is negative force and acceleration and velocity are vector quantities direction is important speed is a scalar quantity speed has magnitude only but as you can see the object with less mass experiences a much larger acceleration the person with more mass experiences a smaller acceleration however the forces are equal according to newton's third law for every action force there is an equal but opposite reaction force now here's another situation imagine if you're in the ocean on a boat let's say this is you and you have a ball in your hand now i want you to imagine the situation so just think of yourself being on the ball in the ocean and if you throw the ball towards the right what do you think is going to happen to you and the boat in what direction will you move now intuitively you know that if you apply a force to throw the ball towards the right you're going to feel a force that's going to push you and the ball towards the left but because the ball has less mass it will have a greater acceleration and so it's going to travel a greater distance now because the combined mass of you and the boat is so much more larger than the ball you won't feel the acceleration as much you might move a little but the distance that the boat moves towards the left is insignificant towards the right but it does move according to newton's third law for every action force there is an equal and option reaction force now let's go over one more example so let's say this is the earth and over here we have the moon which is much smaller than the earth and let's say you're an astronaut somewhere in space and you have a ball in your hand okay let's redraw the picture my drawn is terrible i didn't want to draw the stick figure too big but sometimes bigger is better so this person has the ball on his hand now he's in space floating in space imagine if you're this person and you're floating in space now you don't want to drift deep into outer space you want to get back to planet earth in what direction should you throw the ball now remember you want to throw the ball in a certain direction so that you will be accelerated towards the earth so here are your options do you want to throw the ball in this direction towards the moon towards the earth or above you where should you throw the ball now if you throw the ball let's say towards the earth you're going to feel a force that's going to push you towards the moon which is not where you want to go if you throw the ball south with you you're going to feel a force that's going to push you away from the earth and the moon maybe towards the sun which is not good either so what you want to do is you want to throw the ball towards the moon because if you throw this way you're going to feel an opposite force that will push you this way that is towards the earth and so once you throw the ball away from the earth you're gonna feel a force that's gonna push you towards the earth and while you're in space there's not much friction so the velocity that you acquired as you throw the ball towards the right that velocity will remain constant and so you'll slowly fall towards the earth getting back to where you belong so understanding that principle can help you to travel in space if you want to go towards the moon throw the ball towards the earth and you're going to be pushed towards the moon so basically whatever direction you want to go throw the ball opposite in that direction so if you want to go north throw the ball south if you want to go east throw the ball west and vice versa so now we're going to work on some problems feel free to pause the video and work on each problem that you see from this point on a car travels on the road with a constant velocity what is the horizontal net force acting on the car so what do you think the answer is to that question what is the net force now if you recall anytime an object is moving with constant velocity the net force is always equal to zero now what about the acceleration of the car well according to newton's second law f is equal to ma so if the force is zero the acceleration must also be equal to zero now part c if the frictional force acted on the car is 1500 newtons what force is applied to the car by the engine so let's draw a picture i'm just going to draw a box because it's easy to draw and this box represents the car so let's say the car is moving to the right so v represents the velocity where it's going friction opposes motion so the frictional force is 1500 newtons now the net force is zero which means that the applied force has to be 1500 newtons these two forces cancel out so the net force is zero and therefore the acceleration is zero and if the acceleration is zero the velocity is constant keep in mind acceleration is the rate of change of velocity if the velocity changes then there's an acceleration if the acceleration is zero the velocity will not change a force of 200 newtons is applied on a 10 kilogram box across the frictionless surface that is a horizontal frictional surface what is the acceleration of the box so let's draw a picture and here is the 10 kilogram box and we're going to apply a force of 200 units so to calculate the acceleration we can use this equation f is equal to ma so f divided by m is a the force is 200 newtons the mass is 10 kilograms 200 divided by 10 will give us an acceleration of 20 meters per second squared now what about part b if the box accelerates from rest what will its final speed be after 8 seconds the acceleration tells you how much the speed changes every second so let's make a table so initially the velocity or the speed is zero every second that passes the speed will increase by 20. so one second later it's going to be 20 two seconds later 40 three seconds later 60 four seconds later 80 and i'm going to continue the table here let's see if i can fit in five seconds later it's going to be a hundred six seconds later 120 seven seconds later 140 8 seconds later 160. so after eight seconds the speed of the box will be 160 meters per second now the equation that you can use to calculate this answer is this equation we're looking for the final speed vf the initial speed vo is zero because it started from rest the acceleration is 20 the time is eight twenty times eight if you have eight twenty dollar bills how much money do you have eight twenty dollar bills is 160 so 20 times 8 is 160 so you get 160 meters per second now what about part c how long will it take the box to reach a speed of 500 meters per second if it continues to accelerate at this rate so starting from a speed of zero a is 20 let's solve for t the final speed is 500 so we got to divide both sides by 20. so what is 500 divided by 20 well we can cancel zero so becomes 50 divided by 2 half of 50 is 25. so it's going to take 25 seconds for the box to accelerate from rest to a speed of 500 meters per second a force of 300 newtons is applied across a 20 kilogram box the frictional force acting on the box is 200 newtons what is the net horizontal force on the box so let's begin so we have an applied force of 300 newtons so let's call it a capital f and there's a frictional force of 200 newtons so then that force is in this direction then that force is simply the difference between the two forces so it's 100 newtons directed towards the right if these two forces are in their respective positions now what is the acceleration of the box once you have the net force you can use this equation f equals ma to find the acceleration so the acceleration is the net force of 100 divided by the mass of the box so the acceleration is 5 meters per second squared now what about part c how far will the box travel after 12 seconds if it continues to accelerate at this rate starting from rest so the initial speed is 0 if it starts from rest the time is 12 seconds our goal is to find the distance traveled so we're looking for d what equation has v initial t d and a so make sure you review your kinematics equation you never know when those equations will be helpful the equation that you need is the displacement is equal to the initial speed multiplied by the time plus one half a t squared the initial speed is zero the acceleration is five and the time is twelve and let's not forget to square it so we have a half times five times twelve times twelve a half times twelve is six six times five is thirty and thirty times twelve if we multiply 30 by 10 that's 300 30 times 2 is 60 so 30 times 12 is 360. so this particular box is going to travel 360 meters before it's going to travel 360 meters in 12 seconds that's what i wanted to say an 8 kilogram object speeds up from 20 meters per second to 50 meters per second in six seconds what is the acceleration to find the acceleration you can use this equation perhaps you've seen the same equation written this way a is equal to v final minus v initial divided by t these two equations are the same but you can solve for a and it's going to look like that so let's use the equation on the right side so the acceleration is the change in velocity so 50 minus 20 divided by the time which is 6. 50 minus 20 is 30. 30 divided by 6 is 5. so the acceleration is 5 meters per second squared now part b what is the net horizontal force acting on the object the net force is simply the product of the mass and acceleration so the mass is eight the acceleration is five the net force is 40 newtons now what about part c if the frictional force is 35 newtons what is the applied force so here's the frictional force the net force is 40 newtons what number minus 35 is 40 the applied force has to be 75 as you can see 75 minus 35 is 40. in order for the object to accelerate the applied force has to be greater than 35 it can be less to get the applied force you have to add 35 plus 40 and that will give you 75. if you subtract 35 and 40 you'll get negative 5 and that's not going to be the applied force an 80 kilogram astronaut in space throws a two kilogram package with an acceleration of positive four meters per second squared what force did the astronaut exert on a package so let's draw a picture so let's say this is the astronaut he's in space and he throws the package towards the right the mass of the package is 2 kilograms the mass of the astronaut is 80 kilograms and the package has an acceleration of four meters per second squared to calculate the force that the astronaut exerted on a package we can use this equation f is equal to ma the package has a mass of 2 and an acceleration of 4. so the force applied to it is 8 newtons now what force does the package exert on the astronaut well according to newton's third law for every action force there is an equal but opposite reaction force so if 8 newtons of force was exerted on a package eight newtons of force will be exerted on the astronaut but because it's in the opposite direction let's put a negative sign to it now let's calculate the acceleration so the acceleration is the force divided by the mass so negative 8 divided by 80 is negative 0.1 so this is the acceleration acting on the astronaut as you can see the object with less mass has a larger acceleration whenever the force is constant which it is as you can see these two forces are the same according to newton's third law now for the object with the larger mass it experiences a much smaller acceleration the 80 kilogram person has more mass than the 2 kilogram package and so the acceleration of the 80 kilogram person is much less than the acceleration of the package point one is much less than four a 120 kilogram skater pushes against an 80 kilogram skater after contact the 80 kilogram skater was given an acceleration of 1.5 meters per second squared what is the acceleration of the 120 kilogram scada well according to newton's third law for every action force there is an equal and opposite reaction force so f a equals negative f b so f a we're just going to say is the mass times the acceleration let's say m1 times a1 fb let's call it m2 times a2 now all we got to do is plug in the information the mass of the heavy skater is 120 kilograms we don't know the acceleration of the heavy skater we need to find it the mass of the light skater is 80 kilograms and his acceleration is 1.5 now 80 times 1.5 is 120. and if we divide both sides by 120 we can see that the acceleration of the 120 kilogram skater is negative one the negative sign simply tells you that his acceleration is opposite to the other skater but since he has a larger mass his acceleration should be less than the skater with less mass the scatter with less mass will experience a larger acceleration now what force was exerted on each skater to calculate the force is simply f is equal to ma so we can multiply the mass of the 120 kilogram skater by negative one that will give us a force of negative 120 or we could take the mass of the 80 kilogram skater and multiply by his acceleration of 1.5 which is also 120 but positive so these two forces they're equal in magnitude but opposite in direction so what we're going to do now is a quick review of everything that we've learned so newton's first law of motion an object at rest will continue to be at rest unless acted on by a net force or an unbalanced force also an object in motion will continue in motion unless acted on by net force so keep this in mind if an object is moving with a constant velocity the acceleration is zero and therefore the net force acting on the object is zero and the reverse statement is true if the net force is zero then the object has a constant velocity and also constant speed now newton's second law f is equal to m a the net force is the product of the mass times the acceleration whenever the force is constant if you increase the mass the acceleration decreases and if you decrease the mass the acceleration increases so heavy objects don't move much the light objects are easy to push they will it's easy to give a light object a large acceleration heavy objects tend to have small accelerations so this equation describes newton's second law now newton's third law every action force for every action force i'm going to say there's an equal but opposite reaction force so you could say m1 times a1 is equal to negative m2 times a2 and so that is it for this video now if you want to find more physics videos feel free to check out my channel or even take a look at my website video dash tutor.net i have all of my playlists listed there you can find playlists on general chemistry organic chemistry physics algebra trig precal and even calculus plus some other stuff too so you can check that out so if you like this video feel free to comment below subscribe share it with your friends and that's about it so thanks for watching and have a great day

in this video we&#39;re going to talk about newton&#39;s law of motion and there&#39;s three laws that we&#39;re going to go over let&#39;s talk about the first law so what exactly does newton&#39;s first law of motion state well one part states this an object at rest will remain at rest unless acted on by a force particularly an imbalanced force so let&#39;s say if we have a surface and if there&#39;s a box on the surface if we don&#39;t apply a force this box will not move all the forces that are currently acting on this box cancel they&#39;re balanced forces for example you have the weight force of the box let&#39;s say the box has a mass of 10 kilograms to calculate the weight force it&#39;s equal to m times g m is the mass in kilograms g is the gravitational acceleration so m is 10 kilograms g is 9.8 meters per second squared that is the acceleration due to gravity so the weight force is simply 10 times 9.8 so it&#39;s equal to 98 newtons the gravity exerts a downward weight force on any object now the block is not accelerating downward it&#39;s at rest so there must be some other force that keeps it at rest the force that the ground exerts on the box is known as the normal force and it has to balance the weight force in order to keep the block where it is and so the normal force is also 98. so as you can see these are balanced forces the net force on this box is equal to zero and so it remains at rest unless we apply an unbalanced force then the block may begin to move we may have to overcome static friction but if we apply force then it can move so an object at rest will remain at rest unless acted on by net force so that&#39;s the first part of newton&#39;s first law of motion now what about the second part of it newton&#39;s second law also states that an object in motion will continue in motion unless acted on by a net force it&#39;s basically a statement of the law of inertia now let&#39;s think about this let&#39;s say if we have a surface with let&#39;s say it&#39;s a rough surface let&#39;s use a carpet for example if you try to roll a ball on a carpet for the most part the ball is going to quickly come to a stop it&#39;s not going to move very far and the reason why that happens even though this object is in motion there&#39;s a lot of friction between the surface of the ball and the carpet and friction opposes motion and so because there&#39;s a net force this object will not continue in motion it&#39;s going to come to rest and that&#39;s what we see in real life if you roll a ball eventually comes to a stop it doesn&#39;t continue forever but newton&#39;s first law of motion states that an object in motion will continue in motion unless acted on by force now if you think about it what will happen if we can get rid of friction will the object continue to move forever now imagine if you have a smooth surface let&#39;s say like ice now if we take a puck and slide it across the ice it&#39;s going to move for a very very large distance it&#39;s not going to come to a rest like the ball on the carpet the ball in the carpet is going to stop after a very short distance but this puck is going to slide across the ice for a long time now let&#39;s say if we use a ball and we roll it on ice let&#39;s say if you put it on a frozen lake and you roll it across the lake it&#39;s going to roll for a very very long time until it comes to rest it&#39;s going to take a long time for it to come to rest now why is that why is it that if we roll a ball on a rough surface it takes a very short time to come to rest it comes to stop it comes to a stop quickly but if you take a ball and put it on the icy surface it will roll for a longer time the reason for that is because there&#39;s more friction between a ball and a rough carpet but between the ball and the icy surface there&#39;s less friction and so because there&#39;s less friction this ball will continue to travel for a much longer time now what&#39;s going to happen if we can completely get rid of friction will the object continue to move forever think about it now keep this in mind even though there&#39;s very little friction between the icy surface and the ball you also have air resistance as the ball is moving forward the air molecules can slow it down so you have air resistance and if it&#39;s moving fast this can be air drag as well but where can we find a place where there&#39;s virtually no friction the best place where there&#39;s almost no friction is outer space in outer space there&#39;s virtually no air it&#39;s almost non-existing might have a few molecules here and there but for the most part the pressure is extremely extremely low if you think about it we know that the earth revolves around the sun and the earth is an object in motion and the earth has been revolving around the sun for a very very very long time millions perhaps billions of years and it continues to keep moving and it makes sense because in space there&#39;s virtually no friction it&#39;s not enough to slow the earth down and so it continues to move in its orbit and thus we can see newton&#39;s first law of motion in action here an object in motion will continue in motion unless acted on by a net unbalanced force now you might be wondering all this information is great but how can i apply this information in a problem how will i see a question on a test well there&#39;s some things that you need to know if an object remains at rest then that force acted on the object is equal to zero make sure you understand that concept the second thing is if an object is in motion let&#39;s say if it&#39;s moving with constant velocity then the net force acting on that object is equal to zero make sure you understand that if the net force is not zero then there is a net acceleration but when the net force is zero the acceleration in that direction is also equal to zero which means that the velocity is constant keep in mind acceleration is defined as the change in velocity that is the final velocity minus the initial velocity divided by the change in time so our constant velocity v f and v o will be the same if you take a number and subtract it by the same number you&#39;re going to get zero so in constant velocity v f minus v o is zero zero over t is zero now according to newton&#39;s second law the net force is equal to the product of the mass and the acceleration so if the acceleration is constant and if you increase the mass of the object the net force will increase so the net force is proportional to the mass of the object now let&#39;s say if you keep the mass constant and if you increase the magnitude of the acceleration the net force will increase as well so the net force is also directly proportional to the acceleration now what if we keep the net force constant what is the relationship between the mass and acceleration if you increase the mass the acceleration will decrease provided if the force remains the same if you decrease the mass the acceleration will increase under constant force conditions now let&#39;s put some numbers to it if you double the mass while keeping the acceleration constant what effect will it have on the force by what factor will the force increase by to answer these questions simply plug in the values if you double the mass replace it with two if the acceleration is held constant replace it with one so the force will increase by a factor of two if we triple the mass and keep the acceleration constant the force will increase by a factor of three now what if we double the acceleration and triple the mass what effect will it have on the force so if you triple the mass and double the acceleration three times to a six the force will increase by a factor of six if you quadruple the mass triple the acceleration the force will increase by a factor of 12. so newton&#39;s second law basically states that the net force is equal to the mass times the acceleration now you can also describe newton&#39;s second law of motion using something else so let&#39;s start with the equation f is equal to ma that is the net force is equal to the mass times the acceleration now we said that the acceleration is the change in velocity v final minus v initial which we can write as delta v the triangle represents change is the change in velocity divided by the change in time so delta v over delta t is the same as saying v final minus v initial over t where this t represents a change in time now what is mass times velocity mass multiplied by velocity is equal to momentum indicated by the symbol lowercase p momentum is mass in motion an object at rest has zero momentum an object that&#39;s moving has momentum so let&#39;s say if here&#39;s the question for you which object has more momentum a car moving at 30 miles per hour or a train moving at 30 miles per hour if both objects are moving with the same speed then the one that has more mass will have more momentum the train has a lot of momentum it&#39;s very difficult to stop a train it&#39;s much easier to stop a car than a train so momentum is the product of mass and velocity so an object with a lot of mass and with a lot of speed has a lot of momentum now if mv is equal to p then that means that m delta v has to be equal to delta p that is the change in momentum so let&#39;s replace this term with delta p so we could say that the net force is equal to the rate of change of the momentum respect to time so this is another variation of newton&#39;s second law the net force is the change in momentum divided by the change in time by the way if you start from this equation and if you multiply both sides by delta t you&#39;re going to get another important theorem the force multiplied by the change in time is equal to the mass times the change in velocity the product of the force and the time is known as impulse and mass times the change in velocity is known as the change in momentum so this is known as the impulse momentum theorem the impulse is equal to the change in momentum now what about newton&#39;s third law of motion what exactly does that state the third law states that for every action there is an equal and opposite reaction so f a is equal to negative fb so if you apply a force there&#39;s going to be a reaction force applied to you both forces will have the same magnitude but the direction of the two forces will be opposite to each other so let&#39;s go through some examples let&#39;s say if a person jumps in the air and throws a basketball as the basketball moves in that direction he applies a force on it but he also while in the air he&#39;s going to move back so there&#39;s like a recoil force applied to him now because the mass of the ball is less than the mass of the person the ball is going to travel a further distance away from the person because the ball will experience a greater acceleration remember for the same force if you decrease the mass the acceleration increases these two are inversely related but the force exerted on the ball and on the person is the same so let&#39;s put numbers to this so you can see how it works so let&#39;s say the ball has a mass of two kilograms and the person has a mass of 80 kilograms actually let&#39;s say 100 100 is a nice number now let&#39;s say that the person applies a force of 200 newtons on a ball the person is going to fill a reaction force of 200 newtons in the opposite direction now what is the acceleration of the person and the ball now we know that according to newton&#39;s second law f is equal to m a so the acceleration is the force divided by the mass so if we take 200 divided by 2 the acceleration will be equal to positive 100 meters per second squared now for the person 200 divided by 100 is only two so the acceleration is negative two meters per second squared acceleration is a vector and vectors have magnitude and direction because the person feels a force directed towards the left his force should be negative and therefore his acceleration is negative force and acceleration and velocity are vector quantities direction is important speed is a scalar quantity speed has magnitude only but as you can see the object with less mass experiences a much larger acceleration the person with more mass experiences a smaller acceleration however the forces are equal according to newton&#39;s third law for every action force there is an equal but opposite reaction force now here&#39;s another situation imagine if you&#39;re in the ocean on a boat let&#39;s say this is you and you have a ball in your hand now i want you to imagine the situation so just think of yourself being on the ball in the ocean and if you throw the ball towards the right what do you think is going to happen to you and the boat in what direction will you move now intuitively you know that if you apply a force to throw the ball towards the right you&#39;re going to feel a force that&#39;s going to push you and the ball towards the left but because the ball has less mass it will have a greater acceleration and so it&#39;s going to travel a greater distance now because the combined mass of you and the boat is so much more larger than the ball you won&#39;t feel the acceleration as much you might move a little but the distance that the boat moves towards the left is insignificant towards the right but it does move according to newton&#39;s third law for every action force there is an equal and option reaction force now let&#39;s go over one more example so let&#39;s say this is the earth and over here we have the moon which is much smaller than the earth and let&#39;s say you&#39;re an astronaut somewhere in space and you have a ball in your hand okay let&#39;s redraw the picture my drawn is terrible i didn&#39;t want to draw the stick figure too big but sometimes bigger is better so this person has the ball on his hand now he&#39;s in space floating in space imagine if you&#39;re this person and you&#39;re floating in space now you don&#39;t want to drift deep into outer space you want to get back to planet earth in what direction should you throw the ball now remember you want to throw the ball in a certain direction so that you will be accelerated towards the earth so here are your options do you want to throw the ball in this direction towards the moon towards the earth or above you where should you throw the ball now if you throw the ball let&#39;s say towards the earth you&#39;re going to feel a force that&#39;s going to push you towards the moon which is not where you want to go if you throw the ball south with you you&#39;re going to feel a force that&#39;s going to push you away from the earth and the moon maybe towards the sun which is not good either so what you want to do is you want to throw the ball towards the moon because if you throw this way you&#39;re going to feel an opposite force that will push you this way that is towards the earth and so once you throw the ball away from the earth you&#39;re gonna feel a force that&#39;s gonna push you towards the earth and while you&#39;re in space there&#39;s not much friction so the velocity that you acquired as you throw the ball towards the right that velocity will remain constant and so you&#39;ll slowly fall towards the earth getting back to where you belong so understanding that principle can help you to travel in space if you want to go towards the moon throw the ball towards the earth and you&#39;re going to be pushed towards the moon so basically whatever direction you want to go throw the ball opposite in that direction so if you want to go north throw the ball south if you want to go east throw the ball west and vice versa so now we&#39;re going to work on some problems feel free to pause the video and work on each problem that you see from this point on a car travels on the road with a constant velocity what is the horizontal net force acting on the car so what do you think the answer is to that question what is the net force now if you recall anytime an object is moving with constant velocity the net force is always equal to zero now what about the acceleration of the car well according to newton&#39;s second law f is equal to ma so if the force is zero the acceleration must also be equal to zero now part c if the frictional force acted on the car is 1500 newtons what force is applied to the car by the engine so let&#39;s draw a picture i&#39;m just going to draw a box because it&#39;s easy to draw and this box represents the car so let&#39;s say the car is moving to the right so v represents the velocity where it&#39;s going friction opposes motion so the frictional force is 1500 newtons now the net force is zero which means that the applied force has to be 1500 newtons these two forces cancel out so the net force is zero and therefore the acceleration is zero and if the acceleration is zero the velocity is constant keep in mind acceleration is the rate of change of velocity if the velocity changes then there&#39;s an acceleration if the acceleration is zero the velocity will not change a force of 200 newtons is applied on a 10 kilogram box across the frictionless surface that is a horizontal frictional surface what is the acceleration of the box so let&#39;s draw a picture and here is the 10 kilogram box and we&#39;re going to apply a force of 200 units so to calculate the acceleration we can use this equation f is equal to ma so f divided by m is a the force is 200 newtons the mass is 10 kilograms 200 divided by 10 will give us an acceleration of 20 meters per second squared now what about part b if the box accelerates from rest what will its final speed be after 8 seconds the acceleration tells you how much the speed changes every second so let&#39;s make a table so initially the velocity or the speed is zero every second that passes the speed will increase by 20. so one second later it&#39;s going to be 20 two seconds later 40 three seconds later 60 four seconds later 80 and i&#39;m going to continue the table here let&#39;s see if i can fit in five seconds later it&#39;s going to be a hundred six seconds later 120 seven seconds later 140 8 seconds later 160. so after eight seconds the speed of the box will be 160 meters per second now the equation that you can use to calculate this answer is this equation we&#39;re looking for the final speed vf the initial speed vo is zero because it started from rest the acceleration is 20 the time is eight twenty times eight if you have eight twenty dollar bills how much money do you have eight twenty dollar bills is 160 so 20 times 8 is 160 so you get 160 meters per second now what about part c how long will it take the box to reach a speed of 500 meters per second if it continues to accelerate at this rate so starting from a speed of zero a is 20 let&#39;s solve for t the final speed is 500 so we got to divide both sides by 20. so what is 500 divided by 20 well we can cancel zero so becomes 50 divided by 2 half of 50 is 25. so it&#39;s going to take 25 seconds for the box to accelerate from rest to a speed of 500 meters per second a force of 300 newtons is applied across a 20 kilogram box the frictional force acting on the box is 200 newtons what is the net horizontal force on the box so let&#39;s begin so we have an applied force of 300 newtons so let&#39;s call it a capital f and there&#39;s a frictional force of 200 newtons so then that force is in this direction then that force is simply the difference between the two forces so it&#39;s 100 newtons directed towards the right if these two forces are in their respective positions now what is the acceleration of the box once you have the net force you can use this equation f equals ma to find the acceleration so the acceleration is the net force of 100 divided by the mass of the box so the acceleration is 5 meters per second squared now what about part c how far will the box travel after 12 seconds if it continues to accelerate at this rate starting from rest so the initial speed is 0 if it starts from rest the time is 12 seconds our goal is to find the distance traveled so we&#39;re looking for d what equation has v initial t d and a so make sure you review your kinematics equation you never know when those equations will be helpful the equation that you need is the displacement is equal to the initial speed multiplied by the time plus one half a t squared the initial speed is zero the acceleration is five and the time is twelve and let&#39;s not forget to square it so we have a half times five times twelve times twelve a half times twelve is six six times five is thirty and thirty times twelve if we multiply 30 by 10 that&#39;s 300 30 times 2 is 60 so 30 times 12 is 360. so this particular box is going to travel 360 meters before it&#39;s going to travel 360 meters in 12 seconds that&#39;s what i wanted to say an 8 kilogram object speeds up from 20 meters per second to 50 meters per second in six seconds what is the acceleration to find the acceleration you can use this equation perhaps you&#39;ve seen the same equation written this way a is equal to v final minus v initial divided by t these two equations are the same but you can solve for a and it&#39;s going to look like that so let&#39;s use the equation on the right side so the acceleration is the change in velocity so 50 minus 20 divided by the time which is 6. 50 minus 20 is 30. 30 divided by 6 is 5. so the acceleration is 5 meters per second squared now part b what is the net horizontal force acting on the object the net force is simply the product of the mass and acceleration so the mass is eight the acceleration is five the net force is 40 newtons now what about part c if the frictional force is 35 newtons what is the applied force so here&#39;s the frictional force the net force is 40 newtons what number minus 35 is 40 the applied force has to be 75 as you can see 75 minus 35 is 40. in order for the object to accelerate the applied force has to be greater than 35 it can be less to get the applied force you have to add 35 plus 40 and that will give you 75. if you subtract 35 and 40 you&#39;ll get negative 5 and that&#39;s not going to be the applied force an 80 kilogram astronaut in space throws a two kilogram package with an acceleration of positive four meters per second squared what force did the astronaut exert on a package so let&#39;s draw a picture so let&#39;s say this is the astronaut he&#39;s in space and he throws the package towards the right the mass of the package is 2 kilograms the mass of the astronaut is 80 kilograms and the package has an acceleration of four meters per second squared to calculate the force that the astronaut exerted on a package we can use this equation f is equal to ma the package has a mass of 2 and an acceleration of 4. so the force applied to it is 8 newtons now what force does the package exert on the astronaut well according to newton&#39;s third law for every action force there is an equal but opposite reaction force so if 8 newtons of force was exerted on a package eight newtons of force will be exerted on the astronaut but because it&#39;s in the opposite direction let&#39;s put a negative sign to it now let&#39;s calculate the acceleration so the acceleration is the force divided by the mass so negative 8 divided by 80 is negative 0.1 so this is the acceleration acting on the astronaut as you can see the object with less mass has a larger acceleration whenever the force is constant which it is as you can see these two forces are the same according to newton&#39;s third law now for the object with the larger mass it experiences a much smaller acceleration the 80 kilogram person has more mass than the 2 kilogram package and so the acceleration of the 80 kilogram person is much less than the acceleration of the package point one is much less than four a 120 kilogram skater pushes against an 80 kilogram skater after contact the 80 kilogram skater was given an acceleration of 1.5 meters per second squared what is the acceleration of the 120 kilogram scada well according to newton&#39;s third law for every action force there is an equal and opposite reaction force so f a equals negative f b so f a we&#39;re just going to say is the mass times the acceleration let&#39;s say m1 times a1 fb let&#39;s call it m2 times a2 now all we got to do is plug in the information the mass of the heavy skater is 120 kilograms we don&#39;t know the acceleration of the heavy skater we need to find it the mass of the light skater is 80 kilograms and his acceleration is 1.5 now 80 times 1.5 is 120. and if we divide both sides by 120 we can see that the acceleration of the 120 kilogram skater is negative one the negative sign simply tells you that his acceleration is opposite to the other skater but since he has a larger mass his acceleration should be less than the skater with less mass the scatter with less mass will experience a larger acceleration now what force was exerted on each skater to calculate the force is simply f is equal to ma so we can multiply the mass of the 120 kilogram skater by negative one that will give us a force of negative 120 or we could take the mass of the 80 kilogram skater and multiply by his acceleration of 1.5 which is also 120 but positive so these two forces they&#39;re equal in magnitude but opposite in direction so what we&#39;re going to do now is a quick review of everything that we&#39;ve learned so newton&#39;s first law of motion an object at rest will continue to be at rest unless acted on by a net force or an unbalanced force also an object in motion will continue in motion unless acted on by net force so keep this in mind if an object is moving with a constant velocity the acceleration is zero and therefore the net force acting on the object is zero and the reverse statement is true if the net force is zero then the object has a constant velocity and also constant speed now newton&#39;s second law f is equal to m a the net force is the product of the mass times the acceleration whenever the force is constant if you increase the mass the acceleration decreases and if you decrease the mass the acceleration increases so heavy objects don&#39;t move much the light objects are easy to push they will it&#39;s easy to give a light object a large acceleration heavy objects tend to have small accelerations so this equation describes newton&#39;s second law now newton&#39;s third law every action force for every action force i&#39;m going to say there&#39;s an equal but opposite reaction force so you could say m1 times a1 is equal to negative m2 times a2 and so that is it for this video now if you want to find more physics videos feel free to check out my channel or even take a look at my website video dash tutor.net i have all of my playlists listed there you can find playlists on general chemistry organic chemistry physics algebra trig precal and even calculus plus some other stuff too so you can check that out so if you like this video feel free to comment below subscribe share it with your friends and that&#39;s about it so thanks for watching and have a great day

Transcript for:Newton's Laws of Motion

Transcript for:
Newton's Laws of Motion