so what's the main idea behind newton's second law of motion the basic idea behind it is that the acceleration of an object is directly proportional to the net force and it's inversely proportional to the mass of the object perhaps you've seen this equation the net force is the product of the mass and the acceleration so the acceleration is equal to the net force divided by the mass so if you increase the value of the net force the acceleration will increase now whenever you increase the numerator of a fraction the value of the entire fraction increases but when you increase the denominator of a fraction the value of the whole fraction decreases so if you increase the mass of the object the acceleration will decrease provided that the net force is constant so thus we could say that acceleration and force are directly proportional to each other and the acceleration is inversely related or inversely proportional to the mass of the object so if you double the force what's going to happen to the acceleration if you increase the net force by a factor of 2 the acceleration will double if you increase the net force by a factor of 3 the acceleration will triple now if you double the mass the acceleration will be one half of its original value so it's going to decrease by a factor of two if you triple the mass the acceleration will decrease by a factor of three so it's important that you understand that so let's say if we increase the force by a factor of four and we increase the mass by a factor of two by what factor does the acceleration change to answer a question like this just plug it into the formula so it's going to be four divided by two the acceleration will increase by a factor of two if something doesn't change replace it with a one so let's say if the force let's fix that let's say if the force increases by a factor of eight and the mass is reduced to one-half its value what's the acceleration it's going to be eight divided by a half which if you multiply the top and bottom by two this is 16 over one so the acceleration will increase by a factor of 16. so if you decrease the mass the acceleration will increase if the net force is constant now let's say if we have a box and we apply a force on this box what is the direction of the acceleration so what is the direction of the acceleration vector acceleration and the net force always act in the same direction so the acceleration is going to be in this direction now let's say if there's a five kilogram block that rests on a frictionless surface and you apply a force of 40 newtons what is the acceleration that's acted on the block and what's the direction of the acceleration so using the equation the net force is equal to ma the only force acting on the block is the 40 newton force so that is the net force the mass is 5 kilograms and so the acceleration is going to be 40 divided by five so it's eight meters per second squared and acceleration is in the same direction as the net force now here's another question so let's say if you have an eight kilogram block and you apply a force of 35 newtons west and this time the block is on a surface that contains friction friction opposes the motion let's say with a force of 19 newtons part a calculate the net force and part b calculate the acceleration and determine the direction of the acceleration vector so to find the net force we need to find the sum of all forces in the x direction now this force is acting in the negative x direction and this force is acting in the positive x direction so i'm going to say positive f plus negative f this is negative because it's going towards the left this is positive it's going towards the right so the sign is based on the direction where the force is being applied so the net force in the x direction it's going to be f the frictional force minus the applied force the frictional force is 19 newtons the applied force is 35 newtons so then that force in the x direction or the sum of all forces in the x direction is negative 16 unions so this is the answer to the first part of the problem now here's a question for you if i asked what is the magnitude of the net force what answer would you report if you get a test question to ask you only for the magnitude of the net force you need to report positive 60 newtons the magnitude of a vector is always positive the negative 16 the negative sign tells you the direction that the net force is due west so you can say 16 newtons west so you have the magnitude with direction or you could just say negative 16 newtons which will indicate it's going towards the left so now what is the acceleration so once you have the net force you could find the acceleration in this case in the x direction the net force is m times a so this is in the x direction this has to be in the x direction the acceleration is always in the same direction as the net force so it's going to be negative 16 newtons divided by the mass of 8. so the acceleration in the x direction is negative 16 divided by eight so it's negative two meters per second squared so the negative value tells us that the acceleration vector is towards the left and it makes sense the net force is negative 16. so that means the net force is directed towards the left and based on newton's second law the acceleration vector and the net force vector they have to be in the same direction in this case they're both pointing towards the left or in the west direction so let's say if we have an object and that object is moving towards the right so the velocity is positive and let's say the net force acting on the object is also acting towards the right what's going to happen to the object if the force and the velocity vector are in the same direction the object speeds up so it's accelerating now what's going to happen if the object is moving to the right and the force is directed towards the left whenever the force and velocity vectors if they're opposite direction the object will slow down so in this case it's decelerating now what's going to happen if you have an object that is moving to the right but if the force vector is perpendicular to the object what's going to happen anytime the force and velocity vectors are perpendicular the speed will not change it's not going to speed up and it's not going to slow down rather it's going to turn so it simply changes direction when the force and velocity vectors are perpendicular so it's going to change it's going to turn in the direction of the force so now the ball is moving this way so if the force vector doesn't change if it's still in that direction now it's going to speed up so initially at this instant at point a it's not speeding up but once it reaches points b it's already speeding up now while it's turning it will begin to speed up in this direction but when it's exactly perpendicular it doesn't speed up at that instant now let's work on some problems here's the first one what average force is required to accelerate a 5 kilogram block from rests to a final speed of 54 meters per second and nine seconds so we can start with a picture and so we have a five kilogram block and we're going to apply a force of some value that we don't know we're looking for it and we'll give it some other information we have the final speed and we have the time how can we calculate the force now it's helpful if you write down what you have and what you need to find we know the initial speed is zero it starts from rest the final speed is 54 meters per second and the time is 9 seconds we don't know the acceleration and we don't know the force in order to calculate the average force we need the acceleration now we have to assume that friction is not present because we don't have any information to determine what it is so we're going to assume that the applied force is the only force acting on the block in the x direction and so that's going to represent the net force so let's focus on calculating the acceleration of the block what equation contains these four variables hopefully you've reviewed kinematics at this point vf is equal to vo plus 18. so the final velocity which is 54 and that's equal to the initial velocity of zero plus the acceleration multiplied by the time so the acceleration is 54 divided by nine which is six so it's six meters per second squared now let's move on to the second part now that we have the acceleration so the force is going to be the mass of 5 kilograms times the acceleration of 6 meters per second squared and 5 times 6 is 30. so it's going to be 30 newtons so that is the net average force that is required to accelerate the five kilogram block from rest to a final speed of 54 meters per second in nine seconds now let's move on to number two a 1500 kilogram car moving at a speed of 45 miles per hour comes to a stop after traveling a distance of 200 meters what was the average force exerted by the brakes on the car so i'm going to use a box to represent the car because the box is just very simple to draw and so the mass of the car is 1500 kilograms now the car is moving at a speed of 45 miles per hour now it comes to a stop which means it's slowing down until it stops so therefore the force that brings it to a stop is opposite to the direction of the velocity because remember if force and velocity if they are in the opposite direction then the object slows down now it's going to take a stopping distance of 200 meters to slow it down completely to a stop so our goal is to find the average force so if we could find the acceleration we could find the force so let's make a list of what we have we know the initial speed is 45. actually before we do this let's convert miles per hour to meters per second so we have 45 miles per one hour and one kilometer is point six two one four miles and one kilometers also a thousand meters you wanna set it up in such a way that the unit miles cancel and also you want kilometers to cancel as well so right now you have meters if you don't understand this you may want to watch my video on metric system review and unit conversion and dimensional analysis which i'll teach you how to convert from one unit to another now let's convert hours into seconds so one hour is 60 minutes and one minute is equivalent to 60 seconds so now the unit hours cancel and also minutes cancel so what we have left over is meters per second so now let's do the math we're going to multiply by the numbers on top and divide by the numbers on the bottom so it's 45 divided by 0.6214 times a thousand divided by sixty and then divided by sixty again so you should get twenty point one meters per second so now let's write down what we have so this is the initial velocity 20.1 meters per second what's the final velocity now we know the object comes to a stop it comes to rest so the final velocity is zero we have the displacement which is 200 and our goal is to find the acceleration once we find that we could find the force so what kinematic formula has these variables the equation that you need is v final squared is equal to v initial squared plus two a d so v final is zero v initial is twenty point one and d is two hundred 20.1 squared that's 404.01 and 2 times 200 is 400. so i'm going to take this number and move it to that side so it's going to be negative 404.01 and that's equal to 400a so if we divide both sides by 400 you'll see that the acceleration is negative 1.01 meters per second squared now the reason why it's negative is because the object is slowing down the force is directed towards the left so the acceleration is also directed towards the left and that's why we have a negative value now that we have the acceleration we can calculate the average force so f equals m8 it's going to be the mass of 1500 kilograms times the acceleration of negative 1.01 so the average force is negative 1515 newtons it's negative once again because is directed towards the left it's bringing the car it's slowing the car down to a stop and so that's it for this video hopefully gave you a good idea of newton's second law which is basically f equals m a acceleration is directly proportional to force but acceleration is inversely related to the mass and keep in mind the direction of the acceleration and the force vector is the same and now you know how to solve some problems using the f equals m a formula you