hello everyone so in this lesson we're going to look at a few more examples on work so here we have a box that is being pushed to the right with the force of 10 newtons there is a frictional force of 4 newtons on the box and the box gets pushed over a distance of 10 meters question a determine the work due to the person who is pushing okay so we know that work is equal to the force the force of the person is going to be 10 newtons the displacement or distance is going to be 10. now if you have a box that is being pushed to the right it's obviously going to be moving to the right and the person is also going to be pushing to the right so the angle between those two is 0 degrees so you say cos of 0 which is equal to 1. so 10 times 10 is 100 and that's going to be joules and you could say added to the box you're not going to say to the right because work is a scalar so we can say 100 joules added question b says determine the work done do you or the work due to friction okay so that force is going to be 4 newtons now remember we're not going to say -4 because yeah it's a bit weird how this formula works but i'll show you now how it works this part over here will bring in the minus for us and then the displacement well that was 10 now if you have a box that is busy moving to the right but the friction is always going to try to go against that so if you look at those two the angle is 180 so we'll say here cos of 180 now cos of 180 is -1 and so you're going to end up with -40 joules over here therefore 40 joules is removed from the box is removed from the box so please remember that this part over here must always be positive question c how much energy is actually being added to the box well if you can see this we've got 100 rules being added and then 640 joules is being removed so therefore 60 joules is actually being added so that box will speed up because more energy is being added than energy being removed so this is called your net work net means overall now there's a better way to do this there is a formula where we can use w equals to f change in x cos theta but if we want to look at sorry those of you today if we want to look at the net then we'll add the word net over here and then the force you must use is net so these two must always match so when we were doing the person then we could say person then we use the force of the person when we did friction then we used the force of friction now we're doing the net force and so we misuse well now we're doing the net work so we knew the net force so w net meaning the overall effect is going to be equal to f net now f net is going to be equal to 10 which is to the right minus 4. now that 10 minus 4 is 6 and is that 6 to the right or 6 to the left well that's going to be 6 to the right then the displacement is 10. now we know that because the net force is 6 to the right the object will move to the right and so we will have to say cos of 0 because that 6 newtons is to the right and the object is also moving to the right and if you had to go type this all in you would end up with 60 joules and you would just say 60 joules you don't have to say added and removed i'm just trying to show you exactly how this stuff works so a very popular formula that you're going to start using quite a lot is w net equals to f net change in x and then cos theta but what you need to know is simply that there's this formula called w equals to f change in x cos theta and then whatever force you are looking at so if it's friction then that will be w friction if it's applied force then that will be f applied force if it's w net then you must use fnet here's another example number two says that we have a box that is initially moving over a frictionless floor it then encounters a rough section where the force of friction is four newtons the length of the rough section is 10 meters determine the work of the friction on the box okay so we can say w equals to now we're looking at the the work due to friction so i'm just going to put an f there for friction you don't have to do that and so the force that we're going to have to use must be friction i'm just going to write here friction because remember these two must always match and then we've got the distance and then we've got cos theta so the force of the friction is 4 newtons now i know that that's going against the object but you don't say -4 over there then the distance that we're moving is 10 meters now if you have a box that's initially moving over a horizontal floor it then so it's busy moving to the let's say it's busy moving to the right i didn't say that but let's say it's moving to the right then the friction force will obviously be to the left and so the angle between those two is going to be 180 so you could say cos 180 which is equal to -1 and so the answer is minus 40 joules therefore 40 joules of energy is removed from the box would that cause the box to speed up or slow down well obviously that's going to cause the box to slow down and in a in one or two videos from now we're going to actually start looking at how can we calculate the new velocity if 40 joules of energy is removed from the box but that's all for now guys i like to keep the videos nice and short just so you can walk with the little baby steps and that builds confidence so thank you very much for watching