Work done on lifting/falling things - Solved numerical

let's calculate work done when things are dropped or lifted let's solve two problems on this here's the first one a dumbbell of mass 5 kilogram drops to the ground from a height of 10 meters calculate the work done by gravity we're given G is 10 meters per second square so let's quickly go ahead and draw the situation so we have a dumbbell whose mass is 5 kilogram it's dropped from a height of 10 meters so it just falls down so this dumbbell just falls down from a height of 10 meters and in doing so we need to calculate the work done by gravity hmm let's first write down what are the given things to us I know the mass of this dumbbell so let's write that down the mass is given to be 5 kilograms I know the height the height is given to be 10 meters and I'm also given the value of G to be 10 meters per second Square from this how do I calculate work done well we have seen from previous videos that work done by a force on any object equals the force multiplied by the displacement of that object in our example the object is the dumbbell and the force acting on the dumbbell which we are asked to calculate is the force of gravity so in our case if we multiply the force of gravity on this dumbbell with the displacement of the dumbbell we'll get the work done so before we go ahead and do this great idea to pause the video and see if you can try to get the answer yourself first all right let's see first of all notice we already know the displacement of the dumbbell right number gets displaced by 10 meters which is just the height through which it fell down so we know that so all we need to do now is calculate the force which forces this this is the force of gravity do we know how to calculate force of gravity yes we do so if I keep my dumbbell somewhere over here as it was falling and we know the force of gravity on any object is going to be the mass of that object times G this is the force of gravity so now that we know about the force and displacement let's just plug in and see what we get so force is just the mass times G and the displacement is just the height now one thing we need to be very careful over here is remember work them can be both positive and negative it's positive when the force and displacement are in the same direction it's negative if they're in the opposite direction in our example which one is it a lot is the forces acting downwards even the displacement is downwards so in our case the work done is going to be positive but before we continue and plug in just think about what would have happened if I had thrown the dumbbell up now the force of gravity would still be acting downwards right gravity always acts down but our object our dumbbell would be going upwards in the opposite direction so the displacement would be in the opposite direction of the force of gravity in that case the work done would be negative so if we throw it up you throw this dumbbell up and then gravity will do negative work but of course in our case since the dumbbell is falling down the gravity is doing positive work all right let's just go ahead and substitute the numbers and see what we get again if we had not tried this before great I had to pause the video and see what answer you get once you substitute okay let's go ahead and plug in so the work done let me choose a brighter color so the work done is going to be mass which is five kilograms times G which is 10 meters per second squared this is our gravitational force times the height which is 10 meters and so the work done becomes 5 times 10 is 50 50 times 10 is 500 so we get 500 let's look at the unit's don't forget the unit's kilogram meters per second square let's keep that separate that's the unit of force that's the unit of force times meters now kilogram meters per second squared since it's the unit of force we can also add his Newtons so we write this as Newton's times meters and so that's the work done work done by gravity is 500 Newton meter but of course remember newton meter is also called joules so we can also say 500 joules that is the work done by gravitational force on our dumbbell it's positive all right let's go ahead and solve another one here's the question a woman slowly lowers a 20 kilogram barbell rod through a distance of point two meters as shown below find the work done by the woman on the barbell so she's exercising maybe and so she takes that barbell rod and she's lowering it so let's look at that if we could see it maybe it looks somewhat like this she lowers it this way that's given to us okay we need to calculate how much work the woman does on the barbell so let's see let's again write on what's given to us we know the mass of that barbell Rodge let me write that know here it's given to be 20 kilogram we know the distance through which it moves let me just call it as the height that is given to be 0.2 meters and again we're given g to be taken as 10 meters per second square and again since you are asked to calculate the work done we'll do it as force times displacement we know the displacement that is point 2 meters but what's the force see here we have to calculate the work done by the woman on the barbell so this must be the force that the woman is putting on the barbell how much is that well I guess here's the clue it's given the woman is slowly lowering the 20 kilogram bar well imagine she's slowly lowering it without any acceleration think of it that way all right then can you figure out what that force is going to be and what direction that force is going to be go ahead give it a try pause the video and give that all right let's see let's consider when the barbell is somewhere in between when it's still moving down somewhere over here let's say okay now we know that gravity is pulling down on this barbell so there is a force of gravity on it which is mg but this barbell is moving with a constant speed it's slowly moving no acceleration let's say then the force on that barbell must be balanced right because if the forces are not balanced remember the barb or accelerate and sort of balance this force she must push up on that barbell with exactly the same force and so the force with which he's pushing on the barbell should exactly equal to the weight of that barbell equals mg now of course one question you might ask is if the two forces are exactly equal and balanced why is the barbell moving why does the barbell just not stay at rest at the topmost point that would be a pretty good question okay and here's how that to think about it imagine that at the topmost point her force becomes little smaller than gravity because of which the gravity starts winning and the barbell starts moving down that's how the barbell starts Moyne she momentarily just for a fraction of a second puts a smaller force but then once the barbell is in motion her force will match that of gravity making sure the barbell moves slowly with a uniform speed okay and if you think about it even more then at the bottommost point she needs to now stop that barbell right in order to stop that barbell she now has to put a little larger force than the weight again momentarily and so you see at the top it's a little smaller the bottom is a little larger so they kind of compensate and of course in between for most of the motion the force is equal to that of the weight and so we can say overall our force should equal B should be equal to the weight of the barbell and so if we go ahead and plug in since we know the force our force is equal to the weight for most of the motion it's going to be mg times Hach but one thing to be careful about is it positive or negative work well this time notice her pushes upwards remember it's this force that we are interested in because it's the work done by the woman so her force is upwards and the displacement is downwards and so they're in the opposite direction so the work done becomes negative that's something to be careful about all right now we can just substitute the values of M G and H 10 times 0.2 is to 2 times 20 is 40 and so our answer is going to be negative 40 again the units are going to be mutants which is the unit of force meter Newton meter which is the same thing as a Jew and that's our answer so the work done by that woman on that barbell is going to be negative 40 joules and so I guess the most important thing we saw over here is that whenever you are lowering or raising any object we can say that the force with which you're pushing on the object is pretty much equal to and opposite to the weight of that object the gravitational force acting on that object