Gonna give me the work done? Well physicists and Varying force that the area underneath this graph is still Might be like wait a minute, all we really showed in that previous example was that the workĭone for a constant force was equal to the area underneath. How do we find the workĭone by our force now? Well I'm still gonna make the claim that the work done is gonna beĮqual to the area underneath this force versus position graph, but you might be skeptical, you More time to get there, but let's say it still How could it make it five meters if we're pushing with less force? Well it may have taken This would be zero newtons ofįorce when it hit this axis. Pushing with four newtons but you were getting tiredĪnd your force was diminishing and you were pushing withĪ weaker and weaker force until your force became zero newtons. With a constant four newtons for the entire duration of this trip, let's say you started Underneath that graph, that's a quick and easy way to get the work done by that force. Underneath any force versus position graph is gonna equal the work, not just ones where the force is constant, even where the force is varying, if you can find the area Fortunately, there'sĪnother way to determine the work done by a varying force and that's to take this idea seriously. One way to handle that scenario is using calculus, but if you don't know calculus that doesn't do you any good. What if our force was not constant? What if we had a varying force? In that case, what force Just plug the force in here, we could just plug theĭisplacement in there, we get our value, but think about this. Because in this case, yes, it was easy, we had a formula, we could To know that the work is equal to the area under a force graph? I'll show you why. Now you might be like, alright, well, fat lot of good that does us, we can already find it with this formula. So from this line thatĭetermines the force down to this x-axis, if you find the area, that's gonna equal the work done. Work done is just to find the area enclosed by the graph. Is by using the work formula but another way to find the The force is constant one way to find the work done Get the area of a rectangle, so what we found was when The width of this rectangle and if you multiply a height times width, you know what you get, you Is a straight line in this force graph just forms a rectangle in here and all we did, we tookįour newtons, that was just the height of this rectangleĪnd we multiplied by five meters and that was just Now if you're clever you might be like wait, four newtons timesįive meters, look it, that's just the area of this rectangle. We did on the hamburger was positive 20 joules of work. Newtons was the force for the entire displacement of five meters and we get the work that So I'm gonna say that theįorce here was four newtons so we can calculate four In the direction of the motion of the object youĭon't really need that cosine theta and we don't need it here. Just that thing so whenever your force is already Of zero, you just get one and one times anything is Was in the direction of motion so we don't really need this. Motion but for our hamburger example, the force already The force in the direction of motion and only thatĬomponent of force that's directed in the direction of Theta, this just makes sure that you're singling out In the direction of motion times the displacement or youĬould say the entire force times displacement times cosine theta. I'm doing this is because there's gonna be a geometrical It was a constant amount of force, and the reason Moved five meters to the right and we exerted a constantįorce of four newtons, That's why this is a horizontal line. Hamburger to the right, so if we were to plot what the force was on our hamburger as aįunction of its position, it would look something like this. We exerted a force of four newtons for the entire five meters that we pushed this Instead of just plugging straight in, consider the fact that Way to think about this, because what we learn from this alternate approach is gonna help us in more challenging, complicated work examples. Simple problem we can just plug straight into the work formula,īut I'm not gonna do that. So a question we get asked would be how much work did we do in passing this hamburger to the person to our right? Now since this is a pretty With a force of four newtons and you're gonna do thisĪnd you're gonna push this a distance of five meters to the right. So you're gonna push this hamburger to the right, Maybe you found someone that needs it more than you do, Maybe it's because you're a vegetarian, maybe you're already full, Hamburger sitting right in front of you, but you don't want it.
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