Multiple Definitions of Work
In the previous slide, I gave three equations for work. This slide attempts to compare them and show how they're equivalent, but for different cases.
You do work if you put a force on an object and it moves a distance. That's it! The definition is surprisingly simple, but very powerful. It gives us an idea of why the concept of energy is interesting (because it can move stuff) and it starts to give us a clue on how to give something energy (apply a force on it and move it a distance.)
Under the simplest equation (labeled "good,") I make the following point:
If the object moves a distance in the direction you pushed it, you've done positive work to it, and if it moves opposite what you've pushed you've done negative work to it. We can think of work as adding and subtracting energy to an object. Imagine a rock sitting still. You push it, and it moves in the direction you pushed. You gave it the ability to do work! It's moving!. Positive work. But now how about an object moving and you push it backwards. It keeps moving forwards, but slows down. You've taken away its ability to do work. Negative work.
Under the next equation, (labeled "better") I point out a catch: that only forces acting in the direction of motion accomplish work. If I push a chair straight into the ground, it doesn't move, so no work is accomplished. If I push it at an angle, partially into the ground, the part going into the ground, labeled Fpy here, doesn't accomplish anything. So only the part parallel to motion does.
It's important to note that Fp and d are vectors, they have direction. Work doesn't. In math, there's a term for multiplying vectors like this- it's called the dot product.
Under the final equation, I show what work really is: the area under the curve on a (distance, Force) graph. Variable forces can totally do work: we just have to find their areas. The first two equations are true only for constant forces. For anything else, like I have listed on the far side, we need to find the area under the curve.
Note that distance can have any of the following letters: (x,y,z,r,s,h)
Multiple Definitions of Work
In the previous slide, I gave three equations for work. This slide attempts to compare them and show how they're equivalent, but for different cases.
You do work if you put a force on an object and it moves a distance. That's it! The definition is surprisingly simple, but very powerful. It gives us an idea of why the concept of energy is interesting (because it can move stuff) and it starts to give us a clue on how to give something energy (apply a force on it and move it a distance.)
Under the simplest equation (labeled "good,") I make the following point:
If the object moves a distance in the direction you pushed it, you've done positive work to it, and if it moves opposite what you've pushed you've done negative work to it. We can think of work as adding and subtracting energy to an object. Imagine a rock sitting still. You push it, and it moves in the direction you pushed. You gave it the ability to do work! It's moving!. Positive work. But now how about an object moving and you push it backwards. It keeps moving forwards, but slows down. You've taken away its ability to do work. Negative work.
Under the next equation, (labeled "better") I point out a catch: that only forces acting in the direction of motion accomplish work. If I push a chair straight into the ground, it doesn't move, so no work is accomplished. If I push it at an angle, partially into the ground, the part going into the ground, labeled Fpy here, doesn't accomplish anything. So only the part parallel to motion does.
It's important to note that Fp and d are vectors, they have direction. Work doesn't. In math, there's a term for multiplying vectors like this- it's called the dot product.
Under the final equation, I show what work really is: the area under the curve on a (distance, Force) graph. Variable forces can totally do work: we just have to find their areas. The first two equations are true only for constant forces. For anything else, like I have listed on the far side, we need to find the area under the curve.
Note that distance can have any of the following letters: (x,y,z,r,s,h)