 In this example, I'm going to find out how to calculate the work that is required to lift an object by height h at a constant speed. So, remember the work formula. How do we calculate the work formula? Work is the force times the displacement and its cosine of the angle in between. So, I will need to figure out the force, the displacement, I know it, the displacement. In this case, it will be my height and for the angle, I'm going to have to look at it. So, let's start with the free body diagram of this object here. So, the object I'm going to lift. What forces are acting on it? Well, there is gravity, force of gravity, which is mg, which is going down. And then there is the force of lifting it. So, whatever pole I'm using to lift it, it's my force that goes up. And then we have the displacement, which should be up. So, what's the angle between those two? The angle between the force that goes up and this placement in the opposite direction. Yes, it's zero degrees. So, zero degrees. Now, if I go up at v equals constant, what does that mean for acceleration? Constant velocity means that acceleration is zero. And if the acceleration of an object is zero, what does Newton say about that? Yes, Newton's first law. First law, if the acceleration is zero, then the sum of all forces must be zero. The acceleration is zero. Or the other way around, if the sum of all forces, the acceleration must be zero, meaning in upwards direction, let's call this y, in y direction, I have the sum of all forces must be zero. So, I have plus my force minus the force of gravity. So, plus fg as vectors is zero. If I look at the directions, I have plus the force. And then I'll up and minus and g is zero. So, long story short, the force required to lift an object at a constant velocity must be equal to gravity. So, now I have it, f is mg. So, the work required to lift it is s, as gravity, as height. Does that look familiar? Yes, that just is the equation for potential gravitational energy in mgh. So, I did some work to lift the object. By that, I increased the energy of the object. I increased the energy of the object by what? I mgh, by the potential energy. So, my potential energy final is my potential energy initial plus the work done.