Newton's Laws Legacy Problem #29 Guided Solution

Here we have a description of a skydiver who's falling downwards, as skydivers usually do. And she opens her parachute, and immediately she begins to accelerate upward. For an instant in time, that acceleration value is 8.66 meters per second per second up. So, as I read this, what I'm going to do is write down my known information, and one of the things I know is that A equals 8.66 meters per second per second up. And the up of that is not a trivial thing. That's going to be very important as we go through this problem. I also know that the mass of the skydiver, m, equals 53.4 kilograms, and I know that's the mass because I recognize the connection between quantities and the units that are used to express those quantities, kilograms used for mass. Now, I'm going to draw a free-body diagram depicting the forces acting on my skydiver, and I'm always going to draw f-graph down because f-graph acts on all objects universally, and that value can be calculated as m times g, and I know the m value. Then I'm going to draw a second force up, and it's f-air, or something like that. Now, this f-air force in the up direction has got to be bigger than the f-graph force in the down direction. The reason I know that is because I'm told the acceleration is up. To have an up acceleration, an object must have more up force than down force. It matters not which direction the object moves because forces have very little to do with direction of motion and everything to do with the direction of acceleration. Now, with the m and the a known here, I can calculate the f-net. So when I go my mass times my acceleration, I get a value for f-net. It ends up for me being about 462 point something newtons up. And what a net force tells me is it tells me two things. It tells me who wins the tug-of-war between forces and by how much. Who wins and by how much. So the net force here is 462 newtons up. So who wins? Well, the up force does. The f-air wins the battle, the tug-of-war between the two forces. By how much does it win? Well, it wins by 462 newtons. And so what that's telling me is this unknown up force that I'm trying to calculate has got to be greater than the down force by amount of 462 newtons. I can calculate the down force as mg and then I can add 462 newtons to it to make the up force, my unknown quantity, bigger than the down force by that amount. And that's how you approach these f-net equal ma problems. You'll notice that I took my time to read it, to identify known information, to construct a diagram representing the forces, and then I used my understanding of relationships to think through how to get from known information to unknown information.