Newton's Laws Legacy Problem #19 Guided Solution

Good problem solvers have good habits, and those habits center around reading the problem carefully and constructing a diagram to represent the physical situation, listing what is known and what is unknown, and then plotting out a strategy on how to get from that known information to the unknown information. Rather than rushing to their calculator, they take the time to think about the situation to get a visual representation and to plot out a strategy. So here our object is Natalia, who is in a skydiving tunnel, and she's got a force of gravity pulling her down, and then there's an air resistance pushing her up. If you're having difficulty picturing this, you can simply think of her falling through the air as a skydiver, or use the link to go to the Wikipedia page that describes the so-called skydiving tunnel and the act of body flight. So she's suspended in the air, there's a downed force of gravity on her body, and an up force of air resistance. Now what we want to do is eventually calculate the acceleration, that's our big unknown. So I'm going to begin by drawing a free body diagram of Natalia, that is I'm going to represent the forces acting on Natalia's body, using my conceptual understanding of the situation. So I just draw a box, that's Natalia, I draw a downed force that's going to be labeled F grab, it's just simply an arrow pointing down, I draw an up force, an arrow pointing up, that's air resistance, that resists the downward fall of Natalia, I label it F air, and I say it's equal to 521 Newtons. My M, or mass, equals 46.8 kilograms. I know that's the mass because it's given in units of kilograms. Now what I want to do is eventually get an F net, so that I can calculate an acceleration. That's going to be sort of my strategy. So how do I get the F net? You can always find the F net if you know all the values of all the individual forces acting upon the object. So if you look at your free body diagram, you know the up force, but you don't yet know the down force, but you can calculate it. After all, F grab is equal to MG, and the M is given, and the G is 9.8 Newtons per kilogram. So take the mass of 46.8 and multiply it by 9.8, and you now have the down force. The down force and the up force are going opposite directions, and so now you have to add them up. You'd add them up by calling the down negative and the up positive, and you'd call the 521 positive plus the negative value for F grab. You get the net force, and now you're ready to calculate the acceleration. A equals F net over M, where the M is 46.8 kilograms, and you get your acceleration. The direction of the acceleration is always, always, always in the direction of the net force or the unbalanced force, and it's the up force that's not getting balanced by the down, so the acceleration is upwards.