Newton's Laws Legacy Problem #17 Guided Solution

Good problem solvers do not waste any time rushing to their calculator before they first get a good conceptual and visual understanding of the physical situation described in a problem. That involves reading and thinking about the context of the situation, and in this case the context is of Darren jumping out of an airplane and skydiving. What we observe is that there is an upward force, or at least an air resistance force, on Darren as he is falling from the plane. 118 Newtons of air resistance it says. So my picture of Darren is he is in the air, gravity is pulling him down, and there is air resistance on his body pushing up on him. And I represent this situation by a free body diagram. I represent each force, there are only two, by arrows pointing in the direction in which they act upon Darren. So there is a down force F-grab and I just draw a box and then draw an arrow down and I label it F-grab. And then there is an up force, F-air. Air resistance always resists these forces, always resists these objects as they move through the air. Thus, if Darren is falling down, the air resistance is up. So just draw an arrow, label it F-air, and say it is equal to 118 Newtons. Now we have to calculate the acceleration, that is the unknown, and it gives us a hint. Begin by drawing a free body diagram and determine the net force. And that is imperative, there is no way you could calculate the acceleration without knowing the F, the F-net. Because if you think of the equation, A equals F-net over M, the two things we need to know are F-net and M. The M is given, 82.5 kilograms. To get the F-net, you need to use your diagram and your noodle, that is your mind. So how do you get the F-net? Well, you need to know both individual forces. The F-air is easy, it is given, 118 Newtons. The F-grab, on the other hand, is not given. You can use what you know about forces, and particularly the downforce F-grab, in order to calculate the weight of an object, that is the force of gravity that acts upon it, is equal to Mg, where the M is given as 82.5 kilograms. I know that to be the M because it is expressed in units of kilograms, and I am always looking at units as I read problems. So I take the 82.5 kilograms and I multiply it by the 9.8 Newtons per kilogram, or meters per second per second, and that gives me a force down in Newtons. Once I get that downforce, I just write it on the diagram. Then I look at my two forces and I ask, what do they add up to? After all, that is the net force, the vector sum, the vector addition of the two forces. So you got one down and one up, the down is bigger than the up, so you take the downforce, you call it, and you subtract from it the upforce, and what you get is the net force. It's in the direction down, divided by the mass of 82.5 kilograms, and you have your acceleration. The direction of the acceleration is always, always, always in the same direction as the net force.