Newton's Laws Legacy Problem #28 Guided Solution

This problem represents a good example of the importance of reading a problem very carefully. It's a question about a Harrier jump jet, which probably many of us don't even know what it is, but it describes it as an object that undergoes vertical takeoff. It is capable of rotating its jets from a horizontal to a vertical orientation and thrusting air downwards at high speeds in order to produce upward thrust. Now, what we're told, or what we're asked for here, is we're asked to calculate the amount of thrust that would cause this airplane to accelerate upward at 0.40 meters per second per second. In order to determine this value of the upward thrust, I need to construct a diagram of the situation. And so I draw the gravity force directed straight down. Its value is going to be mg, and I happen to know the m here is 8600 kilograms, so I should be able to calculate that value. And then I know there's a thrust force up, so you could label another air on your free-body diagram, label it F applied or F thrust or F something. We wish to know that value. We don't know what it is, and that's what we wish to calculate. We do know that the acceleration is upward at 0.40 meters per second per second. So I write down a equals 0.40 meters per second per second, and m equals 8600 kilograms, and I ask, how can I take this known information and plot a strategy to get to the unknown information of F thrust? Well, as I think through the quantities, the first thing that comes to my mind is that I ought to be able to calculate F net. So I have a good conceptual understanding that F net is ma, and I have both m and a. So I can calculate the net force, and I can get a value that comes out for me to be about 3440 newtons. Now, that direction is an up force. What up tells me when I'm speaking of F net is it tells me that the sum of the ups is greater than the sums of the downs. Well, there's only one up, and it's F thrust, and it's greater than the down by the amount of F net. In effect, what F net tells you with its magnitude and direction is it tells you who wins the battle of wars between the forces and what the winning margin is. And so here, the thrust wins the war, the tug-of-war war, and it wins by an amount of 3440 newtons. So how do you calculate it? Well, you make sure its value is 3440 newtons greater than the down force value, and the down force value is just mg. So calculate the down force F graph, add 3440 newtons to it, and you get your up force.