Newton's Laws Legacy Problem #21 Guided Solution

A good problem solver always reads the problem carefully and gets a good visual picture of what's going on. They often represent this picture by means of a diagram, and in this unit that diagram is often a free-body diagram, depicting the forces acting upon the object. Here we read of a model rocket that's accelerating upwards, as model rockets do, when taking off. We're given the acceleration, a, equal 45.9 meters per second per second, and we're given the mass, m, equal 0.104 kilograms. We're asked to determine the upward thrust experienced by the rocket. So I begin by drawing a free-body diagram for this rocket, showing the forces that act upon it, and there are two. There's an upward force, and we're asked to calculate its value, and then there's a downwards force. I'm going to call the upwards force F-thrust, or F-applied, or F-something, and I'm going to represent it by an up arrow in my diagram. And there's a down force, and that's simply the F-grab, as it usually is. I can calculate the F-grab because I've been given the mass of the object. Always the force of gravity is equal to the m times the g, where the g is 9.8 newtons per kilogram. So I can calculate that value right now. I should do it 0.104 times 9.8 gives me about 1.02 newtons down. I'm interested in the up force. Now I have to strategize. What do I know? What am I looking for, and how can I get to it? Well, the up force, the F-thrust, can be found if you do the net force, and the net force can be found if you know m and a, and when you know, that's exactly what you know here. You simply can go to 0.104 kilograms times the acceleration of 45.9 meters per second per second, and you can calculate the net force. Now it's an upwards net force to correspond with the upwards acceleration. So now I have to think, what does the net force tell me? It tells me what the two forces add up to, or what all the forces add up to. Here the thrust plus the negative, or the downward gravity, has got to be equal to this net force value. So in order for that to be true, the net force, or the thrust force, must be bigger than the down force by the amount F-net. So to find the thrust, I simply take the down force and add to it the net force. That will give me the answer.