I am having difficulty comprehending when you break down individual forces into
ID: 2060325 • Letter: I
Question
I am having difficulty comprehending when you break down individual forces into components and not the others. In my class the other day, we went over three problems and in each one, the force that we broke down into x and y components was different, and I don't get what determines when it needs to be in components or not. I have put the example problems and what was used for components below. This is strictly a concept I do not get, and it is making it difficult for me in starting problems and knowing how to break them down, so any help would be much appreciated.1. Question about a skiier being pulled up a ramp (at an angle) at constant velocity on a frictionless surface.
Normal force, tension from the rope skiier is being pulled up on, and mg are the forces- mg was broken into components x and y.
2. A box has a string attached and is suspended in the air. no velocity and no friction
the forces acting are normal, mg, and tension. tension is broken down into x and y components
3. Box with two strings attached is suspended in the air at identical angles. Normal force, mg, and tension are the forces acting on it, but x and y components for both ropes (T1 and T2)
Explanation / Answer
You break up the force that is at an angle in the xy plane, for example in your first problem: The skier being pulled up a ramp. Think about an xy cooridinate plane being place on top of the diagram of problem. 1)Tension is running parallel to ramps surface, The normal force is perpendicular(at a 90o angle) of the ramps surface. Now for a momement imagine that the ramps surface is x axis of the grid(kind of like your tilting you head to make the surface of the ramp the horizontal). This would make the Normal force vector form the y-axis of the coordinate plane. Now lets think about gravity for a moment. It always acts straight down, not always directly opposite to the normal force. Gravity in terms of our xy cooridinate plane is at an angle to the now horizontal surface of the ramp, so we must break it up into components along the x and y axis
2)Again the same process for problem number two, although there is no Normal forces since it is suspended in the air, only tension and gravity act on the object. in this scenario gravity froms the y-axis and the the x-axis can be drawn perpendicular to the y-axis through the object. Now notice that tension will be at angle relative to both axis. Again you must break up this force into x and y components.
3)This situation is essentially the same as problem two except now there are two tensions involved rather than just one so you have to break them up into their x and y components.
Basically the idea is that you have to identify the force vector that forms an angle other than 90o or 0o with the x and y axis that you define for the problem.
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