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(II) A train locomotive is pulling two cars of the same massbehind it, Fig. $39 .$ Determine the ratio of the tension in thecoupling (think of it as a cord) between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right),$ to that between the first car and thesecond $\operatorname{car}\left(F_{12}\right),$ for any nonzero acceleration of the train.

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$F_{\mathrm{T} 1} / F_{\mathrm{T} 2}=2$

Physics 101 Mechanics

Chapter 4

Dynamics: Newton's Laws of Motion

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

Moment, Impulse, and Collisions

Cornell University

Hope College

University of Sheffield

Lectures

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

04:30

In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. In the case of a constant force, the resulting change in momentum is equal to the force itself, and the impulse is the change in momentum divided by the time during which the force acts. Impulse applied to an object produces an equivalent force to that of the object's mass multiplied by its velocity. In an inertial reference frame, an object that has no net force on it will continue at a constant velocity forever. In classical mechanics, the change in an object's motion, due to a force applied, is called its acceleration. The SI unit of measure for impulse is the newton second.

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just to draw the freed by the diagram of the train cars. We have trained car, too. Train car one and the front trigger. So going to the right brother. Yeah, going to the right would be forced. Tensions up to going to the left would, of course, be again forced tensions of to do to the Newton's third Law of Motion and then going to the right here would be force tensions of one so we can apply it for the first car Some of force isn't for the first car would be equal to the force. Tensions of one minus forced tensions up to and we know this is zero because the train is moving at a constant velocity for the second car. Some of forces, except to would be equal to F sub too. And this would equal m a. My apologies. This is not moving at a constant velocity, has some sort of acceleration. My apologies. So it's and so it's Ah, some of forces is going to equal the mast, the total systems, mass times acceleration, and in this case, there is an acceleration, so we cannot cancel that out just yet. However, here we can say that the force attention sub one minus force. Tensions have to equals m A, which also equals force tensions of two according to the sum of forces for the second car. So essentially we can say that the force tensions of one he's gonna equal to times the force cinch for extensions up to. And so we can say that the ratio forced entrance of one divided by force tensions of two is gonna equal to. And so this would be our final answer. That is the end of the solution. Thank you for watching.

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