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$\bullet$$\bullet$A short train (an engine plus four cars) is accelerating at1.10 $\mathrm{m} / \mathrm{s}^{2} .$ If the mass of each car is $38,000 \mathrm{kg},$ and if each carhas negligible frictional forces acting on it, what are (a) theforce of the engine on the first car, (b) the force of the first caron the second car, (c) the force of the second car on the thirdcar, and (d) the force of the third car on the fourth car? In solv-ing this problem, note the importance of selecting the correctset of cars to isolate as your object.

a. $1.672 \times 10^{5} \mathrm{N}$b. 1.25400 $\mathrm{kg} \times 10^{5} \mathrm{N}$c. $8.36 \times 10^{4} \mathrm{N}$d. $4.18 \times 10^{4} \mathrm{N}$

Physics 101 Mechanics

Chapter 5

Applications of Newton's Law

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

Cornell University

University of Michigan - Ann Arbor

University of Sheffield

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Okay, so we have ah engine with four cars attached to it. And so we're assuming never re starting with yourself in the mass of the engine is negligible compared to the masses of the cars, which each car way has a massive and okay, so he's just way to go about. This is two Joffrey money diagrams. Please call. So you'll note that there's no frictional force, meaning acceleration will be in in the in the direction of the force in every case, because others just force in the positive ex direction of which we consider to be right in this case. Ah, and so acceleration is in that direction because there's only one force acting in that direction for each car. So the first car has so at the first car e of four em because gift you have for the masses of four cars acting on this one and force F orm. Similarly, the second car There's the force, too, and the three massive attached to great such TM. Similarly, CIA's 2 a.m. three d has mass m and force for okay, so going ahead and solving all of these. By the way, Newton's second Law is all we need here. There isn't much calculation here except for suffer this that force in the extraction. We master of exploration and extraction, Sasha the extractions and given you have Mass. So let's start. But a where f one, the only force of extraction, will be called four times m Time's A because that's the total mass is for him. All right, so four times four kinds, 38,000 kilograms, 1,000 kilograms times 1.1 meters per second squared. That gives us 1.67 times 10 to the five. No. All right. Similarly, for part B, you have f to central question. Now you have two equals three AM terms air and so three times 38,000 times 1.1 not writing down units over. You get the Yes, that's one, 25 times 10 to the five Naples and similarly apart. See, after we will be calls to two m this time, eh? And I'm not going to write down stuff here, Exaggerations sama. Em is the same. So that comes out to be a 0.26 parents tend to before Newton's finery Part d the car in the fourth car forest, The forest and M is, uh on the right hand side, and so that comes out to the 4.18 times 10 to the floor, and that's it.

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