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A super high-speed 14 -car Italian train has a mass of640 metric tons $(640,000 \mathrm{kg}) .$ It can exert a maximum force of400 $\mathrm{kN}$ horizontally against the tracks, whereas at maximum constant velocity $(300 \mathrm{km} / \mathrm{h}),$ it exerts a force of about 150 $\mathrm{kN}$ .Calculate $(a)$ its maximum acceleration, and $(b)$ estimate theforce of friction and air resistance at top speed.

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a.$0.625 \mathrm{~m} / \mathrm{s}^{2}$b. $F_{\max }=F_{\text {air }}=4 \times 10^{5} \mathrm{~N}$

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

University of Michigan - Ann Arbor

University of Washington

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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so here for part A. We're going to assume that the maximum horizontal force occurs when the train is moving extremely slowly and the air resistance is negligible. So when the train is moving very slowly, um, air resistance isn't going to prove a big part of isn't going to ah account for a large part of the motion? Therefore, the maximum acceleration would be equal to the maximum force that the train can exert on the train tracks essentially divided by the mass of the train itself. So this would be four times 10 to the fifth Newtons, divided by 6.4 times 10 to the fifth kilograms, and this is equaling point 6 to 5 meters per second squared now at top speed. However, let's say that train moves slowly at top speed. However, we assume that the train is moving a constant velocity. Therefore, the net ah, the net force on the train will be zero at top speed. We have a constant velocity, which means that we haven't no we have no acceleration, which means that force net well, equal zero Newton's. And given this the air, this means that the air resistance and the friction forces together must be That must be equal to the, uh, the maximum magnitude of the pushing force. Essentially. So here. If we wanted to say Sigma Force Sigma, uh, some of forces in the ex direction would equal forcing next minus the force of the air resistance. We know that this is equaling m times the mass of the train times acceleration in the ex direction. However, we know that the acceleration in the extraction would be zero in this case. Therefore hath Max would be equal to the force of the air resistance and this would be equal to four or rather, yeah, four times 10 to the fifth Newton's. So this would be our final answer. That is the end of the solution. Thank you for watching.

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