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(II) Superman must stop a $120-\mathrm{km} / \mathrm{h}$ train in 150 $\mathrm{m}$ to keepit from hitting a stalled car on the tracks. If the train's massis $3.6 \times 10^{5} \mathrm{kg}$ , how much force must he exert? Compare to the weight of the train (give as $\% ) .$ How much force does thetrain exert on Superman?
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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 the train is coming to a stop. We know that if the initial would be equal to 120 killem kilometers per hour, let's convert one meter per second for every 3.6 kilometers per hour and this is giving us 33.33 meters per second. Of course the train is coming to a stop, so the final would be zero meters per second and we need to calculate average velocity. This would be equal to the final squared minus V initial squared, divided by two times Delta acts. We know the final square to zero, so eliminate that term and this is equaling negative 33.33 meters per second. Quantity squared, divided by two times Ah, the distance of 150 meters. Now at this point Ah, this would equal the average acceleration And the force that is, um that Superman is, um, exerting on the train would be in the opposite direction of the initial velocity off the train because again, this train is coming to a stop so we can say that to the average force would be equal to the mass of the train times the average our average deceleration in this case, so it would be 3.6 times 10 to the fifth kilograms multiplied by negative 33.33 meters per second. Quantity squared, divided by two times, 150 meters. And this is giving us negative 1.33 times 10 to sixth Nunes now. Ah, this would be the force that Superman needs to exert on the train. In order for the train to stop comparing this to the actual weight of the train, we could say force average divided by the mass of the train times acceleration due to gravity, this would equal 100 was a 1.33 times 10 to the sixth. Newton's divided by 3.6 times 10 to the fifth kilograms multiplied by 9.8 meters per second squared. This is going to give us approximately point three 89 or we can say 38.9% of the trains wait. And after this they're asking us what is the force that the train exerts on Superman. Well, in this case, due to Newton's third Law, every force has an equal every reaction has an equal and opposite reaction. Therefore, we can say that train exerts a 1.33 times 10 to the sixth Newton Force on Superman inthe e direction of the initial velocity. That is the end of the solution. Thank you for watching.
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