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History

   The first world war was a time of trial and error. A time when the modern world collided with the old and horse mounted cavalry was still being used despite the fact that they made easy targets for the new machine guns. Aircraft were, for the first time, being used for war as a means of gathering intelligence and dropping ordinance on enemy positions and tanks were making their debut in the world of modern war. The first tanks were based off civilian tractors. As such they were slow, big, and vulnerable to sinking in the muddy battlefields of France, which for 1916 was not bad considering the only other platform for ground based attack was a horse. The tank changed the way wars were fought and sparked development of technology like bigger engines and better track designs, which help people all over the world with construction, mining, and many other tough jobs in sub-optimal work zones.
   


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MK V Tank

-One of the very first tanks, the British MK V-
 

Relevance To Physics

Tanks are a great example of what an understanding of physics can yield to real world influence. Without physics, tank designers would have to do a lot of trial and error which would waste resources and time to determine factors like armor thickness and angle, how wide the tracks should be to spread the tanks' waste to prevent it from sinking into the ground, how the engine's power can best be transferred to the tracks to move the tanks, and many other factors. 
Physics Equations

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Kinetic energy
F=MA

These are probably the two biggest and most relevant equations to most aspects of tanks.