183_projects:problem14_spring2022 [Projects & Practices in Physics]

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====== Project 14: Part A: Showdown at boar tiger corral ======

{{course_planning:boar_tiger_defense2.png?|}}

Your success at the Thunderdome command center has led to your being raised to the rank of subcommander in the Scorched Earth Army. You have been sent to a remote outpost in Icy Cape, Alaska. The outpost is the first line of defense against boar tigers for the rest of humanity. It is located at the shore of a large frozen lake across from which is the boar tiger breeding ground. The outpost was formerly a foundry for metal working; several large rectangular blocks (5 $\mathrm{m}$ wide; 1 $\mathrm{m}$ high; 1 $\mathrm{m}$ deep) of steel rest on the frozen lake. The blocks are not solid, but have a wall thickness of 10 $\mathrm{cm}$. The steel made at this foundry has a density of 7850 $\mathrm{kg/m^3}$.

Roving in packs of precisely 101, boar tiger hide cannot be penetrated by conventional weaponry (i.e., bullets and knives). During the last winter, the high commander of the outpost, Dr. Hodge, commissioned the deployment of cannons to defend the outpost. The cannons were engineered to fire .3 $\mathrm{m}$ diameter cannonballs at a speed of 1600 $\mathrm{m/s}$. These cannonballs are made of clay with a very thin steel shell ($m = 200 kg$). These were found to be ineffective against the packs of boar tigers resulting in many casualties. However, in that attack, Dr. Hodge observed that boar tigers were afraid of objects with swinging or sweeping motions.

Dr. Hodge has asked you to design a defense system that can defend against packs of boar tigers using the cannons (already in place) and the large, rectangular steel blocks. In his mind, it could be possible to have the steel blocks slide and rotate along the ice, sweeping up the attacking boar tigers along the way.

To determine if such a defense mechanism is feasible, Dr. Hodge requires that you determine how the steel block will move and with what speed it could be expected to strike boar tigers.  

====== Project 14: Part B: Showdown at boar tiger corral ======

After the epic showdown, the leaders of the boar tiger defense team decide to commission the development of an arcade game simulating the battle.  The head of the development team, Boris Grishenko (Борис Грищенко), recently resigned.  He leaves for you a partially completed section of code which aims to <wrap caution>show the paths that the cannonball and block trace out in time.</wrap>  Pick up where he left off.

{{183_projects:F15_P13_splash.png}}

To make things more exciting, the defense team requests that:
  * the cannonball can be shot with a muzzle velocity of $v=1600\,{\rm m/s}$
  * the mass of the cannonball be increased to $m_{\rm ball}=400\,{\rm kg}$
  * the mass of the block be fixed at $m_{\rm block}=1700 {kg}$
  * the cannonball can only strike the block perpendicularly

While you are at it, <wrap caution>generate a plot of the total energy before and after the collision.</wrap>  This plot will help to determine how many points are gained/lost in the arcade game.

https://www.glowscript.org/#/user/paul.w.irving/folder/Public/program/RotatingBlocks