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--- 183_projects:problem11a_fall2024 [2024/08/13 17:54] – hallstein
+++ 183_projects:problem11a_fall2024 [2024/11/04 13:35] (current) – hallstein
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-====== Project 12: Part A: Post-Apocalypse Now, Part 2 ======
+==== Kick Off Questions ====
+  * What is meant by inertia?
+  * What is moment of inertia dependent on?
+  * What is translational kinetic energy?
+  * If you have a coin rolling across a table, what type of energies will it have?
+  * What is the equation for rotational kinetic energy?
+====== Project 11: Part A: Engineering a movie stunt 1 ======
 <WRAP info>
+==== Project 11A: Learning goals ====
-==== Project 12A: Learning goals ====
+  * For a multi-particle system, determine the center of mass, the momentum of the center of mass, and how the center of mass momentum is changing.
+  * For a multi-particle system, explain and/or predict the motion of the center of mass.
-  * For single-particle systems where little or no heat is exchanged with the surroundings, use conservation of energy ($\Delta E_{\rm sys}=W_{\rm ext}$) to explain and/or predict the final state of the system (this includes choosing a system, and setting up initial and final states consistent with that system).
+  * For a multi-particle and/or deformable system, use conservation of energy for the center of mass system ($\Delta K_{\rm trans,cm}=W_{\rm cm}$) to explain and/or predict the final state of the center of mass.
-  * For multi-particle systems where little or no heat is exchanged with the surroundings, use conservation of energy ($\Delta E_{\rm sys}=W_{\rm ext}$) to explain and/or predict the final state of the system (this includes accounting for the potential energy of each pair of interacting particles; gravitational potential energy).
+  * For a multi-particle system, use conservation of energy ($\Delta E_{\rm sys}=W_{\rm ext}+Q$) to explain and/or predict the final state of the system (this includes using rotational and vibrational kinetic energies as well as the moment of inertia for the particles and/or system).
-  * This project is predominantly a review of some of the topics covered on Exam 2.
 </WRAP>
 <WRAP info>
-==== Project 12A: Learning Concepts ====
+==== Project 11A: Learning Concepts ====
-  * Energy Conservation
+  * Rotational and Translational Kinetic Energy
-  * Friction
+  * Local Gravitational Potential Energy
-  * Potential Energy
+  * Moment of Inertia
-  * Kinetic energy
+  * Conservation of Energy
-  * Constant Force Motion/Kinematics
+  * Relationship between Linear and Angular Velocity
-  * Thermal Energy
-  * Specific Heat Capacity
-  * Thermal Equilibrium
 </WRAP>
-{{course_planning:thunderdome3.png?|}}
+You and your team have been hired by Marvel Entertainment to develop a stunt for the next offering in the Marvel Cinematic Universe -- Squirrel Girl - New Warrior. This film introduces a new character: Squirrel Girl.
-Stuck in the wilderness for a number of days and unable to contact the people in your bunker, your team along with Willard and Kilgore set out to find a new safe haven. After traversing the scorched wasteland for several days you see postings for "Thunderdome", which promises "sanctuary for all". When your team arrives at Thunderdome, you are greeted by the leader of the community Auntie Entity ("Tina" for short), and a 5-story former engineering building with each floor 12 meters high. Your team is told that you all can become community members if you can design a defense system based on a bow design that the community has been working on. The defense system consists of a support anchored to the floor to hold a horizontally aligned spring-loaded harpoon launcher in place.  There is a defense system in place on floors 2 through 5, as well as the roof.
-In addition to vicious [[183_notes:supplemental|boar tigers]], zombies have begun to overrun other settlements in the area and Auntie wants to be prepared for their imminent arrival.
-They request some specifics for the machine and indicate some constraints:
-  * There is an ample supply of 3 kg harpoons.
-  * The harpoons can only be fired horizontally but must have the greatest variation in range possible.
-  * It must fire carbon steel harpoons at or below 270 K (it has been found that cooled projectiles have a greater effect on zombies)
-  * Initial tests suggest that to penetrate zombie flesh, harpoons must have a speed of at least 200 m/s.
-The engineering building is 60m from a solid, concrete defensive wall of height 30m and thickness 10m surrounding the Thunderdome. Beyond the wall is a 10m horizontal flat ledge followed by a plain that is 10m below ground level to capture the zombie hoards. Inside the building is an abandoned elevator shaft that extends from the ground floor to the roof. The layout of the engineering building and its surroundings is depicted above.
-You are also supplied with the following materials:
+In a scene meant to take place near the climactic end of the movie, Squirrel Girl (played by Anna Kendrick) is searching for Tippy Toe her squirrel companion on a large hill. While searching, she disturbs a large boulder, which begins to roll down the hill after her. In the scene, Squirrel Girl is meant to sprint down the mountain while the boulder rolls behind her, catching up, but not running over her.
-  * A spring with a lock mechanism that enables it to be locked at various compressions with a spring constant of (15000 N/m). There is no crank strong enough to compress this stiff spring.
+The production studio has designed several boulders (some solid spheres, some hollow spheres, and some cylindrical ones) for the stunt, but does not want to manufacture and ship all of them to the set. Also, they have yet to choose a stunt person because they aren't sure how fast that person will need to run down the hill. They've asked your team to design the stunt including the hill and to produce a graph that demonstrates how the speed of the boulder will change as it rolls down the hill. It's foam, but it's big.
-  * On each floor of the engineering building is one defender, an anchored harpoon launcher support, a harpoon launcher, and one concrete block of mass 400kg resting on an adjustable, steel inclined plane adjacent to the elevator shaft.
-  * You can also request an amount of ice (at $250\,{\rm K}$) but you have to be specific as supplies are low.
-The spring-loaded harpoon launchers are detachable and can easily be moved from floor to floor, or to the bottom of the elevator shaft. The plan is to drop the concrete blocks down the elevator shaft onto the spring to compress the spring.  Design the defense system to find the minimum angle for the boulder to fall down the elevator shaft and the range/locations outside the defensive wall that your system can reach with the required specifications. Indicate your supply needs to meet Aunty Entity's requirements to keep Thunderdome safe.
+Remember this is Hollywood, so make sure the stunt is exciting!
-**Post-Solution questions:**
-  * A 90 kg zombie is moving 1 m/s directly toward Thunderdome.  If a harpoon launched with the maximum possible velocity strikes this zombie and embeds in the zombie’s flesh, what is the velocity of the zombie immediately after being struck with the harpoon?
-  * Willard suggests you can increase the range of the harpoons if the harpoon launcher is not anchored to the floor, and thereby would recoil.  Would this work?  Use the lowest workable launch speed to confirm your prediction.  What is the new launch speed, and what is the recoil speed of the launcher/support?  The anchor and spring launcher have a mass of 400 kg (excluding the harpoon).
-  * Draw a free-body diagram of the harpoon launcher as it slides along the concrete floor. What is the frictional force acting on the launcher during this slide, and using forces how far does it slide.  After all, you don’t want it to fall into the elevator shaft.
-  * Sketch the trajectory of one of the launched harpoons. For a point halfway from where it is launched to where it strikes a zombie, draw a free-body diagram showing all forces acting on the harpoon. In the past when objects were in freefall, we used a vertical-horizontal coordinate system. Here, we'd like to investigate what the parallel and perpendicular components of the net force look like, and how they affect the motion. With this in mind, sketch the parallel and perpendicular components of the net force acting on the arrow.
-We can use the momentum principle to express the net force as:
-$$\vec{F}_{net}=\frac{d\vec{p}}{dt}=\frac{d\mid\vec{p}\mid}{dt}\hat{p} + \frac{d\hat{p}}{dt}\mid\vec{p}\mid$$
-  * Which term is the parallel component of the net force, and which term is the perpendicular component of the net force?
+**Post-Solution Conceptual questions:**
-  * Which component causes the direction of the momentum to change, and which component causes its magnitude to change?
+  - As the boulder rolls down, what types of energies are involved in your system?
+  - Is energy conserved? How do you know?
+  - How does changing the moment of inertia change the speed as a function of height?
+  - Qualitatively, draw a graph of what the positions of the boulder and the stunt woman look like as a function of time.
+  - Turns out, the foam lining the perimeter of the boulder (a mass equal to one-thousandth of the total mass) changes temperature by $\Delta T = 2 K$ in rolling from the top to the bottom of the hill.  How can you account for this energy loss in your energy sum?