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Project 11: Part A: Engineering a movie stunt 1
Project 11A: 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 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 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).
Project 11A: Learning Concepts
- Rotational and Translational Kinetic Energy
- Local Gravitational Potential Energy
- Moment of Inertia
- Conservation of Energy
- Relationship between Linear and Angular Velocity
Project 11A: 5 Questions to test pre-reading
- 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?
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.
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.
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.
Remember this is Hollywood, so make sure the stunt is exciting!
Post-Solution Conceptual questions:
- 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?