183_projects:problem11_fall2022

# Project 11 Part a : Engineering a movie stunt

• Rotational and Translational Kinetic Energy
• Moment of Inertia
• Conservation of Energy
• Relationship between Linear and Angular Velocity
• Point Particle versus Real Systems

Your success with the squirrel girl stuntwork has lead to your being hired by Marvel Entertainment again for the new Doctor Strange film. Benedict Cumberbatch is Doctor Stephen Vincent Strange, a neurosurgeon who protects the Earth from magical threats both foreign and domestic.

In one of the final scenes, Doctor Strange has been captured by Nightmare and has been sent to the Dark Dimension using a teleportation system constructed by Dormammu. The teleportation system is located on a small island above the Arctic circle. Ms. Marvel and Spiderman arrive to save Doctor Strange by crossing into the Dark Dimension. They find a sled that can be used to launch them into the teleportation system. Spidey uses his web shooters to attach a web strand to the teleportation system and accelerate he and Ms. Marvel into the teleportation system.

For this stunt, the current plan is to use a sled ($M_{\rm sled} = 1500\,{\rm kg}$) with a wire reel system attached to the front end. The wire will be attached to a snowmobile and the sled will be dragged across the ice while the wire unwinds from the reel. The sled must be traveling with a speed of 30 m/s at a distance of 100 m from its starting location.

Unfortunately, the island was chosen for its beauty and not any sort of safety considerations. The island itself is only 2.5 km across at its widest point, so the wire cannot unwind too much or the snowmobile will end up in the frozen arctic waters.

The reel is hoop-shaped, but its mass has not been chosen. Your team is meant to decide how to proceed with the stunt, and report back to the production company. Find the appropriate force that the snowmobile should exert on the wire/sled, and determine the mass of the reel. Some initial testing of reels of different masses and radii have shown (for a constant force) that the relationship between the angular speed of the reel and the linear speed of the sled is related to the ratio of the masses of the sled and reel. The equation that best fits this data is given below,

$$\omega_{\rm reel} = \dfrac{M_{\rm sled}}{m_{\rm reel}}\dfrac{v_{\rm sled}}{R_{\rm reel}}$$

# Project 11: Part B: Saving a space station

The satellite with HAL is on it's way back to Earth but behind the satellite is a number of small asteroids. A member of the recovery team, David Lightman, tells you that there is a defunct Earth defense floating space station that is very far from Earth which can be hacked into. You have been tasked with operating this projectile defense system (PDS for short). PDS has the ability to launch defense projectiles from the space station headquarters (positioned at the center of the space station) to divert incoming attack projectiles (asteroids heading for Earth). Before the first firing of a projectile from the defense system, your boss would like to see a simulation showing how the incoming attack projectile's motion can be changed by the defense projectile to be sure that you can be trusted with the PDS.

• The mass of a defense projectile is about $20\,{\rm kg}$, made out of sticky Space Clay™.
• The average mass of an attack projectile is about $5$ times that of a defense projectile, usually made of a solid metallic material.

Complete the code below to simulate before and after an interception (collision) for a worst case scenario: an attack projectile being launched directly towards headquarters at its largest ever recorded velocity $\langle 225,-400,0 \rangle\,{\rm m/s}$ from its closest ever recorded position $\langle -500,900,0 \rangle\,{\rm m}$. For this worst case scenario defense to be successful, you must push the incoming attack projectile back along its incoming path so that its velocity is $\langle -450,800,0 \rangle\,{\rm m/s}$. Your code should be general enough to handle other attack and defense projectile initial conditions.

Furthermore, the Department of Projectile Energy (DoPE) for the Thunderdome, your home base, would like a report on the loss of kinetic energy during the collision as it interested in further harnessing the power of the PDS once this asteroids problem is over. Use VPython's graphing capabilities to help answer how much energy is lost.

• 183_projects/problem11_fall2022.txt