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Project: To Launch a T.N.D.
After such accurate advice was given by S.P.A.R.T.A.N. task force regarding the safety of the Lakeview scientists electrical equipment, you have been hired to assist the Stormchaser scientists with a top secret project. This time, in an effort to prevent future storms, you are tasked with overseeing the design and launch of an experimental government device know as a T.N.D. (Thundercloud Neutralizing Drone). This device works by remaining stationary in the center of a storm cloud, where it can be remotely triggered to neutralize the charges in the cloud and stop the storm. It is spherical in shape with a radius of $r_{TND} = 2$ m, and has a mass of $m_{TND} = 250$ kg. It also has a small propulsion system that allows it to maintain its altitude, which can be turned on remotely. In order to prepare the T.N.D. for a future storm, it will be launched upward via a massive spring to the proper height in the atmosphere where it will await a thundercloud. Once at thundercloud height, its propulsion system will hold it in place while it neutralizes the cloud.
You are tasked with overseeing the preparations for the launch, the mechanism for which is depicted in the image below:
The right (blue) sphere is the positively charged T.N.D., and is placed on a frictionless track. The left (red) sphere is a negatively charged T.P.D. (T.N.D. Preparation Device), and it has the same mass and radius as the T.N.D. It is held in a fixed position; its sole purpose is to attract the T.N.D. along the track towards the spring. The T.N.D. is currently held in place by the green wall, which is removable. The distance between the two gray walls is $d = 85$ m. The massive spring has a spring constant of $k_s = 4.6 \times 10^6$ N/m, and a rest length of $L_0 = 13$ m.
To complicate things, the scientists inform you of two major restrictions to the safety and capabilities of the mechanism:
1. The track is not built to contain the T.N.D. at any speed; the maximum speed it should reach on the track is $|\vec{v}_{max}| = 35$ m/s.
2. The spring is very large. In order for the compressed spring-T.N.D. system to fit on a transport truck, the spring must be compressed at least $\Delta x_{min} = 6$ m in length.
You must assess how much charge is to be placed on the T.P.D. and T.N.D. so that the experimental mechanism is both safe and effective. Once compressed, the spring-T.N.D. system can be transported by truck to any desired launch location, where the T.N.D. can be remotely launched by the spring into the atmosphere to hopefully mitigate some of the crazy weather in Lakeview.
Learning Goals:
- Review approach to energy problems - choosing an appropriate system, and mapping energy interactions with a system and its surroundings.
- Review previous energy types, such as translational kinetic energy, local gravitational potential energy, spring potential energy, and rotational kinetic energy.
- Incorporate electric energy as a new form of energy.
- Distinguish between electric energy, potential, field, and force
Conceptual Questions
- What is the general approach to solving a physics problem using energy?
- What is the difference between electric force and electric field?
- What is the difference between electric potential energy and electric potential?
- What is the difference between electric force and electric potential energy?
- What is the difference between electric field and electric potential?
- What are the different types of energy you have worked with, and how are they quantified?
- What assumptions did you need to make to simplify this problem?
- Is this problem realistic? Why or why not?