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| 184_notes:examples:week3_spaceship_asteroid [2018/02/03 20:17] – [Solution] tallpaul | 184_notes:examples:week3_spaceship_asteroid [2021/05/19 14:37] – schram45 | ||
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| - | =====Preventing an Asteroid Collision===== | + | [[184_notes: |
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| + | =====Example: | ||
| Suppose your friend is vacationing in Italy, and she has lent you her spaceship for the weekend. You have gathered together a group of friends and you are currently cruising through the heavens together and having a great time. You are surrounded by nothingness in all directions. Suddenly, the radar starts beeping ferociously. The ship is on a collision course with an asteroid. You are not too worried about survival -- the ship is practically indestructible. However, you know your friend would be devastated if you returned her spaceship with a scratch or dent from the asteroid. You need to prevent the collision. | Suppose your friend is vacationing in Italy, and she has lent you her spaceship for the weekend. You have gathered together a group of friends and you are currently cruising through the heavens together and having a great time. You are surrounded by nothingness in all directions. Suddenly, the radar starts beeping ferociously. The ship is on a collision course with an asteroid. You are not too worried about survival -- the ship is practically indestructible. However, you know your friend would be devastated if you returned her spaceship with a scratch or dent from the asteroid. You need to prevent the collision. | ||
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| * The electric potential energy of a point charge in the electric field of another point charge is $$U_r=\frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r}$$ This was derived in the notes [[184_notes: | * The electric potential energy of a point charge in the electric field of another point charge is $$U_r=\frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r}$$ This was derived in the notes [[184_notes: | ||
| + | ===Assumptions=== | ||
| + | * Asteroid and Central Component are point charges: The asteroid and central component are relatively small compared to the ship. This allows us to use the electric potential energy equation derived in the notes. | ||
| + | * Asteroid is going straight towards the central component: This simplifies the separation vector as both the point charges are in line with each other. | ||
| + | * Ship is a rectangle: Creates a simplified model for the ship, and is a worse case scenario for the ship shape. | ||
| + | |||
| ===Goal=== | ===Goal=== | ||
| * Prevent the asteroid collision using the long-distance wiring setup. | * Prevent the asteroid collision using the long-distance wiring setup. | ||
| - | |||
| - | ===f=== | ||
| - | * The current distance between the ship and the asteroid. | ||
| - | * The distribution of charge on the asteroid. | ||
| - | * The distribution of charge on the central component and on the ship itself. | ||
| ===Representations=== | ===Representations=== | ||