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| course_planning:183_projects:f18_project_14 [2018/12/06 00:21] – hallstein | course_planning:183_projects:f18_project_14 [2018/12/06 17:48] (current) – hallstein |
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| ====== Project 14: Part B: Pool for the Nobel ====== | ====== Project 14: Part B: Pool for the Nobel ====== |
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| {{course_planning:183_projects:pool.png}} | {{183_projects:pool.png}} |
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| Craig and Tom are the leading physicist at their respective research facilities. They are the two leading candidates for the Nobel Prize. Come day of the award, the committee of the prize cannot come to an agreement about who deserves the award. Instead of voting, they decide to hold a single match of pool. | Craig and Tom are the leading physicist at their respective research facilities. They are the two leading candidates for the Nobel Prize. Come day of the award, the committee of the prize cannot come to an agreement about who deserves the award. Instead of voting, they decide to hold a single match of pool. |
| - m<sub>stick</sub> = 0.5 kg | - m<sub>stick</sub> = 0.5 kg |
| - m<sub>cue</sub> = 0.17 kg | - m<sub>cue</sub> = 0.17 kg |
| - m<sub>8-ball</sub> = 0.17 kg | - m<sub>8-ball</sub> = 0.17 kg |
| | - r<sub>ball</sub> = 3.05 cm |
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| __**Part 1: Tom's Up**__ | __**Part 1: Tom's Up**__ |
| There is only the 8-ball remaining. Tom realizes he can win this game, but he is going to have to make a difficult shot. He begins doing some calculations using angular momentum. | There is only the 8-ball remaining. Tom realizes he can win this game, but he is going to have to make a difficult shot. He begins doing some calculations using angular momentum. |
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| Assuming there is no friction, Tom needs to figure out how fast and at what angle the cue ball needs to travel in order to get the 8-ball into the top right corner pocket. Hint: for an elastic collision in 2D, the angle between the two post-collision velocities is 90 degrees. Relative to the top right corner pocket, the location of the 8-ball before cue ball strikes it is <-0.75m, -0.25m, 0m> and the location of the cue ball before the shot is <-1.25m, -0.5m, 0m>. What must the initial velocity of the cue ball be for the final speed of the 8-ball to equal 1 m/s? | Assuming there is no friction, Tom needs to figure out how fast and at what angle the cue ball needs to travel in order to get the 8-ball into the top right corner pocket. Hint: for an elastic collision in 2D between two objects having equal mass, with one object initially attest, the angle between the two post-collision velocities is 90 degrees. Relative to the top right corner pocket, the location of the 8-ball before cue ball strikes it is <-0.50m, -0.25m, 0m> and the location of the cue ball before the shot is <-1.25m, -0.5m, 0m>. What must the initial velocity of the cue ball be for the final speed of the 8-ball to equal 1 m/s? |
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| The judges believe that Tom's shot is impossible and want him to mathematically prove that it works. They want him to find the angular momentum of the cue ball before the collision and the rotational angular speed of the 8-ball after the collision. | |
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| __**Part 2: Craig's Time to Shine**__ | __**Part 2: Craig's Time to Shine**__ |
| Tom, while a brilliant physicist, missed his shot, setting Craig up with the perfect opportunity to win the match and claim his prize. Craig has determined he needs to have the 8-ball traveling at exactly 0.73 m/s for the cue ball to not follow it into the hole. Any faster and he will scratch and lose. Any slower and the 8-ball will not make it into the hole. With the given information, how much force and for what time interval does the stick need to be in contact with the cue ball? | Tom, while a brilliant physicist, missed his shot, setting Craig up with the perfect opportunity to win the match and claim his prize. Craig has determined he needs to have the 8-ball traveling at exactly 0.73 m/s for the cue ball to not follow it into the hole. Any faster and he will scratch and lose. Any slower and the 8-ball will not make it into the hole. With the given information, how much force and for what time interval does the stick need to be in contact with the cue ball? |
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| | __**Part 3: Physicists just cant shoot pool**__ |
| | It turns out Craig blew his shot as well. The judges decided they didn't want to be here all day, so they decided to offer a challenge: Both Tom and Craig were to calculate the angular momentum of the cue ball from Tom's solution relative to the 8-ball before the collision and the rotational angular speed of the 8-ball after the collision. Whoever has the best solution gets the Nobel with a warning to keep their prize money away from pool halls. |
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| | __**Self Assessment**__ |
| | For this week's in-class score, you will self assess. In this, each group member should write out a summary of this week's work focusing on both individual and group contributions. In addition, you should assign yourself a score between 0 and 4, with 4 being max for each of the categories: |
| | * Group Understanding: ___ out of 4 |
| | * Group Focus: ___ out of 4 |
| | * Individual Understanding: ___ out of 4 |
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| [[course_planning:183_projects:F16 Project 14|Fall 2016 Project 14]] | [[course_planning:183_projects:F16 Project 14|Fall 2016 Project 14]] |
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