183_projects:problem7a_fall2024

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183_projects:problem7a_fall2024 [2024/08/13 16:56] – created hallstein183_projects:problem7a_fall2024 [2025/02/24 22:43] (current) – hallstein
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 +==== Kick Off Questions ====
 +The energy principle for a system states the change in energy of the system can be found in terms of work done and heat:
 +$$\Delta E_{sys} = W_{surr} + Q$$
 +  - What do $W_{surr}$ and $Q$ mean as they relate to the system?
 +  - The heat can be positive, negative or zero. What do each of these mean in terms of the direction of its flow?
 +  - The work done by a force is related to the force and the displacement. It can be calculated via the scalar or dot product. What are the conditions for the force and displacement that can result in positive work? Negative work? Zero work?
 +
 +
 ==== Project 7: Energy and Avengers==== ==== Project 7: Energy and Avengers====
  
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 </WRAP> </WRAP>
- 
- 
- 
- 
-/* 
-===== Scenario 7a: Captain America slows down a train ===== 
- 
-There is a train speeding down a track with a constant velocity of 20.9 m/s, which appears to have malfunctioning breaks. Captain America gets in front of the train and slows the train to a stop before the train runs over the cliff. Consider this situation from the time Captain America starts slowing the train down until the train comes to a stop. 
- 
-Choice 1: System = train + Captain America + Earth 
-Choice 2: System = train 
- 
-For this problem, stop your analysis after the energy has distributed to Captain America, do not worry where it goes after that. 
- 
-1. For each choice of system above, answer the following questions: 
- 
-   * Is energy conserved in the system? Why/why not? 
-  *  Is work done on the system? Is it positive or negative? How do you know? 
-  *  Draw the energy bar charts for the scenario. 
-  * Draw an energy vs time graph showing all energies, including the total system energy. 
- 
-2. Pick a system to calculate how much force Captain America must apply to slow the train 
-down in 750 m. 
- 
-3. Which system did you choose for your analysis? Why? 
- 
-*/ 
  
 ===== Scenario 7a: Iron Man speeds up a train ===== ===== Scenario 7a: Iron Man speeds up a train =====
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 Iron Man encounters a train (mass = $1.35 \times 10^6$ kg) that has run out of fuel 1000 m before the train station. He decides to put on his blasters (which have a force of 20 MN), and he pushes the train for 500 m to get it up to speed. He's hoping that friction for the rest of the way will slow down the train by the time it arrives at the station.  Assuming the train's wheels are locked, Iron Man is able to overcome static friction and the coefficient of kinetic friction for steel on steel is $\mu_k = 0.74$.  Iron Man encounters a train (mass = $1.35 \times 10^6$ kg) that has run out of fuel 1000 m before the train station. He decides to put on his blasters (which have a force of 20 MN), and he pushes the train for 500 m to get it up to speed. He's hoping that friction for the rest of the way will slow down the train by the time it arrives at the station.  Assuming the train's wheels are locked, Iron Man is able to overcome static friction and the coefficient of kinetic friction for steel on steel is $\mu_k = 0.74$. 
  
-Choice 1: System = train + iron man + Earth+Choice 1: System = train + Iron Man + Earth
  
 Choice 2: System = train Choice 2: System = train
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   *       Is work done on the system? Is it positive or negative? How do you know?   *       Is work done on the system? Is it positive or negative? How do you know?
   *       Draw the energy bar charts for the scenario.   *       Draw the energy bar charts for the scenario.
-  *       Draw an energy vs time graph showing all energies, including the total system energy.+  *       Draw an energy vs time graph showing all mechanical energies, including the total system mechanical energy.
  
 2. Pick a system to calculate how fast the train will going when it gets to the station. 2. Pick a system to calculate how fast the train will going when it gets to the station.
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   *  Is work done on the system? Is it positive or negative? How do you know?   *  Is work done on the system? Is it positive or negative? How do you know?
   *  Draw the energy bar charts for the scenario.   *  Draw the energy bar charts for the scenario.
-  * Draw an energy vs time graph showing all energies, including the total system energy.+  * Draw an energy vs time graph showing all mechanical energies, including the total system mechanical energy.
  
 2. Pick a system to calculate the maximum height that the arrow will reach in the sky. 2. Pick a system to calculate the maximum height that the arrow will reach in the sky.
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-====== Project 7: Breakneck - Thursday -- The new roller-coaster at Michigan's Adventure ====== 
  
-{{183_projects:theme_park_jpeg.png|}} 
- 
-You are a team of engineers and scientists who are in the process of designing Michigan's Adventures exciting a new attraction "Breakneck".  This ride involves a roller-coaster-like car that can hold 8 passengers, with a mass of 700 kg. This car starts by effectively free falling 60m.  The track curves at the bottom so that the car can slide up an 8-m-high hill before hitting a horizontal straightaway 50m long.  In the middle of the straightaway is a section of track that is used to slow the car down.  You can have the car brake over any or all of the 10m length of that section. 
- 
-Then at the end of the straightaway, a spring-like device hooks under the car.  This device changes the car’s direction just in time to prevent it from apparently falling over the end of the track, sending it back over the braking section again, stopping neatly at the end of the braking area. The car should stop at the end of the braking section, on the way back towards the launch pad. 
- 
-Your tasks are (a) to decide on an appropriate braking force and length of the braking region needed on the straightaway to stop the car at the right location, and (b) the effective spring constant of the turnaround device. The braking system is electromagnetic in nature, and can provide any specified braking force. The car has special accelerometers mounted which relay that information, and adjust the braking force to provide the acceleration you request.   The most important piece of information for these devices is that a person can safely sustain accelerations of 3-4 “g’s” for a brief time, but not more than that. 
- 
-{{183_projects:problem_8_diagram.jpg?800}} 
- 
-/* 
  
 ===== Scenario 7c: Spiderman drops an apple ===== ===== Scenario 7c: Spiderman drops an apple =====
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   * Is work done on the system? Is it positive or negative? How do you know?   * Is work done on the system? Is it positive or negative? How do you know?
   * Draw the energy bar charts for the scenario.   * Draw the energy bar charts for the scenario.
-  * Draw an energy vs time graph showing all energies, including the total system energy.+  * Draw an energy vs time graph showing all mechanical energies, including the total system mechanical energy.
  
 2. Spiderman decides to shoot a web to try to catch the apple before it hits a person on 2. Spiderman decides to shoot a web to try to catch the apple before it hits a person on
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 +/*
 ===== Scenario 7d: Captain Marvel lowers the Infinity Gauntlet ===== ===== Scenario 7d: Captain Marvel lowers the Infinity Gauntlet =====
  
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-Choice 1: System = In finity Gauntlet+Choice 1: System = Infinity Gauntlet
  
-Choice 2: System = In finity Gauntlet + Earth+Choice 2: System = Infinity Gauntlet + Earth
  
 1. For each choice of system above, answer the following questions: 1. For each choice of system above, answer the following questions:
  
-  *  Is energy conserved in the system? Why/why not? +  * Is energy conserved in the system? Why/why not? 
-  *  Is work done on the system? Is it positive or negative? How do you know? +  * Is work done on the system? Is it positive or negative? How do you know? 
-  *  Draw the energy bar charts for the scenario. +  * Draw the energy bar charts for the scenario. 
-  * Draw an energy vs time graph showing all energies, including the total system energy.+  * Draw an energy vs time graph showing all mechanical energies, including the total system mechanical energy.
  
-2. When Captain Marvel lowers the in finity gauntlet, how much work does she do?+2. When Captain Marvel lowers the infinity gauntlet, how much work does she do?
  
 3. Which system did you choose for your analysis? Why? 3. Which system did you choose for your analysis? Why?
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 Black Widow unfortunately finds the Hulk trapped in a net by the ceiling at a height of 12 meters, which is tied to an anchor on the floor. Black Widow wants to rescue the Hulk but doesn't want him mad at her for just dropping him directly to the floor. If the Hulk weighs 566 kg, how much weight should the Black Widow attach to the other end of the rope so that the Hulk will land on the ground with a speed of 3 m/s? Black Widow unfortunately finds the Hulk trapped in a net by the ceiling at a height of 12 meters, which is tied to an anchor on the floor. Black Widow wants to rescue the Hulk but doesn't want him mad at her for just dropping him directly to the floor. If the Hulk weighs 566 kg, how much weight should the Black Widow attach to the other end of the rope so that the Hulk will land on the ground with a speed of 3 m/s?
-*/ + 
-/*+
  
 ====== Project 7f: The Black Widow ====== ====== Project 7f: The Black Widow ======
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 Make sure to indicate what your system is and to draw energy bar charts for the different parts of The Black Widows journey.  Make sure to indicate what your system is and to draw energy bar charts for the different parts of The Black Widows journey. 
  
 +*/
  
  
  
-*/ 
  • 183_projects/problem7a_fall2024.1723568210.txt.gz
  • Last modified: 2024/08/13 16:56
  • by hallstein