The energy principle for a system states the change in energy of the system can be found in terms of work done and heat: $$\Delta E_{sys} = W_{surr} + Q$$

1. What do $W_{surr}$ and $Q$ mean as they relate to the system?
2. The heat can be positive, negative or zero. What do each of these mean in terms of the direction of its flow?
3. 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?

Today, we are transitioning into talking about energy and are going to start small and examine energy from a few different scenarios. These scenarios highlight the idea of choosing systems and will ask you to analyze each problem from two different systems. This will hopefully help you all compare and contrast these two different approaches to solving energy problems.

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 2: System = train

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 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.

3. Which system did you choose for your analysis? Why?

Hawkeye is standing the edge of a tall building (80 m) and needs to fire an arrow into the sky as a warning to the other avengers. He releases the arrow with an initial speed of 50 m/s at an angle of 60 degrees. Consider this situation from the instant after the arrow is launched.

Choice 1: System = Arrow + Earth

Choice 2: System = Arrow

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 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.

3. Which system did you choose for your analysis? Why?