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 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.

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.

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?

Spiderman is chilling on top of a skyscraper (120 m) eating his lunch, when he accidentally drops his apple. The apple then plummets toward an unsuspecting people on the street below.

Choice 1: System = Apple

Choice 2: System = Apple + Earth

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.

2. Spiderman decides to shoot a web to try to catch the apple before it hits a person on the street. Pick a system to calculate how much work Spiderman must do to stop the apple before it hits someone.

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

In the midst of the battle with Thanos, Captain Marvel obtains the very precious infinity gauntlet (m = 2 kg). When she finds it, she raises the gauntlet above her head in victory but then realizes that may be a poor idea considering all the bad guys around. She then lowers the gauntlet again. Consider this time period, when Captain Marvel raises then lowers the infinity gauntlet.

Choice 1: System = Infinity Gauntlet

Choice 2: System = Infinity Gauntlet + Earth

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.

2. When Captain Marvel lowers the infinity gauntlet, how much work does she do?

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

Black Widow unfortunately finds the Hulk trapped in a net by the ceiling, 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?