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Vindjammer - Pirate ship

Pirate ships are found in many amusement parks. They are examples of pendulum rides, where riders sit on both sides of the middle, facing each other. The further away from the middle, the higher you ride on one side, but not quite so high on the other.

The upper graph shows how the G forces vary during the ride in a pirate ship and the lower shows the corresponding angular velocity.

A few questions to consider:

  1. What forces act on the rider in the turning points?
  2. What forces act on the rider as the swing passes the lowest point?
  3. The force on the rider in the turning points depends on the angle θ:  N = mg cos θ. Use the accelerometer graph for the following questions. (Consider the middle part of the ride, when the pendulum reaches the largest angles)
    1. What is the angle between the rider and the acceleration of gravity at the highest turning point? 
    2. What is the angle at the lower turning point?
    3. During what parts of the ride is the angular momentum largest?
    4. What is the acceleration at the bottom of the pendulum motion?
  4. At highest point you face towards the middle of the ride. Which way are you rotating as the swing moves down again (positive or negative "pitch"). (Check also the detailed graph)
  5. The force at the bottom is larger than mg. (Why?). Show that for a mathematical pendulum (point mass on massless string) the force in the lowest point deviates from mg by twice as much as the deviation in the highest point. The relation holds also if you are located in the "radius of gyration". Does this hold for the graphs in the pirate ship?