Pirate+Ship11

The Pirate Ship Evan Newcomer, Dustin Innerst, Matt Scott, Brett Tarlton

"A pirate ship swings guests back and forth, giving them a feeling of weightlessness. The boat is supported by four tubular uprights attached to a main axle, allowing it to swing in a pendulum motion." (http://www.hersheypark.com/rides/detail_printer.php?id=9)

The swinging ship is a pendulum, which means it moves in simple harmonic motion. A pendulum moving in simple harmonic motion follows a repetitive path of motion, swinging along a circular path from a point of maximum displacement through an equilibrium point, at which the pendulum hangs straight down, to another point of maximum displacement. The straight-line distance from the equilibrium point to either of the points of maximum displacement represent the pendulum's amplitude. The time it takes for the pendulum to complete one cycle or oscillation is called its period. A pendulum experiences maximum acceleration (positive and negative) at the two points of maximum displacement. Maximum velocity occurs when the pendulum swings through the equilibrium position.

__**Information On The Pirate Ship (provided by Hershey Park's Website and HussRides.com)**__ Riders per Ship: 54 Ship Length: 13.1 m Height of Ship in Full Swing: 20.1 m Total Ride Net Weight: 25401 kg Length of Support Beam: 15.1 m Maximum Horizontal Movement of Ship: 27 m

__**Period of Ship:**__ T = 2*pie*sqrt(L/g) T = 2*3.14*sqrt(17.5/9.8) T = 8.4 sec.; Measured T (from graph)= 7.9s __**Maximum Amplitude of Motion:**__ x^2 + y^2 = A^2 27^2 + 20.1^2 = A^2 A = 33.7 m __**Maximum Velocity Calculated With Conservation of Energy**__ KE+PE=KE+PE 1/2mv^2=mgh 1/2v^2=gh v=sqrt(2gh) v=sqrt(2*9.8*20.1) v=19.8 m/s
 * 8.4-7.9|/8.4= 5.95% difference
 * E=E **

__**Acceleration** **Graph**__ This acceleration graph is measured in gs. The time scale is doubled. When the distance from peak to peak was measured, it was found to be 3.9s. When this was doubled, it indicated that the period of the swinging pirate ship was 7.8s. The blue sinusoidal curve on the graph represents the vertical acceleration of the ship. When the curve reaches a peak it represents the point at which the ship is traveling at a max acceleration and when the curve passes the equilibrium position (the value about which the acceleration oscillates) the ship is traveling at its maximum velocity.
 * -all data was taken on an i phone using an accelerometer application, the data was then graphed**
 * in Microsoft Excel**

- the time value in the velocity calculation was derived from the acceleration graph at a point at which the velocity should reach a maximum**.**
 * __Calculations & Verifications__**
 * Maximum Velocity Through Harmonic Motion Equation and Angular Frequency Calculations:**


 * Max. Velocity Comparison:**
 * 20.8 -19.8 |/20.8 = 4.81% difference