Pirate Ship Swing Ride

Swing Rides

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Pirate Ship Swing Ride (photo by Ziko van Dijk, via wikimedia commons)

Ship swing rides are often found in amusement parks and at carnivals and fairs. They can serve to illustrate several important principles from physics including torque and rotation, periodic motion and the physical pendulum, and applications to work and energy. This simulation was originally inspired by the Pirate Ride at Hershey Park. The "ship" part of the ride has a center of mass that lies 14 m from the pivot point (approximately the center of the boat). The ship swings freely from the pivot, and is driven by a roller built into the floor directly below the ship. The operator selects either the clockwise torque button, the neutral button or the counter clockwise torque button to change the motion of the ship. Because the drive can only push the ship when it is in contact, the drive is only available when the ship is within 30º of its lowest postion. The box surrounding the drive buttons turns black when the ship coes not contact the drive roller,or white when the drive is available. Depending upon which drive button is selected, the drive mechanism applies a constant torque on the ship unless the ship moves out of contact with the drive roller. Thus the drive can be used to speed up or slow down the ride.

Ship being driven by a clockwise torque, whose button is green indicating the torque is being applied.

In addition to the drive controls, there is a play/pause button, a reset button and a check buttons to display the force of gravity and the reaction force of the seat on the rider for three positions (far left, middle and far right) and plot the g-forces (apparant weight of the riders compared to their normal weight) as a function of time.Hershey Park ride does not go much beyond 90º, although some versions of this ride do go all the way around. Try driving the ride through a complete sequence from start to finish (don't forget the ride must be brought to rest so that your riders can safely disembark.

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Consider

• On some rides, which seat you get can affect your ride. Is there any variation in the g-gorces experienced by our three riders? Is this difference significant? Are there other aspects of this ride which vary based upon your seat selection?
• When swinging freely, when does the ship have the greatest speed? When does it have the least speed?
• When the ship is swinging freely, when do the riders have the greatest centripetal acceleration due to their circular motion? When would they be likely to experience the greatest g-forces?
• Restart the ride and have it do small swings. Determine the period of oscillations ; it may be helpful to examine the g-force graph and determine the time between cycles of maximum g-force (clicking on the graph displays the "time location" of the cursor). Does this result agree with the theoretical value for the simple pendulum?
• How does the size of the swings (i.e. the amplitude) affect the period of the swings? Try going from small sqings to swings that nearly carry the ship all the way arround.
• Try to estimate the torque produced by the drive by using the Work energy theroem. The work done by a constant torque is W=τΔθ. Note the angular width of the entire ship is about 60º which is about 1 radian. The ship's mass in the simulation is kg. Hint: try figuring out how many "pushes" it takes to get the ship to swing up 90º so that its height from its lowest position is 14 m.

As you may recall from the Moving section, any force can be broken down into two components that are perpendicular to one another. In this example, the weight vector can be broken down into one component that is parallel to the tension in the rope (W2, but pointing down instead of up) and another component that is perpendicular to the rope (W1). When you are on a swing, your motion is always perpendicular to the rope. That is, you don't slide up or down the rope when you are swinging. This means that the forces along the rope must be balanced - the tension in the rope, T, must be equal and opposite W2. The remaining component, W1, is the net force. Looking at the diagram, you can see that W1 acts to pull you back toward the equilibrium position. As you get farther from equilibrium on either side, W1 gets larger and both W2 and T get smaller. In fact, the tension in the rope is smaller than your weight when you are anywhere but in the equilibrium position.

The Period of Oscillation for a Swing

A swing is one example of a pendulum. You have probably seen a pendulum on an old-fashioned clock. It has a length of wire that goes from a pivot point up top to a weight of some sort attached to the bottom. A pendulum is an oscillator, just like a person on a swing or a weight bouncing on a spring. Recall that the period of a weight bouncing on a spring depends on the stiffness of the spring and the amount of weight attached to the end. For a pendulum, the period of oscillation depends only on its length. The amount of weight that is swinging back and forth doesn't matter!

As an example, compare what happens when you ride on a big swing and when you ride on a small swing. It takes a lot longer to go back and forth on a big swing than it does on a small swing. For the large swing on the left below, it takes 2 seconds to get from one side to the other, so it takes 4 seconds to complete one full oscillation, where you return to your starting point. The period is therefore 4 seconds. The frequency is the number of oscillations (or cycles) completed per second and in this case, it is 1/4 cycles/sec (or 0.25 cycles/sec). For the small swing on the right, it takes 1 second to go from one side to the other, so the period is 2 seconds and the frequency is 1/2 cycles/sec (or 0.5 cycles/sec). This is true for pendulums in general. The period is long for a long pendulum and short for a short pendulum. We can also say that the frequency is low for a long pendulum and high for a short pendulum.

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