University of Göteborg, Sweden

Ann-Marie.Pendrill@fy.chalmers.se and M.Axelsson@zool.gu.se

For CAL-laborate

What is up? What is down? What is a straight line? With beating heart we face the unusual movements.

An amusement park is a large hands-on physics laboratory, full of rotating coordinate systems, free-falling bodies and vector additions. It gives ample opportunity to experience Newton's laws with eyes, hands and body. The amusement park Liseberg in Göteborg is the largest amusement park of Scandinavia. It has long physics traditions - Albert Einstein gave a talk at Liseberg 1923! Liseberg has many rides well suited for physics investigations, using simple equipment, as well as electronic accelerometers. Some investigations can easily be adapted to the local playground.

The heartbeat responds in different ways, both to the various accelerations and rotations of the body, but also to the thrill already in the queue. It can be monitored with electrodes on the body and the signal sent down to ground to be viewed in real time by the classmates.

This is an eye-catching example of the equivalence principle: The angle is determined by the ratio between the centripetal force and the weight. Since the intertial mass (entering the centripetal force) and the gravitational mass (entering the weight, mg), are equal, the angle is independent of the mass. Eötvös used the rotating earth as a giant merry-go-round by letting weights of different material balance from a rod suspended as a torsion balance. Refined Eötvös experiments are still performed, e.g. at the Eöt-Wash group at university of Washington, giving lower and lower limits for possible deviations from the equivalence principle./1/

Some exercises for the reader:

- Estimate the acceleration by looking at the picture.
- What is the apparent weight of a person on the ride.
- Estimate to rotation time, using the information that the chains are 4.3 m.

Many amusement park now offer visitors the possibility to experience "two seconds of weightlessness". One example is the Space Shot, ("Uppskjutet") at Liseberg. After a quick tour up, the seats are decelerated to a stop before starting the free fall. Following the fall it lands softly on an pressurized air. (The Free Fall e.g. at Gröna Lund in Stockholm, is instead decelerated by eddy currents produced by strong magnets.) The experience of weightlessness can be enhanced by taking along a small mug of water (1 cm of water is quite enough) and watch the water falling (don't pick a seat with headwind!). In the right conditions, the water seems to move slowly upward. Try it!

Figure 2: Accelerometer data for the space shot. The vertical axis is chosen so that standing on the ground gives "-1g". From the figure we see that the rider experiences about 3.5 g for a short moment at the start and after 1.5 s of approximate weightlessness experiences 2.5g, the 2.0g etc during the bouncing off the pressurised air. | Often, the accelerations in an amusement park instead cause the rider to be significantly heavier than usual. "The Space Shot's emphasis is on the sudden blast upward from the bottom." /2/ Fig 2 shows accelerometer data for the space shot, obtained with a "calculator based laboratory" (CBL) connected to a graphical calculator. The data can also be used to estimate the velocity at various points of the ride, and even the position. It is a good exercise in numerical sensitivity; The resolution of the accelerometer is about 0.013g. What is the resulting uncertainty in the position after the ride (where, of course, we know that the rider is safely back to the starting point)? |

A more visual accelerometer is provided by a slinky. Fig. 3 shows three slinkys, one unloaded, one stretched by external forces, and one hanging free. Note how the spacing of the turns of the hanging slinky increases with the increasing load from the lower turns.

A few exercises for the reader:

- What do you expect the slinky to look like at the top?
- How long would the slinky be with half the number of turns? (more suitable to take along on a ride!)?
- How do you expect a (half) slinky to look at the start of the "Space Shot"

Exercises for the reader:

- Using the accelerometer data, estimate the maximum angle at every turn.
- How does the period depend on the amplitude?
- The distance from the center is about 12 m. What would be the period of a mathematical pendulum of this length? What would be the length of a mathematical pendulum with the period of this attraction?

A roller coaster also provides good examples of vector addition, as the train slopes and curves in different directions. In several places the tracks are built imitate the free fall parabola.

The acceleration can be measured in several different ways. A "horizontal accelerometer" is provided by a little mass on a string, e.g. a Liseberg rabbit from one of the shops. It will bounce considerably, and needs to be stopped now and then, e.g. passing over the top of a hill. Watch the angle the rabbit makes to the track! (Remember, you and the rabbit undergo the same acceleration, but the rabbit hanging from the string does not feel the "normal force" from the seat.) The slinky can again be taken along as a vertical accelerometer, or more precise data can be recorded using electronic devices.

Exercises for the reader

- Neglecting friction, what speed would you expect from 45 m height difference?
- At every instant all parts of the train has the same speed. Nevertheless, the ride in the front, back and middle are different. Why? In which seat will you feel the lightest? The heaviest?
- How do you expect the "rabbit-on-a-string" to hang as the train accelerates down a hill? As it turns to the left?
- Is the reading from a vertical accelerometer sufficient to provide information about "g-forces"?

After the first year, more systematic instructions and information were presented on the WWW, with help enlisted from a few students in a summer project, paid by the science faculty at Göteborg university. The pages have since been revised and extended, in view of experiences gained from working with the material in subsequent courses, and, of course, as new attractions have been added to the park. These pages, available at www.science.gu.se/slagkraft/, are now used by many schools from various parts of Sweden in their preparation for excursions to Liseberg. During the year 2000, the "FRN" provided support to enable graduate students to direct visits for school classes - and giving all of us easier access to children's thoughts.

During a visit to an amusement park the equations come alive. Second derivatives are felt throughout the body. The block on the inclined plane is replaced by a train in the slope of a roller coaster and "Gedanken experiments" from the textbooks can be realised in one of the most attractive hands-on laboratories available.

- The Eot-Wash group at University of Washington: http://mist.npl.washington.edu:80/eotwash/
- http://www.s-spower.com/, Manufacturer Information about the "Space Shot" and the Turbo Drop
- See the presentation of experiments at Gröna Lund at http://www.physto.se/gronalund/

http://www.science.gu.se/slagkraft/

http://www.fy.chalmers.se/LISEBERG/callab.html

Ann-Marie Pendrill is professor of physics at Göteborg university, and a guest professor at Högskolan i Skövde, Michael Axelsson is assistant professor at the department of zoology

17 october 2000 AMP