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# 21. The Lisebergbanan helix

Behind Tyrolen (at the previous location for Fisketuren) you find the lowest point of Lisebergbanan, at 19.5 m, somewhat below the station. The highest points is at 65m, and the train has travelled 1022.6m before reaching the lowest point.

• What speed would the train have if it hadn't lost any energy along the track?
• If the highest speed would instead be 80 km/h, how much energy has been lost for every meter of track? (Express in terms of an elevation loss, i.e. ΔE/mg.)

If the Lisebergsbanan is running, you can try to measure the time for the train to pass a point close to Tyrolen. The length of the train is 14 m, which can be used to calculate the speed from your time measurement.

### The Helix of Helix

Slightly north of the Helix of Lisebergbanan, you find the lowest point (at 17 m) of Helix in its helix (see short video) just before the second launch. The train leaves the end of the first launch with a speed 21.3 m/s at an elevation 36.7m.

• What speed would you expect in the lowest point if no energy were lost?
• Use the video to estimate the speed, using the length 12.5 m between the first and last axis of the train.
• How much energy is lost (i.e. converted to heat) before the train reaches the lowest point?  (Express in terms of elevation loss ΔE/mg)
• How much energy is lost per meter track? The train has traveled 480m after leaving the first launch.