The train rolls out of the station and into a corkscrew element before reaching the first of the two launches

• Launch 1 is 44.6 m long, with a 7.2° slope. It finishes at an elevation 36.7 m and the train reaches the speed of 21.3 m/s,
• Launch 2 is 69.5 m long, with a 9.7° slope. It finishes at an elevation 42.4 m and the train reaches the speed of 23.5 m/s

What elevation could the train reach after the first launch? After the second launch? (Neglect energy losses and the length of the train.) You may compare to the Lisebergbanan where the lifthill reaches an elevation of 65 m and to the lowest and highest points of the track (after leaving the station). Look also at the elevation curve below.

The graph is obtained by a WDSS sensor, and based on barometer data. Can you identify the two launches?

The screen shots below show that the speed is kept close to constant during the second launch. (Picture from Phys.Ed. 55 035015 2020). After the target speed of 23.5 m/s is reached, the LSM system maintains the speed while the train moves upward. The mass of an empty train is 8730 kg. Use M ≈ 10 tonnes for the estimates below.

1. What power is needed during the constant velocity part of the launch?
2. How much energy is added during this part of the second launch? (Not yet accounting for the speed increase at the beginning of the launch)
3. What is the average power needed if one train leaves the station every minute?
4. How large is the kinetic energy of the train at the end of the second launch?
5. What amount of sugar has chemical energy comparable to the kinetic energy of a Helix train at the end of the second launch? The chemical energy of sugar is about 4 kcal/g or 17 kJ/g=17 MJ/kg. How many 4-gram sugar lumps does this energy correspond to?
6. It has been said that “chemistry is physics on electron volt level.” Express the chemical energy density of sugar in the unit eV/u, where u is the atomic mass unit (Dalton). 1u ≈ 1.66 × 10−27 kg and 1eV ≈ 1.6×10−19 J.