# 3. The lift hill in Lisebergbanan

The lift hill of Lisebergbanan takes you up a 30° slope with constant velocity - with the same inclination as the escalator towards the Helix station. Since you move with constant velocity, all forces must cancel.

- Which forces act on your body in the lift hill?
- Why does it feel different from moving up the escalator?
- Which forces act on the train moving up the hill with constant velocity?

The graph shows the changes in elevation during a tour in the Lisebergbanan (measured with the barometer in a WDSS.)

- How long time does it take to reach the highest point?
- How long is the track of the lift hill, where the inclination is 30° and the elevation difference is 45m. (Remember that a 30-60-90° triangle is a half equilateral triangle.)
- What is the speed of the train during the lift hill?
- Do you move faster or slower than in the escalator? By what factor?

## Forces on the body in the lift hill

The force from the train must counteract the force of gravity. The seat pushes you straight up from the seat, which implies a force upwards/backwards in the image (N_{z}). At the same time, the backrest pushes you upwards/forwards. (N_{x}).

Forces on the body are usually expressed in terms of a body-fixed coordinate system, with the x-axis pointing forwards (in your own coordinate system) and the z-axis points upward along the spine, as in the image to the right. (To have a right-handed coordinate system, the y-axis must then point to the left)

Can you think of other situations where the backrest pushes you forward, e.g. in a bus or in bumper cars?

## Lift hills in other roller coasters at Liseberg

What forces act on your body in different lift hills?

- Rabalder 25°
- Lisebergbanan 30°
- Balder 40°
- Valkyria 45°

The graph shows how the force from the seat (up from the track, red) and the force from the back rest (in the direction of the track, green) acting on you in the lift hill depend on the slope of the track.

What does it feel like if you look up into the sky - can you imagine travelling vertically?