Acceleration
Forces and Motion

# Rollercoaster!

Stories from Physics for 11-14 14-16

An engineer, Alfred Clark, published a series of articles about the dynamics of rollercoasters in Rollercoaster! the official publication of American Coaster Enthusiasts. Clark examines roller coaster riders’ perceptions that they float out of their seats on the first hill of a roller coaster. He calculates that, even for the extreme 72-degree hill on the Intamin Shuttle roller coaster, the normal force exerted on riders, which they perceive as their weight, will be only be reduced to about 30% of its original value. Clark suggests the effects of friction and the sensation of wind may affect the riders’ perceptions.

In the third paper in the sequence, Clark analyses the differences between travelling in the first and last cars of a roller coaster. He argues that the train of cars decelerates while climbing a hill until the central car reaches the top. It then accelerates once the centre of mass of the roller coaster starts to fall. This means that riders in the first car experience a less thrilling ride than other passengers because their car reaches peak height while slowing down. Riders in the last car accelerate over the hill and experience a whipping motion. At the top of the hill, riders in the first car experience a tangential force that makes them slide forwards whereas those in the final car will be pushed backwards into their seats. The effect is reversed at the bottom of a hill and riders in the middle car will experience the greatest acceleration.

### References

###### Acceleration
appears in the relation F=ma a=dv/dt a=-(w^2)x
is used in analyses relating to Terminal Velocity
can be represented by Motion Graphs