# Roller Coaster Physics

ROLLER COASTER DESIGN

Designing a roler coaster is very tricky. Patrons of theme and amusement parks want to be thrilled , but generally do not want to be injured.

Downard accelerations of greater than 10 g cause bodily harm.

Negative (i.e upward) accelerations of greater than about 5 g also cause damage ( "red out")

The drawing shows a car a the left which is going to the right where therre is a loop , the maximum hight of the loop (or the diameter of the loop represente by a circle is "h").

1) After a thriller first drop, a roller coaster car travels at speed Va into a loop of height h=15m. Find the range of velocities such that the net acceleration at the top of the loop is less than 5g and more than 0g.

Assume the car travels with speed Va all the way through the loop.

2) Compute the total work done by the car to reach the top of the loop.

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#### Solution Preview

Speed Va m/sec

radius = r = 15/2 = 7.5 m

Ac = Centripetal Acceleration = Va^2/r (m/s^2)

1g = 9.8 m/s^2

Ac = Va^2/(7.5*9.8) g's = Va^2/0.0136 g's

At the top of the coaster, since the weight acts vertically down, the net ...

#### Solution Summary

The solution provides step by step calculations for the speed of a car going along the roller coaster track.