100 Essential Things You Didn't Know You Didn't Know by John D. Barrow

Author:John D. Barrow
Language: eng
Format: epub, azw3, mobi
ISBN: 9781407020051
Publisher: Random House

50

Roller Coasters and Motorway Junctions

What goes up must come down.

Anon.

There was a been on one of those ‘tear drop’ roller coasters that take you up into a loop, over the top and back down? You might have thought that the curved path traces a circular arc, but that’s almost never the case, because, if the riders are to reach the top with enough speed to avoid falling out of the cars at the top (or at least to avoid being supported only by their safety straps), then the maximum g-forces experienced by the riders when the ride returns to the bottom would become dangerously high.

Let’s see what happens if the loop is circular and has a radius r and the fully loaded car has a mass m. The car will be gently started at a height h (which is bigger than r) above the ground and then descend steeply to the base of the loop. If we ignore any friction or air resistance effects on the motion of the car, then it will reach the bottom of the loop with a speed Vb =√2gh. It will then ascend to the top of the loop. If it arrives there with speed Vt, it will need an amount of energy equal to 2mgr + ½mVt2 in order to overcome the force of gravity and ascend a vertical height 2r to the top of the loop and arrive there with a speed Vt. Since the total energy of motion cannot be created or destroyed, we must have (the mass of the car m cancels out of every term)

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