Saturday 22 August 2015

Back to the circus: loop the loop calculation

I posted last week about the motorbikes at Zippos Circus. Upside down, the centripetal force must be equal to weight + normal reaction force. Centripetal force = mass x speed squared /radius of curvature so the faster the bike is going, the bigger the centripetal force. The weight will remain the same so the normal reaction force will increase. This is because the bike will try to go in a straight line due to its inertia. The metal cage will have to push back harder, hence the larger reaction force. Thus there is a speed at which normal reaction force = zero. The bike will no longer be in contact with the metal so the driver will be falling not driving. Centripetal force = weight mg. Simple cancelling means v squared = radius x g. Having seen a brave woman stand up between the bikes, I'd estimate the radius as 2 metres. So v squared = 20 and minimum speed to maintain contact is 4.5 metres per second. That's 16 km per hour - which is actually not very fast.